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Ostapenko, Vladimir; Kovyrkina, Olyana

On construction of combined shock-capturing finite-difference schemes of high accuracy. (English) Zbl 1368.65144

Dimov, Ivan (ed.) et al., Numerical analysis and its applications. 6th international conference, NAA 2016, Lozenetz, Bulgaria, June 15–22, 2016. Revised selected papers. Cham: Springer (ISBN 978-3-319-57098-3/pbk; 978-3-319-57099-0/ebook). Lecture Notes in Computer Science 10187, 525-532 (2017).
Summary: We show that compact scheme of the third order of weak approximation (unlike the TVD scheme) allows to obtain the second order of integral convergence in intervals crossing the front line of the shock wave and, as consequence, to conserve the high order of local convergence in the domain of shock influences. It allows to use the compact scheme as a basis scheme in construction of combined shock-capturing finite-difference schemes of high accuracy.
For the entire collection see [Zbl 1360.65014].

MSC:

65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
35L67 Shocks and singularities for hyperbolic equations
65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs

Keywords:

shock-capturing difference schemes; monotonicity and high accuracy of finite difference schemes; discontinuous solutions; integral order of convergence; shock wave
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References:

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