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

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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. 
@article{MM_2019_31_1_a0,
     author = {M. A. Lozhnikov},
     title = {On a difference scheme on triangular meshes for gas dynamics equations},
     journal = {Matemati\v{c}eskoe modelirovanie},
     pages = {3--26},
     publisher = {mathdoc},
     volume = {31},
     number = {1},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MM_2019_31_1_a0/}
}
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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/