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., 2016, Volume 17, Issue 4,Pages <nobr>402

Implicit and time reversible CABARET schemes for quasilinear shallow water equations

V. M. Goloviznin^a, D. Yu. Gorbachev^b, A. M. Kolokolnikov^b, P. A. Maiorov^b, P. A. Maiorov^b, B. A. Tlepsuk^b

^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.

UDC: 519.63

Received: 25.08.2016