scholarly journals VERIFICATION OF AN ENTROPY DISSIPATIVE QGD-SCHEME

2019 ◽  
Vol 24 (2) ◽  
pp. 179-194 ◽  
Author(s):  
Alexander Zlotnik ◽  
Timofey Lomonosov
Keyword(s):  
Gas Dynamics ◽  
Convergence Rates ◽  
Necessary Conditions ◽  
Practical Relevance ◽  
L1 Norm ◽  
Gas Dynamics Equations ◽  
Nonlinear Statement ◽  
The Cauchy Problem ◽  
Practical Convergence ◽  
Explicit Finite Difference

An entropy dissipative spatial discretization has recently been constructed for the multidimensional gas dynamics equations based on their preliminary parabolic quasi-gasdynamic (QGD) regularization. In this paper, an explicit finite-difference scheme with such a discretization is verified on several versions of the 1D Riemann problem, both well-known in the literature and new. The scheme is compared with the previously constructed QGD-schemes and its merits are noticed. Practical convergence rates in the mesh L1-norm are computed. We also analyze the practical relevance in the nonlinear statement as the Mach number grows of recently derived necessary conditions for L2-dissipativity of the Cauchy problem for a linearized QGD-scheme.

scholarly journals On L2-dissipativity of a linearized difference scheme on staggered meshes with a quasi-hydrodynamic regularization for 1D barotropic gas dynamics equations

2021 ◽  
pp. 1-27
Author(s):  
Alexander Anatolievich Zlotnik ◽  
Timofey Alexandrovich Lomonosov
Keyword(s):  
Difference Scheme ◽  
Gas Dynamics ◽  
Sufficient Conditions ◽  
Viscosity Coefficient ◽  
Neumann Condition ◽  
Gas Dynamics Equations ◽  
Von Neumann ◽  
Barotropic Gas ◽  
Constant Solution ◽  
The Cauchy Problem

We study an explicit two-level finite difference scheme on staggered meshes, with a quasi-hydrodynamic regularization, for 1D barotropic gas dynamics equations. We derive necessary conditions and sufficient conditions close to each other for L<sup>2</sup>-dissipativity of solutions to the Cauchy problem for its linearization on a constant solution, for any background Mach number M. We apply the spectral approach and analyze matrix inequalities containing symbols of symmetric matrices of convective and regularizing terms. We consider the cases where either the artificial viscosity coefficient or the physical viscosity one is used. A comparison with the spectral von Neumann condition is also given for M=0.

Systematization of relaxation gas dynamics equations. A review

2010 ◽  
Vol 45 (4) ◽  
pp. 517-536
Author(s):  
V. S. Galkin ◽  
S. A. Losev
Keyword(s):  
Gas Dynamics ◽  
Gas Dynamics Equations

Comparison of the numerical and self-similar solutions of Sedov’s problem on a point explosion in gas

2020 ◽  
Vol 15 (3-4) ◽  
pp. 212-216
Author(s):  
R.Kh. Bolotnova ◽  
V.A. Korobchinskaya
Keyword(s):  
Gas Dynamics ◽  
Numerical Solutions ◽  
Similarity Theory ◽  
Compressible Medium ◽  
Initial Moment ◽  
Point Explosion ◽  
Perfect Gas ◽  
Gas Dynamics Equations ◽  
Self Similar ◽  
Similar Solutions

Comparative analysis of solutions of Sedov’s problem of a point explosion in gas for the plane case, obtained by the analytical method and using the open software package of computational fluid dynamics OpenFOAM, is carried out. A brief analysis of methods of dimensionality and similarity theory used for the analytical self-similar solution of point explosion problem in a perfect gas (nitrogen) which determined by the density of uncompressed gas, magnitude of released energy, ratio of specific heat capacities and by the index of geometry of the explosion is given. The system of one-dimensional gas dynamics equations for a perfect gas includes the laws of conservation of mass, momentum, and energy is used. It is assumed that at the initial moment of time there is a point explosion with instantaneous release of energy. Analytical self-similar solutions for the Euler and Lagrangian coordinates, mass velocity, pressure, temperature, and density in the case of plane geometry are given. The numerical simulation of considered process in sonicFoam solver of OpenFOAM package built on the PISO algorithm was performed. For numerical modeling the system of differential equations of gas dynamics is used, including the equations of continuity, Navier-Stokes motion for a compressible medium and conservation of internal energy. Initial and boundary conditions were selected in accordance with the obtained analytical solution using the setFieldsDict, blockMeshDict, and uniformFixedValue utilities. The obtained analytical and numerical solutions have a satisfactory agreement.

scholarly journals Double asymptotic expansion of the resolving operator of the cauchy problem for the line-arized system of gas dynamics

2019 ◽  
Vol 484 (2) ◽  
pp. 134-137
Author(s):  
A. I. Allilueva ◽  
A. I. Shafarevich
Keyword(s):  
Cauchy Problem ◽  
Asymptotic Expansion ◽  
Gas Dynamics ◽  
Acoustic Modes ◽  
Small Viscosity ◽  
The Cauchy Problem ◽  
Linearized System

We obtain double asymptotic expansion (with respect to smoothness and small viscosity) of the resolving operator of the Cauchy problem for the linearized system of gas dynamics. We derive estimates for the summands and for the residual in the Sobolev scale.We describe explicitly hydrodynamic and acoustic modes.

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