Abstract
The CABARET scheme is compared with some of those from the family of MUSCL-type schemes. Description and analysis of these schemes are presented as applied to the linear advection equation. For the CABARET scheme, a new formulation is proposed that can be treated as a modification of the MUSCL scheme. In MUSCL-type schemes, we consider three types of limiters, i.e., TVD, TVB, and the new Non-Oscillatory Low-Dissipative (NOLD) limiter. The schemes are tested on a set of linear problems (discontinuous and continuous profiles, uniform and nonuniform grids) and on the nonlinear blast wave problem.
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