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Num. Meth. Prog., 2016, Volume 17, Issue 4, Pages 402–414 (Mi vmp846)  

Implicit and time reversible CABARET schemes for quasilinear shallow water equations

V. M. Goloviznina, D. Yu. Gorbachevb, A. M. Kolokolnikovb, P. A. Maiorovb, P. A. Maiorovb, B. A. Tlepsukb

a Nuclear Safety Institute, RAS, Moscow
b Lomonosov Moscow State University, Faculty of Computational Mathematics and Cybernetics

Abstract: A new implicit unconditionally stable scheme for the one-dimensional shallow water equations is proposed. This implicit scheme retains all the features of the explicit CABARET (Compact Accurately Boundary Adjusting-REsolution Technique) difference scheme. Dissipative and dispersion properties of this new scheme are analyzed; an algorithm of its numerical solution is discussed. Some examples of solving the Riemann problem are considered.

Keywords: CABARET scheme, shallow water equations, conservative schemes, time reversible schemes, numerical simulation.

Full text: PDF file (1318 kB)
UDC: 519.63
Received: 25.08.2016

Citation: V. M. Goloviznin, D. Yu. Gorbachev, A. M. Kolokolnikov, P. A. Maiorov, P. A. Maiorov, B. A. Tlepsuk, “Implicit and time reversible CABARET schemes for quasilinear shallow water equations”, Num. Meth. Prog., 17:4 (2016), 402–414

Citation in format AMSBIB
\Bibitem{GolGorKol16}
\by V.~M.~Goloviznin, D.~Yu.~Gorbachev, A.~M.~Kolokolnikov, P.~A.~Maiorov, P.~A.~Maiorov, B.~A.~Tlepsuk
\paper Implicit and time reversible CABARET schemes for quasilinear shallow water equations
\jour Num. Meth. Prog.
\yr 2016
\vol 17
\issue 4
\pages 402--414
\mathnet{http://mi.mathnet.ru/vmp846}


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