Geodesic
Kinetic schemes for the gas dynamics equations
Numerical methods and programming, Tome 10 (2009) no. 1, pp. 62-74.

Voir la notice de l'article provenant de la source Math-Net.Ru

In addition to the approximation of mass, momentum, and energy conservation laws, in numerical solutions to the gas dynamics equations it is necessary to require that the entropy should not decrease. The fulfillment of this entropy condition allows one to obtain a unique solution to the problem under study if its solution is uniquely specified by initial and boundary conditions. However, such a fulfillment represents a difficulty for numerical calculations. In the case of hyperbolic equations, an entropy decrease is excluded by introducing the Neumann's artificial viscosity, by the application of Godunov's method with the exact solution to the Riemann problem and with approximate solutions whose schematic viscosity is greater than that for the exact one, and by the application of the relaxation kinetic method. In this paper, the example of the scalar conservation law is used to conduct the entropy analysis modifications for Godunov-type schemes. New kinetic versions of numerical methods for the gas dynamics equations are proposed on the basis of flux approximations at the cell boundaries with the use of approximate Riemann solvers and jump conditions with the maximum estimation of wave speeds.
Keywords: hyperbolic equations; Godunov schemes; gas dynamics; Riemann problem; difference schemes. 
@article{VMP_2009_10_1_a7,
     author = {A. V. Safronov},
     title = {Kinetic schemes for the gas dynamics equations},
     journal = {Numerical methods and programming},
     pages = {62--74},
     publisher = {mathdoc},
     volume = {10},
     number = {1},
     year = {2009},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMP_2009_10_1_a7/}
}
TY  - JOUR
AU  - A. V. Safronov
TI  - Kinetic schemes for the gas dynamics equations
JO  - Numerical methods and programming
PY  - 2009
SP  - 62
EP  - 74
VL  - 10
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/VMP_2009_10_1_a7/
LA  - ru
ID  - VMP_2009_10_1_a7
ER  - 
%0 Journal Article
%A A. V. Safronov
%T Kinetic schemes for the gas dynamics equations
%J Numerical methods and programming
%D 2009
%P 62-74
%V 10
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/VMP_2009_10_1_a7/
%G ru
%F VMP_2009_10_1_a7
A. V. Safronov. Kinetic schemes for the gas dynamics equations. Numerical methods and programming, Tome 10 (2009) no. 1, pp. 62-74. http://geodesic.mathdoc.fr/item/VMP_2009_10_1_a7/