Displaying similar documents to “An entropy stable finite volume method for a compressible two phase model”

A discrete kinetic approximation for the incompressible Navier-Stokes equations

Maria Francesca Carfora, Roberto Natalini (2008)

ESAIM: Mathematical Modelling and Numerical Analysis

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In this paper we introduce a new class of numerical schemes for the incompressible Navier-Stokes equations, which are inspired by the theory of discrete kinetic schemes for compressible fluids. For these approximations it is possible to give a stability condition, based on a discrete velocities version of the Boltzmann H-theorem. Numerical tests are performed to investigate their convergence and accuracy.

Incompressible limit of a fluid-particle interaction model

Hongli Wang, Jianwei Yang (2021)

Applications of Mathematics

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The incompressible limit of the weak solutions to a fluid-particle interaction model is studied in this paper. By using the relative entropy method and refined energy analysis, we show that, for well-prepared initial data, the weak solutions of the compressible fluid-particle interaction model converge to the strong solution of the incompressible Navier-Stokes equations as long as the Mach number goes to zero. Furthermore, the desired convergence rates are also obtained.

Formal passage from kinetic theory to incompressible Navier–Stokes equations for a mixture of gases

Marzia Bisi, Laurent Desvillettes (2014)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

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We present in this paper the formal passage from a kinetic model to the incompressible Navier−Stokes equations for a mixture of monoatomic gases with different masses. The starting point of this derivation is the collection of coupled Boltzmann equations for the mixture of gases. The diffusion coefficients for the concentrations of the species, as well as the ones appearing in the equations for velocity and temperature, are explicitly computed under the Maxwell molecule assumption in...

Vorticity dynamics and numerical Resolution of Navier-Stokes Equations

Matania Ben-Artzi, Dalia Fishelov, Shlomo Trachtenberg (2010)

ESAIM: Mathematical Modelling and Numerical Analysis

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We present a new methodology for the numerical resolution of the hydrodynamics of incompressible viscid newtonian fluids. It is based on the Navier-Stokes equations and we refer to it as the vorticity projection method. The method is robust enough to handle complex and convoluted configurations typical to the motion of biological structures in viscous fluids. Although the method is applicable to three dimensions, we address here in detail only the two dimensional case. We provide numerical...

Propagation of chaos for the 2D viscous vortex model

Nicolas Fournier, Maxime Hauray, Stéphane Mischler (2014)

Journal of the European Mathematical Society

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We consider a stochastic system of N particles, usually called vortices in that setting, approximating the 2D Navier-Stokes equation written in vorticity. Assuming that the initial distribution of the position and circulation of the vortices has finite (partial) entropy and a finite moment of positive order, we show that the empirical measure of the particle system converges in law to the unique (under suitable a priori estimates) solution of the 2D Navier-Stokes equation. We actually...

Weak-strong uniqueness for Navier-Stokes/Allen-Cahn system

Radim Hošek, Václav Mácha (2019)

Czechoslovak Mathematical Journal

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The coupled Navier-Stokes/Allen-Cahn system is a simple model to describe phase separation in two-component systems interacting with an incompressible fluid flow. We demonstrate the weak-strong uniqueness result for this system in a bounded domain in three spatial dimensions which implies that when a strong solution exists, then a weak solution emanating from the same data coincides with the strong solution on its whole life span. The proof of given assertion relies on a form of a relative...

An existence proof for the stationary compressible Stokes problem

A. Fettah, T. Gallouët, H. Lakehal (2014)

Annales de la faculté des sciences de Toulouse Mathématiques

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In this paper, we prove the existence of a solution for a quite general stationary compressible Stokes problem including, in particular, gravity effects. The Equation Of State gives the pressure as an increasing superlinear function of the density. This existence result is obtained by passing to the limit on the solution of a viscous approximation of the continuity equation.