A comparison between the CABARET scheme and the MUSCL-type schemes

The CABARET scheme is compared with some schemes from the family of MUSCL-type schemes. Description and analysis of these schemes are presented as applied to the linear constant-coefficient advection equation. A new representation, which can be treated as a modification of the MUSCL scheme, is proposed for the CABARET scheme. Three types of limiters are considered in the MUSCL-type schemes: TVD, TVB and a new NOLD limiter. The schemes are evaluated on a number of linear problems (discontinuous and continuous profiles, uniform and non-uniform mesh) as well as on the nonlinear blast wave problem.