Conservative limiting method for high-order bicompact schemes as applied to systems of hyperbolic equations

Abstract

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 collocation finite-element schemes and bicompact schemes is established. The proposed method is tested on one-dimensional gas dynamics problems that include the Sedov problem, the “peak test” Riemann problem, the Shu–Osher problem, and the “blast wave” problem. Additionally, the method is tested as applied to a two-dimensional problem for the quasilinear Hopf equation. It is shown on these examples that bicompact schemes with conservative limiting are significantly more accurate than hybrid bicompact schemes.