A conservative limiting method for bicompact schemes
In this work, a new limiting method for bicompact schemes is proposed that preserves them conservative. The method is based upon a finite-element treatment of the bicompact approximation. An analogy between Galerkin schemes and bicompact schemes is established. The proposed method is tested on one-dimensional gasdynamics problems that include the Sedov problem, the Riemann 'peak' problem, and the Shu-Osher problem. It is shown on these examples that bicompact schemes with conservative limiting are significantly more accurate than hybrid bicompact schemes.