Finite Volume Methods

A new formulation of the immersed boundary method with a structure algebraically identical to the traditional fractional step method is presented for incompressible flow over bodies with prescribed surface motion. Like previous methods, a boundary force is applied at the immersed surface to satisfy the no-slip constraint. This extra constraint can be added to the incompressible Navier-Stokes equations by introducing regularization and interpolation operators. The current method gives prominence to the role of the boundary force acting as a Lagrange multiplier to satisfy the no-slip condition. This role is analogous to the effect of pressure on the momentum equation to satisfy the divergence-free constraint. The current immersed boundary method removes slip and non-divergence-free components of the velocity field through a projection. The boundary force is determined implicitly without any constitutive relations allowing the present formulation to use larger CFL numbers compared to some past methods. Symmetry and positive-definiteness of the system are preserved such that the conjugate gradient method can be used to solve for the flow field. Examples show that the current formulation achieves second-order temporal accuracy and better than first-order spatial accuracy in L 2 -norms for oneand two-dimensional test problems. Results from two-dimensional simulations of flows over stationary and moving cylinders are in good agreement with those from previous experimental and numerical studies.

Population balance equations have been used to model a wide range of processes including polymerization, crystallization, cloud formation, and cell dynamics. Rather than developing new algorithms specific to population balance equations, it is proposed to adapt the high-resolution finite volume methods developed for compressible gas dynamics, which have been applied to aerodynamics, astrophysics, detonation waves, and related fields where shock waves occur. High-resolution algorithms are presented for simulating multidimensional population balance equations with nucleation and size-dependent growth rates. For sharp distributions, these high-resolution algorithms can achieve improved numerical accuracy with orders-of-magnitude lower computational cost than other finite difference and finite volume algorithms. The algorithms are implemented in the ParticleSolver software package, which is applied to batch and continuous processes with one and multiple internal coordinates.

In numerous applications of image processing, e.g. astronomical and medical imaging, data-noise is well-modeled by a Poisson distribution. This motivates the use of the negative-log Poisson likelihood function for data fitting. (The fact that application scientists in both astronomical and medical imaging regularly choose this function for data fitting provides further motivation.) However difficulties arise when the negative-log Poisson likelihood is used. Chief among them are the facts that it is non-quadratic and is defined only for vectors with nonnegative values. The nonnegatively constrained, convex optimization problems that arise when the negative-log Poisson likelihood is used are therefore more challenging than when least squares is the fit-to-data function.

Direct numerical simulation (DNS) and large-eddy simulation (LES) are carried out to investigate the frequency effect of zero-net-mass-flux forcing (synthetic jet) on a generic separated flow. The selected test case is a rounded ramp at a Reynolds number based on the step height of 28 275. The incoming boundary layer is fully turbulent with Rθ=1410. The whole flow in the synthetic jet cavity is computed to ensure an accurate description of the actuator effect on the flow field. In a first step, DNS is used to validate LES of this particular flow. In a second step, the effect of a synthetic jet at two reduced frequencies of 0.5 and 4 (based on the separation length of the uncontrolled case and the free-stream velocity) is investigated using LES. It is demonstrated that, with a proper choice of the oscillating frequency, separation can be drastically reduced for a velocity ratio between the jet and the flow lower than one. The low frequency is close to the natural vortex shedding freq...

In this article we are interested in the derivation of efficient domain decomposition methods for the viscous primitive equations of the ocean. We consider the rotating 3d incompressible hydrostatic Navier-Stokes equations with free surface. Performing an asymptotic analysis of the system with respect to the Rossby number, we compute an approximated Dirichlet to Neumann operator and build an optimized Schwarz waveform relaxation algorithm. We establish the wellposedness of this algorithm and present some numerical results to illustrate the method.

An interface capturing method based on a numerically revisited procedure for velocity and pressure coupling is worked out. The new treatment of density discontinuity is formulated in the framework of the finite volume methodology for arbitrary unstructured grids. A simple analytical pressure-like model case is presented to illustrate the accuracy of the numerical implementation of the treatment of discontinuous variables. Then, the method is implemented in a viscous flow solver and applied to free-surface flows, including the two-dimensional Rayleigh-Taylor instability problem and three-dimensional hydrodynamic flows for the prediction of ship waves around the Series 60 model ship with and without drift angles. These latter simulations show excellent agreement with the experimental results illustrated by comparisons of free-surface elevations and also velocity field.

The laminar field and heat transfer enhancement of forced convection in various counterflow porous channels with a joint aluminum plate was studied, using control volume technique and SIMPLE procedure for the velocity-pressure Coupling. Hydrodynamic and heat transfer results are reported for three configurations: (1) nonporous channels (NPC) (2) both channels filled by porous structure (BPC), and (3) only the channel contains hot fluid, filled by porous structure and other one is nonporous (HPC). The effectiveness, pressure drop and temperature difference are evaluated for wide ranges of Darcy, Reynolds and Prandtl numbers, also effects of thermal conductivity ratio is considered. The results show that as the Darcy, Reynolds or Prandtl number decreases, an increase in effectiveness is obtained. Also increase of thermal conductivity ratio causes to different effects on effectiveness in each case.

Abstract
Dam-break flows usually propagate along rivers and floodplains, where the processes of fluid flow, sediment transport and bed evolution are closely linked. However, the majority of existing two-dimensional (2D) models used to simulate dam-break flows are only applicable to fixed beds. Details are given in this paper of the development of a 2D morphodynamic model for predicting dam-break flows over mobile beds. In this model, the common 2D shallow water equations are modified, so that the effects of sediment concentrations and bed evolution on the flood wave propagation can be considered. These equations are used together with the non-equilibrium transport equations for graded sediments and the equation of bed evolution. The governing equations are solved using a matrix method, thus the hydrodynamic, sediment transport and morphological processes can be jointly solved. The model employs an unstructured finite volume algorithm, with an approximate Riemann solver, based on the Roe-MUSCL scheme. A predictor–corrector scheme is used in time stepping, leading to a second-order accurate solution in both time and space. In addition, the model considers the adjustment process of bed material composition during the morphological evolution process. The model was first verified against results from existing numerical models and laboratory experiments. It was then used to simulate dam-break flows over a fixed bed and a mobile bed to examine the differences in the predicted flood wave speed and depth. The effects of bed material size distributions on the flood flow and bed evolution were also investigated. The results indicate that there is a great difference between the dam-break flow predictions made over a fixed bed and a mobile bed. At the initial stage of a dam-break flow, the rate of bed evolution could be comparable to that of water depth change. Therefore, it is often necessary to employ the turbid water governing equations using a coupled approach for simulating dam-break flows.

Flow and thermal field in nanofluid is analyzed using single phase thermal dispersion model proposed by Xuan and Roetzel [Y. Xuan, W. Roetzel, Conceptions for heat transfer correlation of nanofluids, Int. J. Heat Mass Transfer 43 (2000) 3701-3707]. The non-dimensional form of the transport equations involving the thermal dispersion effect is solved numerically using semi-explicit finite volume solver in a collocated grid. Heat transfer augmentation for copper-water nanofluid is estimated in a thermally driven two-dimensional cavity. The thermo-physical properties of nanofluid are calculated involving contributions due to the base fluid and nanoparticles. The flow and heat transfer process in the cavity is analyzed using different thermo-physical models for the nanofluid available in literature. The influence of controlling parameters on convective recirculation and heat transfer augmentation induced in buoyancy driven cavity is estimated in detail. The controlling parameters considered for this study are Grashof number (10 3 < Gr < 10 5 ), solid volume fraction (0 < / < 0.2) and empirical shape factor (0.5 < n < 6). Simulations carried out with various thermo-physical models of the nanofluid show significant influence on thermal boundary layer thickness when the model incorporates the contribution of nanoparticles in the density as well as viscosity of nanofluid. Simulations incorporating the thermal dispersion model show increment in local thermal conductivity at locations with maximum velocity. The suspended particles increase the surface area and the heat transfer capacity of the fluid. As solid volume fraction increases, the effect is more pronounced. The average Nusselt number from the hot wall increases with the solid volume fraction. The boundary surface of nanoparticles and their chaotic movement greatly enhances the fluid heat conduction contribution. Considerable improvement in thermal conductivity is observed as a result of increase in the shape factor.

In this paper, we present a new two-layer model of Savage-Hutter type to study submarine avalanches. A layer composed of fluidized granular material is assumed to flow within an upper layer composed of an inviscid fluid (e.g. water). The model is derived in a system of local coordinates following a non-erodible bottom and takes into account its curvature. We prove that the model verifies an entropy inequality, preserves water at rest for a sediment layer and their solutions can be seen as particular solutions of incompressible Euler equations under hydrostatic assumptions. Buoyancy effects and the centripetal acceleration of the grain movement due to the curvature of the bottom are considered in the definition of the Coulomb term. We propose a two-step Roe type solver to discretize the presented model. It exactly preserves water at rest and no movement of the sediment layer, when its angle is smaller than the angle of repose, and up to second order all stationary solutions. Finally, some numerical tests are performed by simulating submarine and sub-aerial avalanches as well as the generated tsunami. (F. Bouchut), Didier.Bresch@univ-savoie.fr (D. Bresch), castro@anamat.cie.uma.es (M.J. Castro Díaz), mangeney@ipgp.jussieu.fr (A. Mangeney).

Abstract
An efficient numerical scheme is outlined for solving the SWEs (shallow water equations) in environmental flow; this scheme includes the addition of a five-point symmetric total variation diminishing (TVD) term to the corrector step of the standard MacCormack scheme. The paper shows that the discretization of the conservative and non-conservative forms of the SWEs leads to the same finite difference scheme when the source term is discretized in a certain way. The non-conservative form is used in the solution outlined herein, since this formulation is simpler and more efficient. The time step is determined adaptively, based on the maximum instantaneous Courant number across the domain. The bed friction is included either explicitly or implicitly in the computational algorithm according to the local water depth. The wetting and drying process is simulated in a manner which complements the use of operator-splitting and two-stage numerical schemes. The numerical model was then applied to a hypothetical dam-break scenario, an experimental dam-break case and an extreme flooding event over the Toce River valley physical model. The predicted results are free of spurious oscillations for both sub- and super-critical flows, and the predictions compare favourably with the experimental measurements

This paper reports on an exemplary study of the performance of commercial computational fluid dynamic (CFD) software programs when applied as engineering tool for microfluidic applications. Four commercial finite volume codes (CFD-ACE+, CFX, Flow-3D and Fluent) have been evaluated by performing CFD-simulations of typical microfluidic engineering problems being relevant for a large variety of lab-on-a-chip (LOAC) applications. Following problems are considered as examples: multi lamination by a split and recombine mixer, flow patterning on a rotating platform (sometimes termed ''lab-on-a-disk''), bubble dynamics in micro channels and the so called TopSpot Ò droplet generator for micro array printing. Hereby mainly the capability of the software programs to deal with free surface flows including surface tension and flow patterning of two fluids has been studied. In all investigated programs the free surfaces are treated by the volume-of-fluid (VOF) method and flow patterning is visualised with a scalar marker method. The study assesses the simulation results obtained by the different programs for the mentioned application cases in terms of consistency of results, computational speed and comparison with experimental data if available.

In this paper, the effects of volumetric heat sources on natural convection heat transfer and flow structures in a wavy-walled enclosure are studied numerically. The governing differential equations are solved by an accurate finite-volume method. The vertical walls of enclosure are assumed to be heated differentially whereas the two wavy walls (top and bottom) are kept adiabatic. The effective governing parameters for this problem are the internal and external Rayleigh numbers and the amplitude of wavy walls. It is found that both the function of wavy wall and the ratio of internal Rayleigh number (Ra I ) to external Rayleigh number (Ra E ) affect the heat transfer and fluid flow significantly. The heat transfer is predicted to be a decreasing function of waviness of the top and bottom walls in case of ðRa I =Ra E Þ > 1 and ðRa I =Ra E Þ < 1.

A novel finite volume method, described in Part I of this paper (Sahin and Owens, Int. J. Numer. Meth. Fluids 2003; 42:57–77), is applied in the linear stability analysis of a lid-driven cavity flow in a square enclosure. A combination of Arnoldi's method and extrapolation to zero mesh size allows us to determine the first critical Reynolds number at which Hopf bifurcation takes place. The extreme sensitivity of the predicted critical Reynolds number to the accuracy of the method and to the treatment of the singularity points is noted. Results are compared with those in the literature and are in very good agreement. Copyright © 2003 John Wiley & Sons, Ltd.

Numerical simulations of two-dimensional laminar flow past a triangular cylinder placed in free-stream at low Reynolds number (10⩽Re⩽250) are performed. A finite volume method, second-order accurate in space and time, employing non-staggered arrangement of the variables with momentum interpolation for the pressure–velocity coupling is developed. Global mode analysis predicts Recr=39.9 which confirms the results of earlier studies. Vortex shedding phenomena is found to be similar to the square cylinder with no second bifurcation in the range of Re studied. A discussion on the time-averaged drag coefficient, rms of lift coefficient and Strouhal number is presented. Particle tracking and the instantaneous streaklines provide an excellent means of visualizing the von Kármán vortex street. Copyright © 2006 John Wiley & Sons, Ltd.

Pollutant transport by shallow water flows on nonflat topography is presented and numerically solved using a finite volume scheme. The method uses unstructured meshes, incorporates upwinded numerical fluxes and slope limiters to provide sharp resolution of steep bathymetric gradients that may form in the approximate solution. The scheme is non-oscillatory and possesses conservation property that conserves the pollutant mass during the transport process. Numerical results are presented for three test examples which demonstrate the accuracy and robustness of the scheme and its applicability in predicting pollutant transport by shallow water flows. In this paper, we also apply the developed scheme for a pollutant transport in the strait of Gibraltar. The scheme is efficient, robust and may be used for practical pollutant transport phenomena.

A numerical scheme is presented for accurate simulation of fluid flow using the lattice Boltzmann equation (LBE) on unstructured mesh. A finite volume approach is adopted to discretize the LBE on a cell-centered, arbitrary shaped, triangular tessellation. The formulation includes a formal, second order discretization using a Total Variation Diminishing (TVD) scheme for the terms representing advection of the distribution function in physical space, due to microscopic particle motion. The advantage of the LBE approach is exploited by implementing the scheme in a new computer code to run on a parallel computing system. Performance of the new formulation is systematically investigated by simulating four benchmark flows of increasing complexity, namely (1) flow in a plane channel, (2) unsteady Couette flow, (3) flow caused by a moving lid over a 2D square cavity and (4) flow over a circular cylinder. For each of these flows, the present scheme is validated with the results from Navier–Stokes computations as well as lattice Boltzmann simulations on regular mesh. It is shown that the scheme is robust and accurate for the different test problems studied.

In recent time, environmental awareness and concern over the rapid exhaustion of fossil fuels have led to an increased popularity of biodiesel as an alternative fuel for automobiles. However, there are concerns over enhanced degradation of automotive materials in biodiesel. The present study aims to investigate the impact of palm biodiesel on the degradation behavior of elastomers such as nitrile rubber (NBR), polychloroprene, and fluoro-viton A. Static immersion tests in B0 (diesel), B10 (10% biodiesel in diesel), B100 (biodiesel) were carried out at room temperature (25 °C) and at 50 °C for 500 h. At the end of immersion test, degradation behavior was investigated by measuring mass, volume, hardness as well as tensile strength and elongation. The exposed elastomer surface was studied by scanning electron microscopy (SEM). Fourier Transform Infrared (FTIR) spectroscopy was carried out to identify the chemical and structural changes. Results showed that the extent of degradation was higher for both polychloroprene and NBR while fluoro-viton exhibited good resistance to degradation and was least attacked.

http://www.sciencedirect.com/science/article/pii/S096014811000128X

We compare the lattice Boltzmann equation (LBE) and the gas-kinetic scheme (GKS) applied to 2D incompressible laminar flows. Although both methods are derived from the Boltzmann equation thus share a common kinetic origin, numerically they are rather different. The LBE is a finite difference method, while the GKS is a finite-volume one. In addition, the LBE is valid for near incompressible flows with low-Mach number restriction Ma < 0.3, while the GKS is valid for fully compressible flows. In this study, we use the generalized lattice Boltzmann equation (GLBE) with multiple-relaxation-time (MRT) collision model, which overcomes all the apparent defects in the popular lattice BGK equation. We use both the LBE and GKS methods to simulate the flow past a square block symmetrically placed in a 2D channel with the Reynolds number Re between 10 and 300. The LBE and GKS results are validated against the well-resolved results obtained using finite-volume method. Our results show that both the LBE and GKS yield quantitatively similar results for laminar flow simulations, and agree well with existing ones, provided that sufficient grid resolution is given. For 2D problems, the LBE is about 10 and 3 times faster than the GKS for steady and unsteady flow calculations, respectively, while the GKS uses less memory. We also observe that the GKS method is much more robust and stable for underresolved cases due to its upwinding nature and interpolations used in calculating fluxes.

The effect of initial conditions on the growth rate of turbulent Rayleigh-Taylor (RT) mixing has been studied using carefully formulated numerical simulations. A monotone integrated large-eddy simulation (MILES) using a finite-volume technique was employed to solve the three-dimensional incompressible Euler equations with numerical dissipation. The initial conditions were chosen to test the dependence of the RT growth coefficient (α b ) and the self-similar parameter (β b = λ b /h b ) on (i) the amplitude, (ii) the spectral shape, (iii) the longest wavelength imposed, and (iv) mode-coupling effects. With long wavelengths present in the initial conditions, α b was found to increase logarithmically with the initial amplitudes, while β b is less sensitive to amplitude variations. The simulations are in reasonable agreement with the predictions for α b from a recently proposed model, but not for β b . In the opposite limit where mode-coupling dominates, no such dependence on initial amplitudes is observed, and α b takes a universal lower-bound value of ∼ 0.03 ± 0.003. This may explain the low values of α b reported by most numerical simulations that are initialized with annular spectra of short-wavelength modes and hence evolve purely through mode-coupling. Small-scale effects such as molecular mixing and kinetic energy dissipation showed a weak dependence on the structure of initial conditions. Initial density spectra with amplitudes distributed as k 0 , k −1 and k −2 were used to investigate the role of the spectral slopes on the development of turbulent RT mixing. Furthermore, in a separate study, the longest wavelength imposed in the initial wavepacket was also varied to determine its effect on α b . It was found that the slopes of the initial spectra, and the longest wavelength imposed had little effect on the RT growth parameters.

In an isothermal liquid, only the Coulomb force which is the force acting on the free charges, can contribute to the net electrohydrodynamic (EHD) motion. In the absence of a direct charge injection or induction, the charges can be generated through the dissociation process of the fluid. The generated charges by dissociation are redistributed by the applied electric field, resulting in the heterocharge layers around the electrodes. The pumping of an isothermal liquid without ion injection is associated with the heterocharge layers of finite thickness in the vicinity of the electrodes. This type of pumping is referred to as the conduction pumping. This paper investigates the pressure head generated by the conduction pumping mechanism theoretically through the numerical solutions. For this purpose, a theoretical model for the static case (i.e., without a fluid motion) is established and a numerical code using finite volume method is developed. Electric potential, electric field, charge density, and electric body force distributions for the selected electrode configuration are presented. The generated pressure as a function of the applied voltage is also presented. The numerical results confirm the EHD conduction pumping concept theoretically.

This paper presents an adaptive technique to animate deformable bodies in real-time. In contrast to most previous work, we introduce a multi-resolution model that locally refines or simplifies the simulated object over time in order to optimize the computational effort. We use the mixed Finite-Volume/Finite-Element method to derive fast, local discrete differential operators over irregular grids with tight error bounds. The linear elasticity equations can be simulated using an arbitrary non-nested hierarchy of volumetric meshes, allowing the computation load to be automatically concentrated where and when needed. Real-time simulation, with a guaranteed frame rate, can be achieved as demonstrated through a series of examples on our video.

In this Note, a numerical approach based on the finite volume method and a full multigrid acceleration is used, applied to the classical Rayleigh Bénard convection problem. Fine grids corresponding to 256 2 nodes are used and Benchmark solutions are proposed for Rayleigh numbers ranging from 10 3 to 10 6 . Some streamlines and isotherms are presented to analyze the natural convection flow patterns set up by the buoyancy force.

Nanofluids are liquid/solid suspensions with higher thermal conductivity, compared to common working fluids. In recent years, the application of these fluids in electronic cooling systems seems prospective. In the present study, the laminar mixed convection heat transfer of different water–copper nanofluids through an inclined ribbed microchannel–– as a common electronic cooling system in industry––was investigated numerically, using a finite volume method. The middle section of microchannel's right wall was ribbed, and at a higher temperature compared to entrance fluid. The modeling was carried out for Reynolds number of 50, Richardson numbers from 0.1 to 10, inclination angles ranging from 0° to 90°, and nanoparticles' volume fractions of 0.0–0.04. The influences of nanoparticle volume concentration, inclination angle, buoyancy and shear forces, and rib's shape on the hydraulics and thermal behavior of nanofluid flow were studied. The results were portrayed in terms of pressure, temperature, coefficient of friction, and Nusselt number profiles as well as streamlines and isotherm contours. The model validation was found to be in excellent accords with experimental and numerical results from other previous studies. The results indicated that at low Reynolds' flows, the gravity has effects on the heat transfer and fluid phenomena considerably; similarly, with inclination angle and nanoparticle volume fraction, the heat transfer is enhanced by increasing the Richardson number, but resulting in a less value of friction coefficient. The results also represented that for specific Reynolds (Re) and Richardson (Ri) numbers, heat transfer and pressure drop augment‐ ed by increasing the inclination angle or volume fraction of nanoparticles. With regard to the coefficient of friction, its value decreased by adding less nanoparticles to the fluid or by increasing the inclination angle of the microchannel.

A numerical study was performed for the laminar forced convection of water over a bank of staggered micro fins with cross section of the elongated hexagon. A 3-dimensional mathematical model, for conjugate heat transfer in both solid and liquid is developed. For this aim the Navier-Stokes and energy equations for the liquid region and the energy equation for the solid region are solved simultaneously and the pressure drop as well as the heat transfer characteristics was investigated. The length and width of the studied heat sinks are one centimeter and different heights in the range of 200-500 micrometer were examined for the fluid media. The heat removal of the finned heat sink is compared with an optimum simple mirochannel heat sink. The comparison which is presented at equal pumping powers depicts the enhancement of the heat removal for some specific sizes of the finned heat sink.

A hybrid heat sink concept which combines passive and active cooling approaches is proposed. The hybrid heat sink is essentially a plate fin heat sink with the tip immersed in a phase change material (PCM). The exposed area of the fins dissipates heat during periods when high convective cooling is available. When the air cooling is reduced, the heat is absorbed by the PCM. The governing conservation equations are solved using a finite-volume method on orthogonal, rectangular grids. An enthalpy method is used for modeling the melting/resolidification phenomena. Results from the analysis elucidate the thermal performance of these hybrid heat sinks. The improved performance of the hybrid heat sink compared to a finned heat sink (without a PCM) under identical conditions, is quantified. In order to reduce the computational time and aid in preliminary design, a onedimensional fin equation is formulated which accounts for the simultaneous convective heat transfer from the finned surface and melting of the phase change material at the tip. The influence of the location, amount, and type of PCM, as well as the fin thickness on the thermal performance of the hybrid heat sink is investigated. Simple guidelines are developed for preliminary design of these heat sinks.

A new generalized local time-step scheme is introduced to improve the computational efficiency of the finite-volume time-domain (FVTD) method. The flexibility of unstructured FVTD meshes is fully exploited by avoiding the disadvantage of a single short time step in the entire mesh. The great potential of this scheme is fully revealed in the FVTD simulation of electromagnetic (EM) problems with both large and fine structures in close proximity. The scheme is based on an automatic partition of the computational domain in subdomains where local time steps of the type 2 1 1 ( = 1 2 3 ...) can be applied without violating the stability condition. Interfaces between subdomains are reduced to a generic two-level system which requires a very limited number of time interpolations during the FVTD iteration, therefore resulting in a very simple and robust technique. The application of local time stepping to three-dimensional EM problems demonstrates a significant speed-up of the computation without compromising the accuracy of the results. Index Terms-Computational electromagnetics, conformal meshing, dielectric antennas, finite-volume time-domain (FVTD) method, numerical analysis.

In this article a mathematical model for two-dimensional batch crystallization process with fines dissolution is presented. The fines dissolution is useful for improving the quality of a product and facilitates the downstream process like filtration. The crystals growth rates can be size-dependent and a time-delay in the recycle pipe is incorporated in the model. The high resolution finite volume schemes, originally derived for general systems in divergence form, are used to solve the resulting model. The schemes have already been used for the simulation of complex problems in gas dynamics and were found to be computationally efficient, accurate, and robust. The numerical test problems of this manuscript verify the capability of the proposed schemes for solving batch crystallization models.

A linear Kalman filter based on a reduced order electrochemical model is designed to estimate internal battery potentials, concentration gradients, and state of charge (SOC) from external current and voltage measurements. The estimates are compared with results from an experimentally validated one-dimensional nonlinear finite volume model of a 6 Ah hybrid electric vehicle battery. The linear filter gives, to within ~2%, performance in the 30%-70% SOC range, except in the case of severe current pulses that draw electrode surface concentrations to near saturation and depletion; however, the estimates recover as concentration gradients relax. With 4 to 7 states, the filter has low order comparable to empirical equivalent circuit models but provides estimates of the battery's internal electrochemical state.

In this paper, a numerical investigation of the two modes of heat transfer, natural convection and surface thermal radiation, in a tilted slender cavity such a collector is presented. The 2-D conservation of mass, momentum and energy are coupled with a radiative model through the boundaries and solved by the finite volume method. The studied parameters are: aspect ratios (8≤A≤16), inclination angles (15°≤≤35°) and Rayleigh numbers (104≤Ra≤106). The results indicated that the radiative surface radiation coupled with the natural convection modifies the flow patterns and the average heat transfer in the slender cavity between the absorber plate and the glass in the collector. The convective heat transfer coefficient and the radiative heat transfer coefficient as a function of the aspect ratio and the inclination angles are shown. It was found that the radiative heat transfer contributes more than 40% of the total heat transfer. A comparison between the present Nusselt numbers against the ones used for the design of solar collectors reported in the literature is presented.

High resolution advection schemes have been developed and studied to model propagation of ows involving sharp fronts and shocks. So far the impact of these schemes in the framework of inverse problem solution has been studied only in the context of linear models. A detailed study of the impact of various slope limiters and the piecewise parabolic method (PPM) on data assimilation is the subject of this work, using the nonlinear viscous Burgers equation in 1-D. Also provided are results obtained in 2-D using a global shallow water equations model. The results obtained in this work may point out to suitability of these advection schemes for data assimilation in more complex higher dimensional models.

"Due to recent increases in computing power, room
acoustics simulation in 3D using time stepping schemes is becoming a viable alternative to standard methods based on ray
tracing and the image source method. Finite Difference Time Domain (FDTD) methods, operating over regular grids, are perhaps
the best known among such methods, which simulate the acoustic field in its entirety over the problem domain. In a realistic room acoustics setting, working over a regular grid is attractive from a computational standpoint, but is complicated by geometrical considerations, particularly when the geometry does not conform neatly to the grid, and those of boundary conditions which emulate the properties of real wall materials. Both such features may be dealt with through an appeal to methods operating over unstructured grids, such as finite volume methods, which reduce to FDTD when employed over regular grids. Through numerical energy analysis, suchmethods lead to direct stability conditions for complex problems, including convenient geometrical conditions at irregular boundaries. Simulation results are presented"

Turbulence and sediment transport models are incorporated into a three-dimensional hydrodynamics model to investigate the mechanisms of morphologic evolution of scour holes within the Indian River Inlet, Delaware, USA. The inlet bed had eroded slightly since stabilizing the channel walls in late 1930s through 1976. The mean rate of bed erosion roughly doubled as a response to anthropogenic activities within the inlet such as the removal of~80 piles remaining from an old bridge. Severe erosion near the in-water bridge supports and cofferdams for the replacement bridge necessitated channel bed stabilization that along with the remained debris from the removal of old bridge piles enhanced the growth of two deep scour holes on the bayside and oceanside of the bridge cofferdams. Scour hole and channel bed evolution has decreased drastically since 1994. The present investigation suggests that, initially, flow concentration through the cofferdams of the replacement bridge was the main reason for scour hole development. Bed shear stress over the forward-facing slope of the scour hole entrains sediment from the bed and extends the scour hole along the inlet and in the vertical direction. Flow separation within the developed scour holes after channel bed stabilization enhances turbulence and appears to be the dominant mechanism for further scour hole development.

This paper treats a one dimensional phase-change problem, ’ice melting’, by a vertex-centered finite volume method. Numerical solutions are obtained by using two approaches where the first one is based on the heat conduction equation with the basic grid (improved by introducing a new adaptive mesh technique), latent heat source approach (LHA), while the second uses the equivalent thermodynamic parameters defined by considering the apparent heat capacity method (AHC). A comparison between the two approaches is presented, furthermore the accuracy and flexibility of the numerical methods are verified by comparing the results with existing analytical solutions. Results indicate that phase-change problems can be handled easily with excellent accuracies by using the AHC method.

We benchmark a family of hybrid finite element–node-centered finite volume discretization methods (FEFV) for single- and two-phase flow/transport through porous media with discrete fracture representations. Special emphasis is placed on a new method we call DFEFVM in which the mesh is split along fracture–matrix interfaces so that discontinuities in concentration or saturation can evolve rather than being suppressed by nodal averaging of these variables. The main objective is to illustrate differences among three discretization schemes suitable for discrete fracture modeling: (a) FEFVM with volumetric finite elements for both fractures and porous rock matrix, (b) FEFVM with lower dimensional finite elements for fractures and volumetric finite elements for the matrix, and (c) DFEFVM with a mesh that is split along material discontinuities. Fracture discontinuities strongly influence single- and multi-phase fluid flow. Continuum methods, when used to model transport across such interfaces, smear out concentration/saturation. We show that the new DFEFVM addresses this problem producing significantly more accurate results. Sealed and open single fractures as well as a realistic fracture geometry are used to conduct tracer and water-flooding numerical experiments. The benchmarking results also reveal the limitations/mesh refinement requirements of FE node-centered FV hybrid methods. We show that the DFEFVM method produces more accurate results even for much coarser meshes.

This paper presents a complete finite volume method for the Cahn-Hilliard and Kuramoto-Sivashinsky type of equations. The spatial discretization is high-order accurate and suitable for general unstructured grids. The time integration is addressed by means of implicit an implicit-explicit fourth order Runge-Kutta schemes, with error control and adaptive time-stepping. The outcome is a practical, accurate and efficient simulation tool which has been successfully applied to accuracy tests and representative simulations. The use of adaptive time-stepping is of paramount importance in problems governed by the Cahn-Hilliard model; an adaptive method may be several orders of magnitude more efficient than schemes using constant or heuristic time steps. In addition to driving the simulations efficiently, the time-adaptive procedure provides a quantitative (not just qualitative) characterization of the rich temporal scales present in phase separation processes governed by the Cahn-Hilliard phase-field model.

The effect of distributed bubble nuclei sizes on shock propagation in a bubbly liquid is numerically investigated. An ensemble-averaged technique is employed to derive the statistically averaged conservation laws for polydisperse bubbly flows. A finite-volume method is developed to solve the continuum bubbly flow equations coupled to a single-bubble-dynamic equation that incorporates the effects of heat transfer, liquid viscosity and compressibility. The one-dimensional shock computations reveal that the distribution of equilibrium bubble sizes leads to an apparent damping of the averaged shock dynamics due to phase cancellations in oscillations of the different-sized bubbles. If the distribution is sufficiently broad, the phase cancellation effect can dominate over the single-bubble-dynamic dissipation and the averaged shock profile is smoothed out.

Abstract
Details are given of the development of a two-dimensional vertical numerical model for simulating unsteady free-surface flows, using a non-hydrostatic pressure distribution. In this model, the Reynolds equations and the kinematic free-surface boundary condition are solved simultaneously, so that the water surface elevation can be integrated into the solution and solved for, together with the velocity and pressure fields. An efficient numerical algorithm has been developed, deploying implicit parameters similar to those used in the Crank–Nicholson method, and generating a block tri-diagonal algebraic system of equations. The model has been applied to simulate a range of unsteady flow problems involving relatively strong vertical accelerations. The results show that the numerical algorithm described is able to produce accurate predictions and is also easy to apply.

The purpose of this study is to identify the potential locations for cavitation induced by total stress on the flow of a liquid through an orifice of an atomizer. A numerical simulation of two-phase incompressible flow is conducted in an axisymmetric geometry of the orifice for Reynolds number between 100 and 2000. The orifice has a rounded upstream corner and a sharp downstream corner with length-to-diameter ratio between 1 and 5. The total stress including viscous stress and pressure has been calculated in the flow field and, from there, the maximum principal stress is found. The total-stress criterion for cavitation is applied to find the regions where cavitation is likely to occur and compared with those of the traditional pressure criterion. Results show that the viscous stress has significant effects on cavitation. The effect of geometry and occurrence of hydraulic flip in the orifice on the total stress is studied. The Navier-Stokes equations are solved numerically using a finitevolume method and a boundary-fitted orthogonal grid that comes from the streamlines and potential lines of an axisymmetric equipotential flow in the same geometry. A level-set formulation is used to track the interface and model the surface tension.

This work presents a new conservative finite-volume numerical solution for the two-dimensional groundwater flow (Boussinesq) equation, which can be used for investigations of hillslope subsurface flow processes and simulations of catchment hydrology. The Boussinesq Equation, which is integrated for each grid element , can take account of the local variations of topography and soil properties within the individual elements. The numerical method allows for wetting and drying of the water-table, without "ad hoc assumptions". The stability and convergence of the method is shown to be guaranteed a priori by the properties of the solver itself, even with respect to the boundary conditions, an aspect which has been neglected in previous literature. The numeric solutions are validated against some approximate analytical solutions, and compared to those of another (1D) numerical solver of the Boussinesq equation. The solver capabilities are further explored with simulations of the Panola experimental hillslope where the bedrock topography, which is accurately known, causes complex wetting and drying patterns; in this situation the importance of a two-dimensional description of subsurface flows to obtain properly simulated discharges becomes clear. Finally, a comparison is made between the results of the presented algorithm and the output of the GEOtop hydrological distributed model, which simulates variably saturated soils; the findings of the comparison are discussed.

Numerical techniques development for the modeling and simulation of free surface flows has generated great interests over the last decades. In hydraulic engineering, the objectives include the predictions of dam break waves' propagation, fluvial floods and other catastrophic flooding phenomenon, the modeling of estuarine and coastal circulations, and the design and optimization of hydraulic structures. Most of the flooding events involve wetting and drying lands which are critical for the numerical modeling, especially when dealing with complex topographies. Extreme slopes and abrupt changes in irregular geometries, have often led to significant numerical errors and stability difficulties, and these are more critical for propagations over complex dry beds. This paper presents a simple and efficient numerical model for the wetting and drying effects over complex bathymetries. An overview of the key methods that have been suggested since the pioneering studies is first presented. A 2-D cell-centered finite-volume scheme is then proposed for solving the shallow-water equations using both structured and unstructured fixed meshes. Steady state C-property and global mass conservation properties are satisfied using appropriate numerical fluxes and wet/ dry interfaces treatments. The resulting numerical model proved stable and robust and was validated through some benchmarks tests, including comparisons with exact solutions and experimental data, and a real case of wetting-drying simulation in a portion of the river "Rivière des Prairies" in a suburb of Laval, Quebec.

The present paper presents a hybrid meshfree-and-Cartesian grid method for simulating moving body incompressible viscous flow problems in 3D space. The method combines the merits of cost-efficient and accurate conventional finite difference approximations on Cartesian grids with the geometric freedom of generalized finite difference (GFD) approximations on meshfree grids. Error minimization in GFD is carried out by singular value decomposition (SVD). The Arbitrary Lagrangian-Eulerian (ALE) form of the Navier-Stokes equations on convecting nodes is integrated by a fractional-step projection method. The present hybrid grid method employs a relatively simple mode of nodal administration. Nevertheless, it has the geometrical flexibility of unstructured mesh-based finitevolume and finite element methods. Boundary conditions are precisely implemented on boundary nodes without interpolation. The present scheme is validated by a moving patch consistency test as well as against published results for 3D moving body problems. Finally, the method is applied on low-Reynolds number flapping wing applications, where large boundary motions are involved. The present study demonstrates the potential of the present hybrid meshfree-and-Cartesian grid scheme for solving complex moving body problems in 3D.

A numerical study describes the conjugate unsteady natural heat convection of air on top of a non-Newtonian polymer-water solution characterized by a power-law model within a sealed vertical thick-walled cylindrical enclosure partially filled with a porous media in the lower section. Enzymes immobilized in an inorganic polymer, silica, used in synthesis processes constitute the porous media. Heating is by a constant high temperature at the bottom and at the vertical walls while the upper horizontal wall remains at the initial cold temperature. The Finite Volume Method allows the solution of the continuity, linear momentum and energy equations for a power law shear thinning fluid in a porous media with the Darcy-Brikman-Forchheimer model. The evolution of fluid mechanics of air and of the non-Newtonian fluid is described by the history of the streamlines. Transient heat transfer by conduction in the sealed tube walls and by natural convection of air and in the non-Newtonian fluid flow in the porous media is characterized by the evolution of isotherms. Experimental results are used to verify that the natural convective heat transfer conjugate computational model allows the prediction of temperature evolution in a thermal resistance challenge for free and immobilized enzymes. A difference of 1% is found between the experimental and the numerical results for the temperature history during the immobilized enzyme convective heating process. The applied numerical method has the capability of designing the enzyme temperature challenge test, by predicting the time needed to reach the uniform target temperature for biocatalyst processing, 500 s, in agreement with the experimental findings. The computational model contributes to the development of a technique to describe the kinetics of both immobilized and free enzyme during heating. This is a key issue for several industries, such as food modification, biofuel development, agroindustry and fishery waste valorization, that require enzymes operating at high temperature ranges in a reliable way for a long time.

Higher-order finite-volume methods have been shown to be more efficient than second-order methods. However, no consensus has been reached on how to eliminate the oscillations caused by solution discontinuities. Essentially non-oscillatory (ENO) schemes provide a solution but are computationally expensive to implement and may not converge well for steady-state problems. This work studies the extension of limiters used for second-order methods to the higher-order case. Requirements for accuracy and efficient convergence are discussed. A new limiting procedure is proposed. Ringleb’s flow problem is used to demonstrate that nearly nominal orders of accuracy for schemes up to fourth-order can be achieved in smooth regions using the new limiter. Results for the fourth-order accurate solution of transonic flow demonstrates good convergence properties and significant qualitative improvement of the solution relative the second-order method. The new limiter can also be successfully applied to reduce the dissipation of second-order schemes with minimal sacrifices in convergence properties relative to existing approaches.