Compressible Flow

Natural gas recovery has increased with the production from unconventional reservoirs with low absolute permeability. In these reservoirs, production is favored, for example, by the use of horizontal wells and the gas-phase slippage effect. This work performs a numerical simulation of two-phase isothermal water-gas flow, accounting for the impact of gas slip and permeability variation as a function of the stress change acting on the porous matrix. The governing equations are discretized using the Finite Volume Method. The obtained algebraic equation systems are linearized and solved by applying a Picard-Newton solution strategy, an operator splitting method, and the iterative preconditioned Stabilized Biconjugate Gradient method. The results are presented in terms of instantaneous gas flow rate and recovered gas volume, considering several production scenarios for the prescribed well pressure. In conclusion, the results showed that it was possible to capture the incorporated physical effects, with slippage favoring production and the change due to the stress effect leading to a decrease in apparent permeability resulting from the pressure drop caused by production.

The ongoing effort to develop an in-house compressible solver with multi-disciplinary physics is presented in this paper. Basic compressible solver combined with IBM technique provides us an effective numerical tool able to tackle the physics phenomena and especially physic phenomena involved in Solid Rocket Motors (SRMs). Main principles are introduced step by step describing its implementation. This paper sheds light on the whole potentiality of our proposed numerical model and we strongly believe a way to introduce multi-physics mechanisms strongly coupled is opened to ablation in nozzle, fluid/structure interaction and burning propellant surface with time.

Interaction behaviors of high-speed compressible viscous flow and thermal-structural response of structure are presented. The compressible viscous laminar flow behavior based on the Navier-Stokes equations is predicted by using an adaptive cell-centered finite-element method. The energy equation and the quasi-static structural equations for aerodynamically heated structures are solved by applying the Galerkin finite-element method. The finite-element formulation and computational procedure are described. The performance of the combined method is evaluated by solving Mach 4 flow past a fiat plate and comparing with the solution from the finite different method. To demonstrate their interaction, the high speed flow, structural heat transfer, and deformation phenomena are studied by applying the present method to Mach 10 flow past a flat plate.

In the last few years, upwind methods have become very popular in the modeling of advection dominated flows and in particular those which contain strong discontinuities. For more than a decade, these methods have been used successfully to solve numerically the one-dimensional Euler equations. Fluctuation distribution has been recently introduced as an alternative to conventional upwinding. In contrast to standard upwinding the fluctuation distribution approach extends naturally to multidimensional flow without requiring any splitting along coordinate directions. The technique uses a narrow-stencil, local, piecewise linear reconstruction of the flow field solution. The flow field is updated in time by propagating a subset of eigenmodes of the convective operator. Different choices of the eigenmode subset lead to different fluctuation distribution schemes. In this paper, schemes for approximating steady solution to the two dimensional of the inviscid fluid equations on unstructured triangular grids are presented, also an analysis of fluctuation splitting schemes applied to scalar advection equations has been performed. Wave models based on Roe's simple wave decomposition have been further developed and tested, providing an exact solution to the linearized equations, and decomposes the flux difference at the interface into a set of simple waves, all aligned with the grid face. In this work, the presented model of fluctuation splitting N combined with Roe wave models implemented in our own Code written in C++ reached the stage where they can be used reliably to achieve maximal computational efficiency to practical steady state problems in aerodynamics (Supersonic oblique shock reflection, Flow in a channel with a Bump, Symmetric Constricted channel flows, flow around NACA 0012 aerofoil, flows in a turbine-blade cascade VKI LS-59 ).

A near-wall two-equation turbulence model of the K -s type is developed for the description of high-speed compressible flows. The Favre-averaged equations of motion are solved in conjunction with modeled transport equations for the turbulent kinetic energy and solenoidal dissipation wherein a variable density extension of the asymptotically consistent near-wall model of So and co-workers is supplemented with new dilatational models. The resulting compressible two-equation model is tested in the supersonic fiat plate boundary layer -with an adiabatic wall and with wall cooling -for Mach numbers as large as 10. Direct comparisons of the predictions of the new model with raw experimental data and with results from the K -w model indicate that it performs well for a wide range of Mach numbers. The surprising finding is that the Morkovin hypothesis, where turbulent dilatational terms are neglected, works well at high Mach numbers provided that the near wall model is asymptotically consistent. Instances where the model predictions deviate from the experiments appear to be attributable to the assumption of constant turbulent Prandtl number -a deficiency that will be addressed in a future paper.

A continuous adjoint approach to aerodynamic design for viscous compressible flow on unstructured grids is developed. Sensitivity gradients are computed using tools of shape deformation of boundary integrals. The resulting expressions involve second-order derivatives of the flow variables that require numerical solvers with greater than second-order accuracy. A systematic way of reducing the order of these terms is presented. The accuracy of the sensitivity derivatives is assessed by comparison with finite-difference computations, and the validity of the overall methodology is illustrated with several design examples.

We consider the initial-boundary value problem for the system of equations describing the flow of compressible isothermal mixture of arbitrary large number of components. The system consists of the compressible Navier-Stokes equations and a subsystem of diffusion equations for the species. The subsystems are coupled by the form of the pressure and the strong cross-diffusion effects in the diffusion fluxes of the species. Assuming the existence of solutions to the symmetrized and linearized equations, proven in , we derive the estimates for the nonlinear equations and prove the local-in-time existence and maximal L p -L q regularity of solutions.

The efficiency and stability of multirotor drones depend heavily on the aerodynamic performance of their propellers. Conventional propeller designs often fail to achieve optimal liftto-drag ratios when subjected to varying flight conditions. This study presents a computational fluid dynamics (CFD)-based methodology for the aerodynamic optimization of quadrotor propellers. The work focuses on parametric design, flow analysis, and performance evaluation using Reynolds-Averaged Navier-Stokes (RANS) simulations. A range of propeller geometries were simulated across different advance ratios and Reynolds numbers to evaluate thrust, torque, efficiency, and noise characteristics. Results demonstrate that optimized blade geometry with adaptive twist and airfoil selection yields up to 15% higher efficiency compared to baseline designs. Furthermore, noise levels were reduced by 8 dB while maintaining thrust requirements. The proposed framework offers a systematic approach to improving multirotor performance, with implications for both civilian and industrial drone applications.

We consider a model of flow of two compressible and immiscible phases in a three-dimensional porous media. The equations are obtained by the conservation of the mass of each phase. This model is treated in its general form with the whole nonlinear terms. The only assumption concerns the dependence of densities on a global pressure. We obtain the existence of weak solutions under different kinds of degeneracies of the capillary terms.

In this paper we study the dependence of the Holder estimates on the geometry of a domain with holes for the Neumann problem. For this, we study the Holder regularity of the solutions to the Dirichlet and Neumann problems in the disk (and in the exterior of the disk), from which we get a relation between harmonic extensions and harmonic functions with prescribed Neumann condition on the boundary of the disk (for both interior and exterior problems).

We systematically derived hydrodynamic equations and transport coefficients for a class of multi-speed lattice Boltzmann models in D dimensions, using the multi-scale technique. The constitutive relation of physical fluid is recovered by a modified equilibrium distribution in Maxwell-Boltzmann type. With the use of the rest particles and the particle reservoir, we were able to add one degree of freedom into the sound speed of the modeled fluid. When the sound speed is tuned small enough, the compressible region of fluid flow can be reached. An example 2-D model is presented, together with the numerical verification for its transport coefficients.

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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...

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We show well-posedness for the equations describing a new model of slightly compressible fluids. This model was recently rigorously derived in Grandi and Passerini (Geophys Astrophys Fluid Dyn, 2020) from the full set of balance laws and falls in the category of anelastic Navier–Stokes fluids. In particular, we prove existence and uniqueness of global regular solutions in the two-dimensional case for initial data of arbitrary “size”, and for “small” data in three dimensions. We also show global stability of the rest state in the class of weak solutions.

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The use of a colocated variable arrangement for the numerical solution of fluid flow is becoming more and more popular due to its coding simplicity. The inherent decoupling of the pressure and velocity fields in this arrangement can be handled via a special interpolation procedure for the calculation of the cell face velocity named PWIM (Pressure Weighted Interpolation Method). In this paper a discussion on the alternatives to extend PWIM to unsteady flows is presented along with a very simple criterium to ascertain if a given interpolation practice will produce steady results that are relaxation dependent or time step dependent. Following this criterium it will be shown that some prior schemes presented as time step independent are actually not, although by using special interpolations can be readily adapted to be. A systematic way of deriving different cell face velocity expressions will be presented and new formulae free of ∆t dependence will be derived. Several computational exercices will accompany the theoretical discussion to support our claims.

The adaptive wavelet collocation and Brinkman penalization methods are applied to the shallow water model and validated. The wavelet method solves the equations on temporally and spatially varying meshes, which allows a higher effective resolution to be obtained with less computational cost. The grid adaptation is achieved by using the ability of wavelet multiresolution analysis to identify and isolate localized dynamically dominant flow structures, eg, vortices, and to track these structures on adaptive computational meshes. In ...

The stability problem of two-dimensional compressible flat-plate boundary layers is handled using the linear stability theory. The stability equations obtained from three-dimensional compressible Navier-Stokes equations are solved simultaneously with two-dimensional mean flow equations, using an efficient shoot-search technique for adiabatic wall condition. In the analysis, a wide range of Mach numbers extending well into the hypersonic range are considered for the mean flow, whereas both two-and three-dimensional disturbances are taken into account for the perturbation flow. All fluid properties, including the Prandtl number, are taken as temperature-dependent. The results of the analysis ascertain the presence of the second mode of instability (Mack mode), in addition to the first mode related to the Tollmien-Schlichting mode present in incompressible flows. The effect of reference temperature on stability characteristics is also studied. The results of the analysis reveal that the stability characteristics remain almost unchanged for the most unstable wave direction for Mach numbers above 4.0. The obtained results are compared with existing numerical and experimental data in the literature, yielding encouraging agreement both qualitatively and quantitatively.

In this article, a linear stability analysis is presented for a liquid jet discharging into a stagnant gas medium. Following the usual approach for a linear analysis, a dispersion relation that relates the amplification factor of a disturbance to its wave number is obtained from the equations of motion for incompressible, viscous, axisymmetric flows in cylindrical coordinates. Surface tension, viscosity of the liquid and electrical charge are the parameters of the problem. It is shown that the surface tension stabilizes the flow in the atomization regime, while the electric charges destabilize it. These results are in agreement with the results of the inviscid analysis. On the other hand, a more viscous liquid jet results in a more stable flow.

Plusieurs travaux récents en cosmologie, physique, anthropologie cognitive, paléontologie, neurosciences, économie et histoire font l'hypothèse du caractère général de la course à la puissance tant dans les processus physiques, biologiques que sociaux, ce qui semble les conduire au diagnostic d'une inévitabilité de la catastrophe écologique. Même si cette hypothèse-qui a toutes les apparences d'un fatalisme-reste évidemment discutable, nous pensons qu'elle n'interdit pas toutefois en elle-même la possibilité d'une inflexion volontariste des trajectoires énergétiques humaines. Mieux : ce serait en l'assumant, dès le départ, en conscience et en connaissance de cause, que nous pourrions nous donner des prises plus lucides, à différentes échelles, et donc aussi plus effectives à moyen-terme sur nos pratiques d'exploration et d'exploitation des énergies et des ressources.

We consider the motion of compressible viscous fluids around a rotating rigid obstacle when the velocity at infinity is non zero and parallel to the axis of rotation. We prove the existence of weak solution. We consider a rigid body S with boundary Γ such that Ω = R 3 \ S is an exterior domain. We assume that the body is rotating around the x 3 -axis with the angular velocity ω = (0, 0, |ω|). The position of the body at time t > 0 is given by the formula S(t) = {y = O(t)x; x ∈ S}, S(0) = S (1.1) * S.

Nozzles are the important part of propellers generating the thrust and enabling the rockets to move in a forward direction. However, their efficient design is imperative to enhance the thrust force and to reduce fuel consumption. Therefore, the aim of this study is to conduct a comparative study of different convergent section angles to evaluate the maximum thrust force of a supersonic nozzle. Computational fluid dynamic (CFD) simulation is performed with different convergent section angles ranging from 42° to 24° by maintaining the same pressure ratio and operating conditions. In addition, the numerical simulation is performed with different working fluids such as air, carbon dioxide, and carbon monoxide. Furthermore, the effect of inlet temperature on Mach number is also analysed. The numerical simulation is performed on an unstructured grid. Meanwhile, the simulation is carried out on a 2D axisymmetric density-based coupled solver with a viscous k-Omega SST turbulence model. The results are validated with previous experimental work and found good agreement with 2.6 percent error. The study revealed that decreasing the convergent angle up to 27° has a favourable effect, and a 1.6 percent increase in thrust force was estimated. Additionally, CO₂ was considered the best working gas with the highest thrust performance, preceded by air, nitrogen, and CO. Furthermore, the inlet temperature has a significant effect on the nozzle Mach number. The findings of this study may be used to design efficient jet engines and rockets.

The paper analyzes the fourteen rock glaciers inventoried in the Pyrenees. The genesis, surface morphology, internal structure, surface dynamics and morphostratigraphical characters are analysed according to studies made on different rock glaciers. The Pyrenean rock glaciers are included in two genetic typologies as talus rock glacier with periglacial origin, and debris-glacier rock glacier, of glaciogenetic origin. Both types are related to different surface shapes and internal structures. The internal structure shows a great diversity, with different structures for each of the four rock glaciers studied. Rock glaciers show a wide range of horizontal displacements, although the displacements are moderate in all cases, except the Argualas rock glacier, with displacements similar to the most frequents alpine ones. In all cases rock glaciers show a trend toward thinning. The study of horizontal and vertical displacement has permitted us to establish two different dynamic models: “push...

In this paper, an important discovery has been found for nonconforming immersed finite element (IFE) methods using the integral values on edges as degrees of freedom for solving elliptic interface problems. We show that those IFE methods without penalties are not guaranteed to converge optimally if the tangential derivative of the exact solution and the jump of the coefficient are not zero on the interface. A nontrivial counter example is also provided to support our theoretical analysis. To recover the optimal convergence rates, we develop a new nonconforming IFE method with additional terms locally on interface edges. The new method is parameter-free which removes the limitation of the conventional partially penalized IFE method. We show the IFE basis functions are unisolvent on arbitrary triangles which is not considered in the literature. Furthermore, different from multipoint Taylor expansions, we derive the optimal approximation capabilities of both the Crouzeix-Raviart and the rotated-Q1 IFE spaces via a unified approach which can handle the case of variable coefficients easily. Finally, optimal error estimates in both H 1 -and L 2 -norms are proved and confirmed with numerical experiments.

An efficient implicit lower-upper symmetric Gauss-Seidel (LU-SGS) solution algorithm has been developed for a high order multi-domain spectral difference method on unstructured hexahedral grids. The LU-SGS solver is preconditioned by the block element matrix, and the system of equations is then solved with an exact LU decomposition approach. In addition, the effects of several parameters on the convergence rate in the implicit scheme have been investigated for both external and internal flows. The implicit scheme has shown a speed up factor of more than an order of magnitude relative to the multi-stage explicit Runge-Kutta scheme for several demonstration problems. he advantage of high-order methods (order of accuracy > 2) over first and second-order ones is well known in the CFD community. Generally speaking, with the same number of degrees-of-freedom (DOFs) or solution unknowns, high-order methods are capable of producing much more accurate results. For problems requiring very high accuracy, e.g., wave propagation problems in computational aeroacoustics, high-order methods have been the main choice. Many high-order methods were developed for structured grids, e.g., ENO/WENO methods 1, compact methods 2-3 , optimized methods 4 , to name just a few. In the last two decades, there have been intensive research efforts on high-order methods for unstructured grids since many real world applications have complex geometries. An incomplete list of notable examples includes the spectral element method 5 , multi-domain spectral method 6-7 , kexact finite volume method 8 , WENO methods 9 , discontinuous Galerkin (DG) method 10-12 , high-order residual distribution methods 13 , spectral volume (SV) 14-17 and spectral difference (SD) methods 18-21 . Among those methods, some are based on the weighted residual form of the governing equations, for instance the DG method 10-12 . Some are based on the integral form of the governing equations, e. g., the k-exact finite volume method 8 and SV methods 14-17 . Others, such as the staggered grid multi-domain spectral method 6-7 and the SD method 18-21 , are based on the differential form. When one chooses a particular method for three-dimensional applications, the cost and the complexity in implementing the method is often an important factor. It is obvious that methods based on the differential form are the easiest to implement since they do not involve surface or volume integrals. This is particularly true when highorder curved boundaries need to be dealt with. We recently developed a high order SD method 22 for the three dimensional Navier-Stokes equations on unstructured hexahedral grids. High order accuracy and spectral convergence are achieved for several benchmark problems. It was also shown that the wall boundaries must be approximated with high-order surfaces. An explicit Runge-Kutta time integration scheme was used in the implementation. Although the explicit scheme is easy to implement and has high-order accuracy in time, it suffered from slow convergence, especially for viscous grids which are clustered in the viscous boundary layer. It is wellknown that high-order methods are restricted to a smaller CFL number than low order ones. In addition, they also

Generalizing prior work of P. W. Anderson and E. R. Huggins, we show that a "detailed Josephson-Anderson relation" holds for drag on a finite body held at rest in a classical incompressible fluid flowing with velocity V. The relation asserts an exact equality between the instantaneous power consumption by the drag, -F•V, and the vorticity flux across the potential mass current, Here Σij is the flux in the ith coordinate direction of the conserved jth component of vorticity and the line-integrals over are taken along streamlines of the potential flow solution u φ = ∇φ of the ideal Euler equation, carrying mass flux dJ = ρ u φ •dA. The results generalize the theories of M. J. Lighthill for flow past a body and, in particular, the steady-state relation (1/2) ijk Σ jk = ∂i h , where h = p+(1/2)|u| 2 is the generalized enthalpy or total pressure, extends Lighthill's theory of vorticity generation at solid walls into the interior of the flow. We use these results to explain drag on the body in terms of vortex dynamics, unifying the theories for classical fluids and for quantum superfluids. The results offer a new solution to the "D'Alembert paradox" at infinite Reynolds numbers and imply the necessary conditions for turbulent drag reduction.

Fully compressible turbulent convection beyond the Oberbeck-Boussinesq limit and anelastic regime is studied in three-dimensional numerical simulations. Superadiabaticity and dissipation number D, which measures the strength of stratification of adiabatic equilibria, cause two limits of compressible convection-nearly top-down-symmetric, strongly superadiabatic convection and highly top-down-asymmetric, strongly stratified convection. The highest turbulent Mach numbers M t follow for a symmetric blend of these two limits, which we term the fully compressible case. Particularly, the strongly stratified convection case leads to a fluctuation-reduced top layer in the convection zone, a strongly reduced global heat transfer, and differing boundary layer dynamics between top and bottom. We detect this asymmetry for growing dissipation number D also in the phase plane, which is spanned by the turbulent Mach number M t and the dilatation parameter δ, which relates the dilatational velocity fluctuations to the solenoidal ones. A detailed analysis of the different transport currents in the fully compressible energy budget relates the low-D convection cases to the standard definition of the dimensionless Nusselt number in the Oberbeck-Boussinesq limit.

Over the last decades, several types of collision models have been proposed to extend the validity domain of the lattice Boltzmann method (LBM), each of them being introduced in its own formalism. The present article proposes a formalism that describes all these methods within a common mathematical framework, and in this way allows us to draw direct links between them. Here, the focus is put on single and multirelaxation time collision models in either their raw moment, central moment, cumulant or regularized form. In parallel with that, several bases (non orthogonal, orthogonal, Hermite) are considered for the polynomial expansion of populations. General relationships between moments are first derived to understand how moment spaces are related to each other. In addition, a review of collision models further sheds light on collision models that can be rewritten in a linear matrix form. More quantitative mathematical studies are then carried out by comparing explicit expressions for the post collision populations. Thanks to this, it is possible to deduce the impact of both the polynomial basis (raw, Hermite, central, central Hermite, cumulant) and the inclusion of regularization steps on isothermal LBMs. Extensive results are provided for the D1Q3, D2Q9, and D3Q27 lattices, the latter being further extended to the D3Q19 velocity discretization. Links with the most common two and multirelaxation time collision models are also provided for the sake of completeness. The present work ends by emphasizing the importance of an accurate representation of the equilibrium state, independently of the choice of moment space. As an addition to the theoretical purpose of the present article, general instructions are provided to help the reader with the implementation of the most complicated collision models.

This paper presents a one dimensional model for the gas dynamics in a chimney. This is a prototype example of a small Mach number flow with strong heat sources. Due to the small Mach number of the gas flow an asymptotic model is derived from a fully compressible model, which then is compared to the original model and to the often used Boussinesq approximation. The Boussinesq approximation is shown to be inappropriate for this application, whereas the small Mach number asymptotic model we propose is shown to be a very good approximation. In particular it allows very fast numerical simulations. Finally, all this is underlined by numerical simulations where we validate the various models.

This paper presents a one dimensional model for the gas dynamics in a chimney. This is a prototype example of a small Mach number flow with strong heat sources. Due to the small Mach number of the gas flow an asymptotic model is derived from a fully compressible model, which then is compared to the original model and to the often used Boussinesq approximation. The Boussinesq approximation is shown to be inappropriate for this application, whereas the small Mach number asymptotic model we propose is shown to be a very good approximation. In particular it allows very fast numerical simulations. Finally, all this is underlined by numerical simulations where we validate the various models.

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The Maréchal approximation for the Strehl ratio versus rms wavefront distortion is widely used in atmospheric scaling law codes, but a complete derivation is absent in the open literature. I present an updated derivation of the first term in Maréchal, then a complete derivation. The Strehl ratio is proportional to the square of the Fourier transform of the probability density function of the random phase noise. For Gaussian noise, the traditional Maréchal formulation is the result. The more general formulation suggests a method for characterization of random phase aberrations.

The massive Thirring (MT) model and its dual the sine-Gordon model are known to be integrable. Some versions of their multi-field extensions have appeared in the literature (see e.g. [1]). On the other hand, the noncommutative (NC) version of the MT model has been proposed recently . Here we discuss some properties of the affine Kac-Moody algebraic formulation of a noncommutative version of the so-called generalized massive Thirring model.

The ideal magnetohydrodynamic (MHD) equations are important in modeling phenomena in a wide range of applications including space weather, solar physics, laboratory plasmas, and astrophysical fluid flows. In vector form these equations can be written as

The ideal magnetohydrodynamic (MHD) equations are important in modeling phenomena in a wide range of applications including space weather, solar physics, laboratory plasmas, and astrophysical fluid flows. In vector form these equations can be written as

For numerical simulations of cavitating flows, many physical models are currently used. One approach is the void fraction transport equation-based model including source terms for vaporization and condensation processes. Various source terms have been proposed by different researchers. However, they have been tested only in different flow configurations, which make direct comparisons between the results difficult. A comparative study, based on the expression of the source terms as a function of the pressure, is presented in the present paper. This analytical approach demonstrates a large resemblance between the models, and it also clarifies the influence of the model parameters on the vaporization and condensation terms and, therefore, on the cavity shape and behavior. Some of the models were also tested using a 2D CFD code in configurations of cavitation on two-dimensional foil sections. Void fraction distributions and frequency of the cavity oscillations were compared to existing ...

In this paper, we present a deterministic mathematical model for the study of overweight, and obesity in a population and its impact on the growth of the number of diabetics. For the construction of the model, we take into account social factors and the interactions between the elements of society. We find the basic reproduction number and prove the global stability of the disease-free equilibrium point. We present theoretical results and find the sensitivity indices to characterize the impact of parameters associated with overweight, obesity and diagnosed diabetes on the basic reproduction number. To validate the model, we perform computational simulations and study the basic reproduction number and compartments. We present the behavior of the compartments for a scenario and study the impact of the variation of parameters associated with overweight by social pressure and diabetes due to causes other than obesity.

Flow and thrust calculations at supersonic speeds require intensive formulas and general assumptions, thus prolonging the preliminary design process. Today, the use of computer programs for aerodynamic design and analysis is inevitable in the development of aircraft. However, in this process, traditional calculation methods are mostly used. By performing the relevant calculations with a source code, time-consuming problems such as data extraction from tables, interpolation or calculation with formulas can be avoided. In this study, a computational tool was created in Python using the formulas contained in compressible flow theory. For the calculation, ISA (International Standard Atmosphere) and altitude values are first obtained from the user to determine the atmospheric conditions. These conditions are known to directly affect static conditions. Then, the data input of one of the selected parameters is made and the remaining parameters according to these input values are presented on the result screen together with the other outputs. These outputs were compared with NASA data and their accuracy was analysed. Two different configurations were created to examine the dependence of compressible flow calculations on atmospheric conditions. In the first one, constant ISA and different altitude values were analysed, while in the other one, constant altitude and different temperature deviations were evaluated. These evaluations revealed the sensitivity of the calculation results to atmospheric variables. The findings provide critical data on how to design and analyse aircraft under different operational conditions. This study, for the first time, provides calculations based on atmospheric variables, enabling them to efficiently obtain the values of parameters that depend on these data. This approach is an innovative contribution to the existing literature, expanding the body of knowledge on the analysis of compressible flows.

Deagglomeration of suspensions of alumina and titania nanopowders (i.e., nanoparticle aggregates) via rapid expansion of supercritical suspensions (RESS) or high‐pressure suspensions (REHPS) was studied. The size distribution of fragmented nanopowders was characterized by online Scanning Mobility Particle Spectrometer (SMPS) and Aerodynamic Particle Sizer (APS), and by offline Scanning Electron Microscopy (SEM). SMPS and SEM measurements indicate that the average agglomerate sizes were well below 1 μm, consistent with the length scales observed in our complementary RESS/REHPS mixing experiments using alumina and silica nanopowders. The APS measurements, on the other hand, were affected by reagglomeration during sampling and yielded an agglomerate size range of 1 to 3 μm. Analysis of the RESS/REHPS process through compressible flow models revealed that both the shear stress in the nozzle and the subsequent impact of the agglomerates with the Mach disc in the free expansion region can...

Lagrangian shock hydrodynamics simulations will fail to proceed past a certain time if the mesh is approaching tangling. A common solution is an Arbitrary Lagrangian Eulerian (ALE) form, in which the mesh is improved (remeshing) and the solution is remapped onto the improved mesh. The simplest remeshing techniques involve moving only the nodes of the mesh. More advanced remeshing techniques involve altering the mesh connectivity in portions of the domain in order to prevent tangling. Work has been done using Voronoi-based polygonal mesh generators and 2D quad/triangle mesh adaptation. This paper presents the use of tetrahedral mesh adaptation methods as the remeshing step in an otherwise Lagrangian finite element shock hydrodynamics code called Alexa.

ALEGRA is an arbitrary Lagrangian-Eulerian (multiphysics) computer code developed at Sandia National Laboratories since 1990. The code contains a variety of physics options including magnetics, radiation, and multimaterial flow. The code has been developed for nearly two decades, but recent work has dramatically improved the code's accuracy and robustness. These improvements include techniques applied to the basic Lagrangian differencing, artificial viscosity and the remap step of the method including an important improvement in the basic conservation of energy in the scheme. We will discuss the various algorithmic improvements and their impact on the results for important applications. Included in these applications are magnetic implosions, ceramic fracture modeling, and electromagnetic launch.