Finite Volume Method

Meshfree solution schemes for the incompressible Navier-Stokes equations are usually based on algorithms commonly used in finite volume methods, such as projection methods, SIMPLE and PISO algorithms. However, drawbacks of these algorithms that are specific to meshfree methods have often been overlooked. In this paper, we study the drawbacks of conventionally used meshfree Generalized Finite Difference Method (GFDM) schemes for Lagrangian incompressible Navier-Stokes equations, both operator splitting schemes and monolithic schemes. The major drawback of most of these schemes is inaccurate local approximations to the mass conservation condition. Further, we propose a new modification of a commonly used monolithic scheme that overcomes these problems and shows a better approximation for the velocity divergence condition. We then perform a numerical comparison which shows the new monolithic scheme to be more accurate than existing schemes.

A new fourth order box-scheme for the Poisson problem in a square with Dirichlet boundary conditions is introduced, extending the approach in . The design is based on a "hermitian box" approach, combining the approximation of the gradient by the fourth order hermitian derivative, with a conservative discrete formulation on boxes of length 2h. The goal is twofold: first to show that fourth order accuracy is obtained both for the unknown and its gradient; second, to describe a fast direct algorithm, based on the Sherman-Morrison formula and the Fast Sine Transform. Several numerical results in a square are given, indicating an asymptotic O(N 2 log 2 (N )) computing complexity.

Le systeme modelisant un ecoulement de deux phases incompressibles dans un gisement petrolier a large porosite est regi par la loi de Darcy-Brinkman. La vitesse de filtration de Darcy conduit a une equation elliptique en pression et une equation parabolique degeneree en saturation. Ce systeme est tres largement utilise en milieu poreux. Dans cette these, on s’interesse a la modification de Brinkman qui consiste a modifier la loi de Darcy en ajoutant un terme de dissipation en vitesse. Ce systeme conduit a une equation elliptique en pression et une equation parabolique non standard en saturation, regularisante en temps. On s’interesse dans un premier temps a l’etude mathematique du systeme Darcy-Brinkman et a la regularite des solutions. Afin de simuler numeriquement les solutions de ce probleme, on propose une premiere etude de convergence d’un schema aux volumes finis sur un maillage admissible et pour un milieu poreux homogene. Ensuite, une methode combinee de type volumes finis-e...

In this paper, we are interested in the displacement of two incompressible phases in a Darcy-Brinkman flow in a porous media. The equations are obtained by the conservation of the mass and by considering the Brinkman regularization velocity of each phase. This model is treated in its general form with the whole nonlinear terms. This paper deals with construction and convergence analysis of a combined finite volume-non conforming finite element scheme together with a phase-by-phase upstream according to the total velocity. Different empiric laws are used to describe the filtration of a fluid through porous media. Darcy law is the most popular one, due to its simplicity. It states that the filtration velocity of the fluid is proportional to the pressure gradient. Darcy law cannot sustain the no-slip condition on an impermeable wall or a transmission condition on the contact with free flow . That motivated H. Brinkmann in 1947 to modify the Darcy law in order to be able to impose the no-slip boundary condition on an obstacle submerged in porous medium . He assumed large permeability to compare his law with experimental data and assumed that the second viscosity µ equals to the physical viscosity of the fluid in the case of monophasic flow. Brinkman law could formally be obtained from the Stokes system describing the microscopic flow, by adding the resistance to the flow [2]. Let T > 0, fixed and let Ω be a bounded set of R d (d ≥ 1). We set Q T = (0, T ) × Ω , Σ T = (0, T ) × ∂ Ω , and η is the outward normal to the boundary ∂ Ω . The mass conservation of two incompressible phases with Darcy-Brinkman velocity of each phase can be written in the following system, (see for more details),

Complete transient, three dimensional numerical simulations of the flow field around a pickup truck were carried out. A simplified truck with smooth underbody and no side mirrors is considered in the study. CFD simulations were carried out using the in-house CFD code called Airflo3d which is an unstructured finite-volume based Navier-Stokes solver. In the simulations k-ε turbulence model with Launder-Kato modification was used. The results show all the flow structures around the truck. Through this research work, our understanding of the complex flow field around a pickup truck could be improved.

This study investigates the energy exchanges occurring in the volume and on the surface of water ponds and their influence on the energy consumption of a building. The mathematical model of water ponds is based on coupling the thermal model of the water pond and the airflow model of the surrounding air. It accounts for the heat transfer by radiation, conduction, convection and the latent heat transfer due to water evaporation. The governing equations are numerically solved by a finite difference method for the thermal model and by a finite volume method for the air flow model. The surface temperature and the spatial profiles of temperature and moisture are presented. The effect of the water pond on the cooling energy consumption is discussed.

In this article we deal with the numerical simulation of semiconductor devices using the Energy-Balance (EB) transport model. This accounts for hot electrons behaviour and nonlocal effects which are of utmost relevance in the simulation of submicron devices. We propose an efficient and accurate solver for the EB equations based on the well-known Gummel's decoupled algorithm to handle iteratively the full system, while the discretization employs cell-centred Mixed Finite Volume (MFV) methods. These are derived from the standard Raviart-Thomas (RT) finite elements of lowest degree through a suitable quadrature formula which diagonalizes the element mass matrix. Numerical results to validate the newly proposed stabilized method are reported including the simulation of a model curved p-n diode, a one-dimensional p-n diode and a realistic state-of-the-art 1 µm-channel nMOS transistor.

To evaluate the efficacy of intensive craniocervical screening before elective cardiovascular surgery. A retrospective analysis of 1134 consecutive patients who underwent routine screening before cardiovascular surgery between November 2004 and December 2014 was conducted. The study was divided into 2 distinct cohorts of patients undergoing surgery: before (n = 500) and after (n = 634) the introduction of intensive screening in January 2009. In 2009, preoperative screening underwent a transition from the evaluation of carotid atherosclerosis alone to that of craniocervical atherosclerosis. Additionally, patients with moderate or greater stenosis on intensive screening underwent single-photon emission computed tomography with acetazolamide. Craniocervical atherosclerosis was classified as no or mild [0-49%: n = 836 (before/after: 370/466)], moderate [50-69%: n = 118 (56/62)] or severe [70-100%: n = 141 (36/105)]. One of 166 (0.6%) patients with moderate or greater stenosis undergoing single-photon emission computed tomography with acetazolamide after the introduction of intensive screening was diagnosed as having impaired cerebral autoregulation. The occurrences of perioperative stroke were 2.8% before the introduction of intensive screening and 0.9% after that (P = 0.033). Notably, intraoperative stroke significantly decreased from 1.4% to 0.2% (P = 0.034). Specifically, the occurrence of perioperative stroke in patients with no or mild stenosis decreased significantly after the introduction of intensive screening, from 2.7% to 0.4% (P = 0.007). The incidence of perioperative stroke decreased following the introduction of intensive screening. Intensive screening may be able to detect patients with a greater risk of perioperative stroke.

Included in methods commonly used for assessing vocational training are oral assessments (OAs) since, in addition to assessing knowledge to a depth rarely achieved in other forms of testing, they give unique insight into students' personal attitudes, which are important factors in the workplace. However, OAs require considerable preparation by the assessors, they can be restricted by time and assessor allocation, it is difficult to fully cover the course fairly, and they can put undue stress on the examinees, hence hindering a true expression of their skills and knowledge. OAs can give insight into a student's personal attitudes, and the purpose here is to find the relationship between OA observed attitudes and those deduced from the computer-aided assessment. For the computer-aided assessments a scheme based on comparing two statements, followed by fuzzy AHP analysis, was used to determine the student's attitude on such topics as general safety, work area tidiness and cleanliness, care and good use of hand tools and accuracy and testing of equipment. The results from the computer-aided approach were then compared with attitudes on the same topics obtained by oral assessment. For this work the important result was that there were strong correlations between the OA observed attitudes and the computer-aided assessment derived attitudes of the students. It also became clear however that for safety, the attitude of students (and perhaps workers) is more complicated than just having a 'good' or 'bad' attitude. Social pressure and organisational influence do seem to play a part so influencing or masking the student's true attitudes. Satisfactory correlations were found between results of students' attitudes when tested using the OA and computer-aided methods. Further work would need to be done to confirm generalization of substituting OA methods with a computer-aided assessment method.

on w a tw k an er pu is ob bstract: In this paper, the interaction between an aluminum plasma produced by laser ablati ith an ambient argon gas at 0.001 atm as soon as the plasma is studied with the help of o-dimensional numerical model over a time interval of 10 μs. It shows that that the simple shoc d drag models are good approximations for the plume expansion regimes appearing after the las lse. A sharpening effect of the plume in the axial direction before the final slowing down stage served in our simulations.

A theoretical approach based on a numerical simulation using experimental data is proposed as a contribution for the study of laser metal cutting under gas assistance. The aim is to simulate the stages of the kerf formation by considering the induced generated melt film dynamics, while it interacts with the laser beam and the assisting gas jet. For normal atmospheric conditions, a 3D model is developed using the finite volume method to solve the governing hydrodynamic equations, supplied with the species conservation equation. The present air, the metallic liquid, and the solid metal are considered as phases, where the interface positions are tracked by implementation of the volume-of-fluid method through Fluent CFD code, whereas an enthalpic method is used to take into account the material melting and resolidification. The results for six operating conditions in relation to the cutting velocity show an interesting agreement with the experimental observations.

Laminar mixed convective flow over a three-dimensional horizontal backward-facing step heated from below at a constant temperature was numerically simulated using a finite volume technique and the most relevant hydrodynamic and thermal features for air flowing through the channel are presented in this work. The channel considered in this work has an aspect ratio AR=4, and an expansion ratio ER=2, while the total length in the streamwise direction is 52 times the step height (L=52s) and the step length is equal to 2 times the step height (l=2s). The flow at the duct entrance was considered to be hydrodynamically fully developed and isothermal. The bottom wall of the channel was subjected to a constant high temperature while the other walls were treated to be adiabatic. The step was considered to be a thermally conducting block.

Fully coupled simulations of hydrodynamics and radiative transfer are essential to a number of fields ranging from astrophysics to engineering applications. Of particular interest in this work are hypersonic atmospheric entries and associated experimental apparatus, e.g., shock tubes and high enthalpy testing facilities. The radiative transfer calculations must supply to the CFD a heating term in the energy equation in the form of the divergence of the radiative heat flux and the radiative heat fluxes to bounding surfaces. It is most efficient to solve the radiative transfer equation on the same grid as the CFD solution, and this work presents an algorithm with improved accuracy compared to more conventional approaches on both structured and unstructured grids. Results are shown for a number of idealized test problems and for shock radiation during hypersonic entry. Issues of parallelization within a radiation sweep are also discussed.

Fully coupled simulations of hydrodynamics and radiative transfer are essential to a number of fields ranging from astrophysics to engineering applications. Of particular interest in this work are hypersonic atmospheric entries and associated experimental apparatus, e.g., shock tubes and high enthalpy testing facilities. The radiative transfer calculations must supply to the CFD a heating term in the energy equation in the form of the divergence of the radiative heat flux and the radiative heat fluxes to bounding surfaces. It is most efficient to solve the radiative transfer equation on the same grid as the CFD solution, and this work presents an algorithm with improved accuracy compared to more conventional approaches on both structured and unstructured grids. Results are shown for a number of idealized test problems and for shock radiation during hypersonic entry. Issues of parallelization within a radiation sweep are also discussed.

We propose and analyze volume-preserving parametric finite element methods for surface diffusion, conserved mean curvature flow and an intermediate evolution law in an axisymmetric setting. The weak formulations are presented in terms of the generating curves of the axisymmetric surfaces. The proposed numerical methods are based on piecewise linear parametric finite elements. The constructed fully practical schemes satisfy the conservation of the enclosed volume. In addition, we prove the unconditional stability and consider the distribution of vertices for the discretized schemes. The introduced methods are implicit and the resulting nonlinear systems of equations can be solved very efficiently and accurately via the Newton's iterative method. Numerical results are presented to show the accuracy and efficiency of the introduced schemes for computing the considered axisymmetric geometric flows.

In This study, an experimental study has been carried out to investigate the effect of adding Al2O3, Al, and Cu nanoparticles to the base fluid (water) on enhancement of heat transfer and heat transfer coefficients in a car radiator. The experiments have been done for distilled water and 3 types of nanofluids with different concentrations (0.5, 1 and 2 vol. %) and in various operational conditions (temperature, flow rate, etc.). Thermal Conductivities of these fluids have been measured experimentally and other thermo-physical properties like density and viscosity are calculated using related models. Results depicted that addition of nanoparticles to the base fluid increases its thermal conductivity, density and viscosity, and decreases its specific heat capacity. The performance evaluation of nanofluids in a radiator system showed that will dramatically enhances the heat transfer and decreases the heat transfer area required, so it is highly recommended to use them in such systems.

Numerical shockwave anomalies for the Euler equations are known to be directly related to the nonlinearity of the jump conditions and ambiguity of sub-cell shock position. To alleviate this behavior, two new flux functions were developed that permit stationary shocks with one intermediate state and an unambiguous stationary shock structure. These functions were demonstrated within a first-order framework in one dimension and shown to dramatically reduce numerical shockwave anomalies with no additional intermediate shock states or smearing. Unfortunately, four states are required for each flux function. In this work, both new flux functions are integrated into a second-order finite-volume scheme, utilizing the same four states used for reducing numerical shockwave anomalies to improve accuracy in smooth regions. Results are shown for several canonical problems and the method is shown to perform well.

Several chemicals were tested and evaluated as antibacterial agents against the Palestinian isolate of Agrobacterium tumefaciens, the causal agent of the crown gall disease. Based on the disk diffusion method on nutrient agar, formaldehyde appeared to be the strongest followed by sulfuric acid, hydrochloric acid, sodium hydroxide, Hypex and Dettol. On the other hand, those chemicals revealed 90-100% inhibition against the bacterial cell contaminating common pins. The other chemicals showed either an intermediate or weak bacterial inhibition of the bacterium on agar nutrient media.

In this work the heat flux generated in a cutting process is simulated using the inverse heat conduction technique based on conjugate gradient method. A three-dimensional formulation is used both to describe the physical phenomenon and to solve the inverse problem. The machining process (turning) is simulated and instrumented with nine thermocouples at the bottom face of the tool, opposite to its main rake face. The signals are automatically received and processed using a data acquisition system and a PC-Pentium. The direct solution, adjoint equation and sensitivity problem are numerically solved using finite volumes method. With this technique the cutting temperatures are estimated for various simulated cutting conditions. In order to validate the method the IHCP is applied in a well-controlled experiment where the heat flux input is known. An uncertainty analysis is also presented.

The article describes the study of solving the integro-differential problem of plant protection from pests using a numerical method and an algorithm for determining unknown parameters. In the work, a mathematical model of a biological system was developed, including a description of the interaction of biological species with arbitrary trophic functions. The article discusses the issues of difference approximation of the plant protection problem and the convergence of the solution of the corresponding difference approximating problem to the solution of the initial differential plant protection problem. In the numerical solution of the problem of plant protection, many parameters are not always determined using field experiments. Based on this, an appropriate algorithm has been developed to determine unknown parameters, which is based on the least squares method.

In order to gain insight into the one-dimensional turbulence (ODT) model of Kerstein [1] as it pertains to residual stress closure in large-eddy simulation (LES), we develop ensemble mean closure (EMC), an algebraic stress closure based on the mappings and time scale physics employed in ODT. To allow analytic determination of the stress the ODT model is simplified, conceptually, such that eddy events act upon a velocity field linearized by the local resolved scale strain. EMC can account for viscous effects, addressing the laminar flow finite eddy viscosity problem without implementation of the dynamic procedure . The algebraic form of the model lends itself to analysis and we are able to derive a theoretical value for the eddy rate constant. This value is a bound on the rate constant for full ODT subgrid closure and yields good results in LES of decaying isotropic turbulence with EMC.

In order to gain insight into the one-dimensional turbulence (ODT) model of Kerstein [1] as it pertains to residual stress closure in large-eddy simulation (LES), we develop ensemble mean closure (EMC), an algebraic stress closure based on the mappings and time scale physics employed in ODT. To allow analytic determination of the stress the ODT model is simplified, conceptually, such that eddy events act upon a velocity field linearized by the local resolved scale strain. EMC can account for viscous effects, addressing the laminar flow finite eddy viscosity problem without implementation of the dynamic procedure . The algebraic form of the model lends itself to analysis and we are able to derive a theoretical value for the eddy rate constant. This value is a bound on the rate constant for full ODT subgrid closure and yields good results in LES of decaying isotropic turbulence with EMC.

A three-dimensional, time dependent, Favre averaged, finite volume Navier-Stokes code has been developed to model compressible and incompressible flows (with and without chemical reactions) in liquid rocket engines. The code has a non-staggered formulation with generalized body-fitted-coordinates (BFC) capability. Higher order differencing methodologies such as MUSCL and Osher-Chakravarthy schemes are available. Turbulent flows can be modeled using any of the

In the current work, a numerical analysis of the thermodynamic second law is investigated for the laminar forced convection flow in a duct adjacent to two inclined backward facing steps. For calculation of entropy generation from the second law of thermodynamics in a laminar forced convection flow, the velocity and temperature distributions are primarily needed. For this purpose, the governing equations including mass, momentum and energy equations are solved by computational fluid dynamic (CFD) techniques to obtain the temperature and velocity fields. For simulating the inclined surface, the blocked-off method is used. The effects of the inclination angle on the entropy generation and Bejan number are also presented. Comparison of numerical results with the available data published in open literature shows a good consistency.

HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L'archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

The increasing volume of vehicles on the road has had a significant impact on traffic flow. Congestion in urban areas is now a major concern. To mitigate congestion, an accurate model is required which is based on realistic traffic dynamics. A new traffic model is proposed based on the conservation law of vehicles which considers traffic dynamics at transitions. Traffic alignment to forward conditions is affected by the time and distance between vehicles. Thus, the well-known Lighthill, Whitham, and Richards (LWR) model is modified to account for traffic behavior during alignment. A model for inhomogeneous traffic flow during transitions is proposed which can be used to characterize traffic evolution. The performance of the proposed model is compared with the LWR model using the Greenshields and Underwood target velocity distributions. These models are evaluated using the Godunov technique and numerical stability is guaranteed by considering the Courant, Friedrich, and Lewy (CFL) condition. The results obtained show that the proposed model characterizes the flow more realistically, and thus can provide better insight into traffic behavior for use in controlling congestion and pollution levels, and improving public safety.

was compared with the analytical solution for some simple cases. Couette flow between two parallel infinite plates (which is equivalent to two concentric cylinders) separated by a narrow gap was considered. Two boundary conditions were considered: 1. Both the plates are at temperature T 0 . 2. One plate (shaft) is at T 0 and the other (bushing) is insulated. This boundary condition is the same as the one we have used for the actual bearing in most of the examples.

Results are presented on two-dimensional numerical simulation of a decaying laser spark after the air breakdown. Radiation loss is modeled in a finite volume framework for a finite wavelength range of the emitted rays. The redistribution of assumed absorbed energy among different parts, namely the blast wave energy, the radiative heat energy and the leftover energy is quantified. About 5% of the absorbed energy is found to be trapped around the breakdown region after the blast wave moves away. A prediction is made about the actual available energy for ignition of a combustible mixture. A distinct rollup motion around the breakdown region is demonstrated from the simulation, which is in accordance with other numerical and experimental observations. Finally, the evolution of the blast wave radius with time is validated against in-house experimental data.

There are three important steps in the computational modelling of any physical process: (i) problem definition, (ii) mathematical model, and (iii) computer simulation. The first natural step is to define an idealization of our problem of interest in terms of a set of relevant quantities which we would like to measure. In defining this idealization we expect to obtain a well-posed problem, this is one that has a unique solution for a given set of parameters. It might not always be possible to guarantee the fidelity of the idealization since, in some instances, the physical process is not totally understood. An example is the complex environment within a nuclear reactor where obtaining measurements is difficult. The second step of the modeling process is to represent our idealization of the physical reality by a mathematical model: the governing equations of the problem. These are available for many physical phenomena. For example, in fluid dynamics the Navier-Stokes equations are considered to be an accurate representation of the fluid motion. Analogously, the equations of elasticity in structural mechanics govern the deformation of a solid object due to applied external forces. These are complex general equations that are very difficult to solve both analytically and computationally. Therefore, we need to introduce simplifying assumptions to reduce the complexity of the mathematical model and make it amenable to either exact or numerical solution. For example, the irrotational (without vorticity) flow of an incompressible fluid is accurately represented by the Navier-Stokes equations but, if the effects of fluid viscosity are small, then Laplace's equation of potential flow is a far more efficient description of the problem.

After introducing the general concept of mimetic differencing, we focus on two specific methodologies, nonoscillatory methods and finite volume approximations. We provide a brief historical account of the development of these two mimetic strategies. We then describe the extension of these strategies to new techniques, a discrete operator calculus and implicit large eddy simulation. In each case, we provide illustrative examples. Further abstraction of these ideas leads to the concept of equations of finite scale, which we advocate as a more appropriate PDE model for constructing numerical algorithms. Published in 2007 by John Wiley & Sons, Ltd.

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The heat flux distribution of an infrared halogen lamp in a Rapid Thermal Processing (RTP) equipment is studied. An overview of lamp modelling in RTP systems is given and for the first time, the infrared lamp bank is modelled by taking into consideration with accuracy a lamp portion in the bank environment. A three-dimensional (3D) lamp model, with a fine filament representation is largely presented. The model assumptions are in particular exposed with focusing on the thermal boundary conditions. The lamp temperature is calculated by solving the radiative heat transfer equation by means of the Monte-Carlo method for ray tracing. Numerical calculations are performed with the finite volume method. A very good agreement is found with experimental data in steady state. The heat amount provided by the lamp is also determined. As a first development, transient calculations are performed with the validated model and the dynamic behaviour of the lamp during heating process is determined with precision. Lastly, the model is discussed and further developments are proposed.

La théorie de l'information s'est particulièrement développée autour des années 50, en fait à partir du moment où C. Shannon a formalisé la circulation de l'information dans un modèle mathématique. On parle alors d'entropie ou de théorie statistique de l'information. Ce dernier utilisera celle-ci comme outil de traitement du signal (Shannon 1975). Nous allons rappeler brièvement les notions les plus importantes de cette théorie. Nous expliciterons ensuite le contexte d'utilisation de celle-ci en bibliométrie, qui est celui des distributions qui étudient les régularités statistiques observées dans le domaine de la production et de l'usage de l'information. Tous ces travaux ont confirmé l'existence de grandes similitudes entre les différentes distributions étudiées dans le domaine de l'information et donc l'existence de régularités et de rapports mesurables, qui autorisent de ce fait la prévision et le concept de lois. Cet article prolonge d...

data, the representativeness of the equations, and the numerical method applied. This contribution reviews and explains the current practice and state of the art of numerical flood simulation models. In particular, the most important and widely used depth averaged model is reviewed and discussed along with its numerical treatment. Proceeding with the two-dimensional flow description and its numerical discretization principles, numerical discretization of depth averaged two-dimensional shallow water equations are presented with special attention given to the correct and robust modeling within the finite volume framework. Some popular finite volume models for solving the depth averaged two-dimensional shallow water equations are described, with special attention to the modeling of shock (bore) waves, the treat of natural topographies, and the appearance of wet/dry fronts.

The propagation, runup and rundown of long surface waves are numerically investigated, initially in one dimension, using a well-balanced high-resolution finite volume scheme. A conservative form of the nonlinear shallow water equations with source terms is solved numerically using a high-resolution Godunov-type explicit scheme coupled with Roe's approximate Riemann solver. The scheme is also extended to handle two-dimensional complex domains. The numerical difficulties related to the presence of the topography source terms in the model equations along with the appearance of the wet/dry fronts are properly treated and extended. The resulting numerical model accurately describes breaking waves as bores or hydraulic jumps and conserves volume across flow discontinuities. Numerical results show very good agreement with previously presented analytical or asymptotic solutions as well as with experimental benchmark data.

The aim of this paper is the investigation of gravity currents moving on both smooth and rough beds by laboratory experiments. Gravity currents were produced in a Perspex tank of rectangular cross-section by lock exchange release experiments. The tank is divided into two parts by a sliding gate: one filled with tap water and the other one filled with salt water to the same height. Nine experiments were performed varying both the bed roughness and the initial density of the gravity current. All the experiments were recorded by a camera and an image analysis technique was applied to measure the spacetime evolution of the gravity current's profile. For the experiments with a smooth bed three different phases were observed in the gravity current’s dynamics: a first slumping or constant speed phase; a second self-similar phase, in which the front speed decreased as t, where t is the time measured from release; a third viscous phase, in which the front velocity decreased as t. In the ...

The Lattice Boltzmann method (LBM) has proved to yield results with accuracy comparable to approaches based on 2D multilayer shallow water equations (MSWE) aimed at simulating gravity currents. The rapid diffusion of the LBM stems from the reduced computational burden required. The handling of complex boundaries is a crucial capability that a numerical method solving the MSWE must exhibit. In this work we show that an approach employing a Finite Volume scheme to solve the Lattice Boltzmann equation (FV-LBE) provides the desired ability for boundary representation at the expense of a reasonable increase in complexity with respect to the LBM approach. In a “time to result” technical framework, the FV-LBE is far superior, this feature being more important for cases where the smallest-to-highest spatial scale ratio to be represented in the simulation decreases.

Numerical investigations using the finite volume (FV) method were conducted to examine the effect of microstructure and microstructural properties on the fracture strength of advanced ceramics with industrial applications. Statistically representative microstructural volumes were created using a diffuse-interface model using OpenFOAM-1.6-ext. Crack initiation and growth was modeled using a recently developed arbitrary crack propaga-* Corresponding Author

An arbitrary crack propagation model using cell-centre finite volume based method is presented. Crack growth in an elastic solid, across an interface perpendicular to the initial crack path and into a second elastic solid is analysed. Crack initiation and the subsequent path of propagation are shown to arise naturally out of the selection of appropriate cohesive parameters. It is shown that the allowable crack propagation path is restricted by the underlying mesh. Results are presented for a number of values of interfacial strength and ratios of elastic properties between the two elastic solids. For higher values of interfacial strength, the crack is shown to propagate straight through the interface, while for lower values of interfacial strength, the crack is shown to change direction and propagate along the interface. It is shown that with careful selection of material and interface parameters it is possible to arrest a propagating crack at the interface. The method represents a useful step towards the prediction of crack propagation in complex structures.

This paper describes the development and application of a frictionless contact stress solver based on the cell-centred finite volume method. The contact methodology, implemented in the open-source software OpenFOAM, is derived from the penalty method commonly used in finite element contact algorithms. The solver is verified on two benchmark tests using the available Hertzian analytical solutions.

The viscous flow development around real two-dimensional multi-element aerofoil configuration is numerically simulated by solving the compressible Reynolds-averaged Navier-Stokes equations. Turbulence is treated using a non-linear one-equation model. A wake turbulence model is devised in order to allow sufficient capturing of the wake behaviour, because the wake flow development significantly influences the overall flow-field for multielement, high-lift configurations. The geometric complexity of such airfoils is overcome by employing block-structured computational grid techniques. Development of aerodynamic flows around the British NHLP (National High-Lift Program) three-element aerofoil configuration with maneuver flap and slat are predicted at low-speed conditions (take-off). The results obtained show encouraging computational method for multi-element airfoils flows in comparison with experimental data.

A pure surface plasmon polariton ͑SPP͒ model predicted that the SPP excitation in a slit-groove structure at metallodielectric interfaces exhibits an intricate dependence on the groove width P. Lalanne et al. ͓Phys. Rev. Lett. 95, 263902 ͑2005͒; Nat. Phys. 2, 551 ͑2006͔͒. In this paper, we present a simple far-field experiment to test and validate this interesting theoretical prediction. The measurement results clearly demonstrate the predicted functional dependence of the SPP coupling efficiency on groove width, in good agreement with the SPP picture.

The purpose of this paper is to establish a new numerical approach to solve, in two dimensions, a semilinear reaction diffusion equation combining finite volume method and Schur complement method. We applied our method for q = 2 non-overlapping subdomains and then we generalized in the case of several subdomains (q ≥ 2). A large number of numerical test cases shows the efficiency and the good accuracy of the proposed approach in terms of the CPU time and the order of the error, when increasing the number of subdomains, without using the parallel computing. After several variations of the number of subdomains and the mesh grid, we remark two significant results. On the one hand, the increase related to the number of subdomains does not affect the order of the error, on the other hand, for each mesh grid when we augment the number of subdomains, the CPU time reaches the minimum for a specific number of subdomains. In order to have the minimum CPU time, we resorted to a statistical study between the optimal number of subdomains and the mesh grid.

This study is devoted to the flood wave propagation modelling corresponding to a realistic situation. The equations that governs the propagation of a flood wave, in natural rivers, corresponds to the free surface flow equations in the Shallow Water case. The obtained two dimensional system, known as Saint Venant's system, is derived from the three-dimensional incompressible Navier Stokes equations by depth-averaging of the state variables. This system is written in a conservative form with hyperbolic homogeneous part. The discretization of the convection part is carried out by the use of the finite volume method on unstructured mesh. To increase the accuracy of the scheme, the MUSCL technique is used. The diffusive part is discretized using a Green-Gauss interpolation technique based on a diamond shaped co-volume. For the numerical experiment, we have studied a realistic channel of the Ourika valley which is located in Morocco. The flood occurred on August 1995 is simulated with the objective of evaluating the behavior of the wave propagation in the channel. The results of the proposed numerical model gives velocities and free surface elevations at different stopped times of the simulation.

En este trabajo se propone un modelo computacional discretizado en volúmenes finitos para hormigón permeable, a partir de datos de permeabilidad obtenidos de ensayos físicos sobre probetas y la velocidad de flujo producida por una tormenta de diseño, con el objetivo de ser utilizado como dispositivo de retención de residuos urbanos en los ingresos a alcantarillas. Se diseña la geometría del módulo en base a la infraestructura existente y las normas correspondientes, considerando el medio parcialmente saturado y un fluido incompresible.

The development of various volume penalization techniques for use in modeling topographical features in the ocean is the focus of this paper. Due to the complicated geometry inherent in ocean boundaries, the stair-step representation used in the majority of current global ocean circulation models causes accuracy and numerical stability problems. Brinkman penalization is the basis for the methods developed here and is a numerical technique used to enforce no-slip boundary conditions through the addition of a term to the governing equations. The second aspect to this proposed approach is that all governing equations are solved on a nonuniform, adaptive grid through the use of the adaptive wavelet collocation method. This

This study gives a description and some applications of a three-dimensional mathematical model, through which the local scour holes around hydraulic structures can be simulated. This model calculates the flow field by solving the Reynolds-averaged Navier-Stokes equations with the widely-used k-ƒÃ model for the turbulence closure. The local scour holes are assumed

In this study, analysis of inundation flow considering overflow from a river channel due to heavy rainfall is carried out for establishment of countermeasures against flood disasters. The numerical simulations and the laboratory experiments are conducted for estimation of these phenomena. Especially, a numerical model for simulation of inundation flow considering overflow from a river channel is proposed and evaluated. The numerical model proposed in this study includes 2D horizontal model and 3D RANS (Reynolds Averaged Navier-Stokes) model. Two models are coupled by simultaneous grid method and all hydraulic quantities are connected in overlapped position of meshes. And, the standard k-ε model for turbulence closure and the VOF (Volume of Fluid) method for free-surface modeling are also included in the numerical model. The proposed 2D-3D numerical coupling model is applied to a domain with a river channel and a floodplain, and the laboratory experiments are also conducted to compare with the numerical results. The numerical results have good agreements with those of experiments for the variations of the inundation flow into a floodplain considering overflow from a river channel and the effects of water level rise by river structures. It is judged that the proposed model can be helpful to establish countermeasures against inundation disasters.

In this paper, the applicability of bandal-like structures as an alternative method for traditional river training structures like groins is investigated. This structure is usually used in Indian Sub-Continents for riverbank protection and improvement of navigation conditions in alluvial rivers. The mechanism behind the utilization of this type of structure which affects the flow patterns and sediment transport process was studied through experimental measurements and numerical simulations. During the calculations, the water flow is computed by solving the Reynolds-averaged Navier-Stokes equations in 3D domain. The k-ε model is used for the turbulence closure and the numerical simulation is conducted on the unstructured meshes with the finite volume method. The main characteristics of the sediment erosion/deposition process around the bandal-like structures are clarified. The promising use of bandal-like structures is demonstrated through the comparisons with conventional structures as impermeable groins.