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This article is cited in 9 scientific papers (total in 9 papers)
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.
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
Linking options:
https://www.mathnet.ru/eng/zvmmf11083 https://www.mathnet.ru/eng/zvmmf/v60/i5/p884
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Abstract page: | 117 | References: | 22 |
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