A class of bound-preserving MUSCL-Hancock schemes in two dimensions

Abstract

In this paper we discuss the MUSCL-Hancock scheme for the two-dimensional conservation laws and derive the bound-preserving conditions by a parameterized convex decomposition method which is proposed in [Journal of Computational Physics, 474:111805, 2023] for one-dimensional problems. The CFL number equals the half of the one-dimensional value and then ensures the speed-up compared with the classical two-stage MUSCL scheme. The bound-preserving slope limiter on the preliminary reconstruction becomes problem dependent. The maximum-minimum preserving slope limiter for the scalar problems becomes the same with its one-dimensional version. A positivity-preserving slope limiter for the Euler system is designed including a different parameter from the scalar problems and more efficient operators than the existing limiters. Numerical experiments are reported to demonstrate the robustness of the proposed scheme.