Geodesic
Numerical modeling of the dynamics of sound waves in active environments using the MUSCL scheme
Matematičeskaâ fizika i kompʹûternoe modelirovanie, no. 1 (2015), pp. 13-22

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The results of the Godunov type method using numerical schemes of the first and second level of precision are compared. Influence of slope limiters and flux computation methods to quality of numerical solution are investigated. Four versions of slope limiters are investigated: minmod, van Leer, van Albada, superbee. Three methods of numerical flux computation also investigated: Lax — Friedrichs, Harten — Lax — van Leer and Harten — Lax — van Leer — Contact. It is shown, that superbee leads to very similar numerical solution quality. Also, the results show, that the use of the MUSCL scheme gives smaller error calculations in $2$ times, regardless of the method numerical solution of Riemann problem. The instability of acoustic waves in active environments are investigated on the basis of the realisation of the method HLLC and MUSCL schemes.The results indicate significant effects of stationary nonequilibrium (generated through its new viscosity-dispersive and nonlinear properties of the medium) on the evolution of the gas-dynamic perturbations.
Keywords: numerical schemes, slope limiters, method of Godunov type, MUSCL, HLLC. 
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     author = {E. V. Bochkareva and S. S. Khrapov},
     title = {Numerical modeling of the dynamics of sound waves in active environments using the {MUSCL} scheme},
     journal = {Matemati\v{c}eska\^a fizika i kompʹ\^uternoe modelirovanie},
     pages = {13--22},
     publisher = {mathdoc},
     number = {1},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VVGUM_2015_1_a2/}
}
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E. V. Bochkareva; S. S. Khrapov. Numerical modeling of the dynamics of sound waves in active environments using the MUSCL scheme. Matematičeskaâ fizika i kompʹûternoe modelirovanie, no. 1 (2015), pp. 13-22. http://geodesic.mathdoc.fr/item/VVGUM_2015_1_a2/