Time reversibility and stream correction in the CABARET scheme for the two-dimensional equation of convective transport

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

a</sup> Nuclear Safety Institute, RAS, Moscow
^b Lomonosov Moscow State University, Faculty of Computational Mathematics and Cybernetics

Abstract: The CABARET (Compact Accurately Boundary Adjusting-REsolution Technique) difference scheme with five different modifications of nonlinear flow correction based on the maximum principle is considered for the two-dimensional linear convection equation. The computational efficiency of these different modifications is analyzed by the results of solving the Crowley's problem on the cone rotation around the axis not coincident with the axis of the cone using condensing orthogonal grids. A number of recommendations are formulated to improve the computational efficiency of the entire class of CABARET schemes for the hyperbolic-type conservation laws and for the processes with dominant grid transfer.

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

UDC: 519.63

Received: 22.08.2016