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Zh. Vychisl. Mat. Mat. Fiz., 2020, Volume 60, Number 5, Pages 884–899 (Mi zvmmf11083)  

This article is cited in 1 scientific paper (total in 1 paper)

On the accuracy of bicompact schemes as applied to computation of unsteady shock waves

M. D. Braginabc, B. V. Rogovab

a Federal Research Center Keldysh Institute of Applied Mathematics, Russian Academy of Sciences, Moscow, 125047 Russia
b Moscow Institute of Physics and Technology (National Research University), Dolgoprudnyi, Moscow oblast, 141700 Russia
c Lavrentyev Institute of Hydrodynamics, Siberian Branch, Russian Academy of Sciences, Novosibirsk, 630090 Russia

Abstract: Bicompact schemes that have the fourth order of classical approximation in space and a higher order (at least the second) in time are considered. Their accuracy is studied as applied to a quasilinear hyperbolic system of conservation laws with discontinuous solutions involving shock waves with variable propagation velocities. The shallow water equations are used as an example of such a system. It is shown that a nonmonotone bicompact scheme has a higher order of convergence in domains of influence of unsteady shock waves. If spurious oscillations are suppressed by applying a conservative limiting procedure, then the bicompact scheme, though being high-order accurate on smooth solutions, has a reduced (first) order of convergence in the domains of influence of shock waves.

Key words: hyperbolic system of conservation laws, bicompact schemes, shallow water equations, orders of local and integral convergence.

Funding Agency Grant Number
Russian Science Foundation 16-11-10033
This work was supported by the Russian Science Foundation, grant no. 16-11-10033.


DOI: https://doi.org/10.31857/S0044466920050063


English version:
Computational Mathematics and Mathematical Physics, 2020, 60:5, 864–878

Bibliographic databases:

UDC: 519.63
Received: 02.09.2019
Revised: 02.09.2019
Accepted:14.01.2020

Citation: M. D. Bragin, B. V. Rogov, “On the accuracy of bicompact schemes as applied to computation of unsteady shock waves”, Zh. Vychisl. Mat. Mat. Fiz., 60:5 (2020), 884–899; Comput. Math. Math. Phys., 60:5 (2020), 864–878

Citation in format AMSBIB
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\paper On the accuracy of bicompact schemes as applied to computation of unsteady shock waves
\jour Zh. Vychisl. Mat. Mat. Fiz.
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\issue 5
\pages 884--899
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\crossref{https://doi.org/10.31857/S0044466920050063}
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\jour Comput. Math. Math. Phys.
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\pages 864--878
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  • Журнал вычислительной математики и математической физики Computational Mathematics and Mathematical Physics
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