Geodesic
Total differential method for compressible gas flow modeling
Matematičeskoe modelirovanie, Tome 17 (2005) no. 3, pp. 99-119.

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A new fundamental method for obtaining the finite-difference schemes is developed. It is based on the characteristic directions of gasdynamic general equations. The existing methods such as Split Coefficient Matrix method, Flux Vector Splitting method and Mesh-Characteristics method are considered to be the particular manifestation of this method. The numerical solution of two 2D aerodynamic problems is an example of the above-mentioned method application. Comparative analysis of calculation results carried out of finite-difference schemes based on two forms of initial differential equations has been effected. The obtained results are in close coincidence with experimental data. 
@article{MM_2005_17_3_a10,
     author = {S. A. Popov},
     title = {Total differential method for compressible gas flow modeling},
     journal = {Matemati\v{c}eskoe modelirovanie},
     pages = {99--119},
     publisher = {mathdoc},
     volume = {17},
     number = {3},
     year = {2005},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MM_2005_17_3_a10/}
}
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S. A. Popov. Total differential method for compressible gas flow modeling. Matematičeskoe modelirovanie, Tome 17 (2005) no. 3, pp. 99-119. http://geodesic.mathdoc.fr/item/MM_2005_17_3_a10/