Geodesic
Hybrid numerical flux for solving the problems of supersonic flow of solid bodies
Matematičeskoe modelirovanie, Tome 33 (2021) no. 5, pp. 47-56

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Numerical modeling of supersonic flow around solid bodies is a complex task due to the possibility of nonphysical instabilities that can affect the solution. In this paper, we propose a new hybrid numerical flux for calculating the fluxes of the Euler part of the Navier–Stokes system of equations. This flux avoids the occurrence of instability and maintains high accuracy on shock waves and boundary layers. This flux is a combination of Godunov's numerical flow and Rusanov–Lax–Friedrichs numerical flow. Numerical simulation of supersonic flow around a cruise missile Tomahawk has been carried out.
Keywords: hypersonic gas dynamics, numerical flux, discontinuous Galerkin method. 
@article{MM_2021_33_5_a3,
     author = {M. E. Ladonkina and O. A. Nekliudova and V. F. Tishkin},
     title = {Hybrid numerical flux for solving the problems of supersonic flow of solid bodies},
     journal = {Matemati\v{c}eskoe modelirovanie},
     pages = {47--56},
     publisher = {mathdoc},
     volume = {33},
     number = {5},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MM_2021_33_5_a3/}
}
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M. E. Ladonkina; O. A. Nekliudova; V. F. Tishkin. Hybrid numerical flux for solving the problems of supersonic flow of solid bodies. Matematičeskoe modelirovanie, Tome 33 (2021) no. 5, pp. 47-56. http://geodesic.mathdoc.fr/item/MM_2021_33_5_a3/