Abstract:
We justified the method of integral convergence for studying the accuracy of finitedifference shock-capturing schemes for numerical simulation of shock waves propagating at a variable speed. The order of integral convergence is determined using a series of
numerical calculations on a family of embedded difference grids. It allows us to model a
space-continuous difference solution of the corresponding Cauchy problem. This approach is used to study the accuracy of explicit finite-difference schemes such as Rusanov scheme, TVD and WENO schemes, which have a higher order of classic approximation, as well as an implicit compact scheme with artificial viscosity of the fourth order of
divergence, which has a third order of both classic and weak approximation.
Citation:
V. V. Ostapenko, N. A. Khandeeva, “To justification of the integral convergence method for studying the finite-difference schemes accuracy”, Mat. Model., 33:4 (2021), 45–59; Math. Models Comput. Simul., 13:6 (2021), 1028–1037
\Bibitem{OstKha21}
\by V.~V.~Ostapenko, N.~A.~Khandeeva
\paper To justification of the integral convergence method for studying the finite-difference schemes accuracy
\jour Mat. Model.
\yr 2021
\vol 33
\issue 4
\pages 45--59
\mathnet{http://mi.mathnet.ru/mm4278}
\crossref{https://doi.org/10.20948/mm-2021-04-03}
\transl
\jour Math. Models Comput. Simul.
\yr 2021
\vol 13
\issue 6
\pages 1028--1037
\crossref{https://doi.org/10.1134/S207004822106017X}
Linking options:
https://www.mathnet.ru/eng/mm4278
https://www.mathnet.ru/eng/mm/v33/i4/p45
This publication is cited in the following 1 articles:
M. D. Bragin, O. A. Kovyrkina, M. E. Ladonkina, V. V. Ostapenko, V. F. Tishkin, N. A. Khandeeva, “Combined numerical schemes”, Comput. Math. Math. Phys., 62:11 (2022), 1743–1781
Citation in format AMSBIB
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