The multi-dimensional limiters for solving hyperbolic conservation laws on unstructured grids

Novel limiters based on the weighted average procedure are developed for finite volume methods solving multi-dimensional hyperbolic conservation laws on unstructured grids. The development of these limiters is inspired by the biased averaging procedure of Choi and Liu [10]. The remarkable features of the present limiters are the new biased functions and the weighted average procedure, which enable the present limiter to capture strong shock waves and achieve excellent convergence for steady state computations. The mechanism of the developed limiters for eliminating spurious oscillations in the vicinity of discontinuities is revealed by studying the asymptotic behavior of the limiters. Numerical experiments for a variety of test cases are presented to demonstrate the superior performance of the proposed limiters.

► A class of multi-dimensional limiters called WBAP is proposed. ► The WBAP limiters can be readily applied on unstructured grids. ► A limit of WBAP limiters satisfies the maximum principle. ► The WBAP limiters capture the discontinuities essentially free from oscillations. ► The schemes using WBAP show excellent convergence in simulating steady flows.