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.