Geodesic
On a difference scheme on triangular meshes for gas dynamics equations
Matematičeskoe modelirovanie, Tome 31 (2019) no. 1, pp. 3-26.

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

The paper suggests a difference scheme for the equations of isentropic ideal gas on triangular meshes. The scheme satisfies the mass conservation law and guarantees positiveness of the density function. The solution of the scheme satisfies the energy inequality. The solution of the scheme is proven to exist.
Keywords: gas dynamics, difference schemes, unstructured meshes, positive density. 
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M. A. Lozhnikov. On a difference scheme on triangular meshes for gas dynamics equations. Matematičeskoe modelirovanie, Tome 31 (2019) no. 1, pp. 3-26. http://geodesic.mathdoc.fr/item/MM_2019_31_1_a0/

[1] Popov I. V., Fryazinov I. V., “Method of adaptive artificial viscosity for gas dynamics equations on triangular and tetrahedral grids”, Mathematical Models and Computer Simulations, 5:1 (2013), 50–62 | DOI | MR | Zbl

[2] Samarskiy A. A., Popov Yu. P., Raznostnie metody resheniya zadach gasovoy dinamiki, Nauka, M., 1992

[3] Amosov A. A., Zlotnik A. A., “Difference schemes of second-order of accuracy for the equa-tions of the one-dimensional motion of a viscous gas”, USSR Computational Mathematics and Mathematical Physics, 27:4 (1987), 46–57 | DOI | MR | Zbl

[4] Popov A. V., Zhukov K. A., “An implicit finite-difference scheme for the unsteady motion of a viscous barotropic gas”, Numer. Methods and Programming, 14:4 (2013), 516–523

[5] Imranov F. B., Kobelkov G. M., Sokolov A. G., “Finite Difference Scheme for Barotropic Gas Equations”, Doklady Mathematics, 97:1 (2018), 58–61 | DOI | DOI | MR | Zbl

[6] Popov I. V., Fryazinov I. V., Stanichenko M. Yu., Taimanov A. V., “Difference schemes on triangular and tetrahedral grids for Navier-Stokes equations of incompressible fluid”, Mathematical Models and Computer Simulations, 2:3 (2010), 281–292 | DOI | MR | Zbl

[7] Samarskiy A. A., Koldoba A. V., Poveshenko Yu. A., Tishkin V. F., Favorskiy A. P., Raznostnie skhemy na neregulyarnyh setkah, Minsk, 1996

[8] Kulikovskiy A. G., Pogorelov N. V., Semenov A. Yu., Matematicheskiye voprosy chislennogo resheniya giperbolicheskih sistem uravneniy, Nauka, M., 2001

[9] Ladyzhenskaya O. A., Matematicheskiye voprosy dinamiki vyazkoy neszhimayemoy zhydkosti, Nauka, M., 1970

[10] Geuzaine S., Remacle J.-F., “GMSH: a three-dimensional finite element mesh generator with built-in pre- and post-processing facilities”, Inter. Journal for Numerical Methods in Engineering, 79:11 (2009), 1309–1331 | DOI | MR | Zbl

[11] Balay S., Gropp W. D., McInnes L. C., Smith B. F., “Efficient Management of Parallelism in Object-Oriented Numerical Software Libraries”, Modern Software Tools for Scientific Computing, eds. Arge E., Bruaset A. M., Langtangen H. P., Birkhauser, Boston, MA, 1997 | MR | Zbl

[12] Liska R., Wendroff B., Comparison of several difference schemes on 1D and 2D test problems for Euler equations, Tech. Rep. LA-UR-01-6225, LANL, Los Alamos, 2001