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Monotone finite-difference scheme preserving high accuracy in regions of shock influence. (English. Russian original) Zbl 1407.65137
Dokl. Math. 98, No. 2, 506-510 (2018); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 482, No. 6 (2018).
Summary: An explicit combined shock-capturing finite difference scheme is constructed that localizes shock fronts with high accuracy and simultaneously preserves the high order of convergence in all domains where the computed weak solutions are smooth. In this scheme, V. V. Rusanov’s explicit nonmonotone scheme of the third order [Sov. Math., Dokl. 9, 771–774 (1968; Zbl 0179.22202); translation from Dokl. Akad. Nauk SSSR 180, 1303–1305 (1968)] is used as a basis one, while the internal scheme is based on the second-order monotone CABARET. The advantages of the new scheme as compared with the WENO scheme of the fifth order in space and third order in time are demonstrated in test computations.

MSC:
65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
35Q35 PDEs in connection with fluid mechanics
76L05 Shock waves and blast waves in fluid mechanics
35L67 Shocks and singularities for hyperbolic equations
Full Text: DOI
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