Geodesic
Free boundary method for numerical solving gas dynamics equations in domains with varying geometry
Matematičeskoe modelirovanie, Tome 26 (2014) no. 5, pp. 99-112

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The paper describes a novel method for numerical solving the Euler equations of compressible fluid dynamics in domains that contain solid, impermeable, and in general case moving entries (objects) with stationary Cartesian grids. The method proposed is based on the approach of immersed boundary, in which calculations are carried out over all cells of a Cartesian grid that covers the whole computational domain including solid entries. The influence of the solid surface on the gas flow is taken into account by introducing effective fluxes of mass, momentum, and energy on the right-hand side of the governing equations. A survey of developed by now methods for solving such class of problems is presented, and advantages of the proposed method are discussed. The method is verified on calculations of a set of problems admitting analytical solutions, and applied to solution of a supersonic blunt body flow. The results obtained are compared with those of standard calculations with a curvilinear grid fitted with the body surface.
Keywords: computational gas dynamics, immersed boundary method, Cartesian grids. 
@article{MM_2014_26_5_a6,
     author = {I. Menshov and M. Kornev},
     title = {Free boundary method for numerical solving gas dynamics equations in domains with varying geometry},
     journal = {Matemati\v{c}eskoe modelirovanie},
     pages = {99--112},
     publisher = {mathdoc},
     volume = {26},
     number = {5},
     year = {2014},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MM_2014_26_5_a6/}
}
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I. Menshov; M. Kornev. Free boundary method for numerical solving gas dynamics equations in domains with varying geometry. Matematičeskoe modelirovanie, Tome 26 (2014) no. 5, pp. 99-112. http://geodesic.mathdoc.fr/item/MM_2014_26_5_a6/