Extended bounds limiter for high-order finite-volume schemes on unstructured meshes

Abstract

This paper explores the impact of the definition of the bounds of the limiter proposed by Michalak and Ollivier-Gooch in [Accuracy preserving limiter for the high-order accurate solution of the Euler equations, J. Comput. Phys. 228 (2009) 8693–8711], for higher-order Monotone-Upstream Central Scheme for Conservation Laws (MUSCL) numerical schemes on unstructured meshes in the finite-volume (FV) framework. A new modification of the limiter is proposed where the bounds are redefined by utilising all the spatial information provided by all the elements in the reconstruction stencil. Numerical results obtained on smooth and discontinuous test problems of the Euler equations on unstructured meshes, highlight that the newly proposed extended bounds limiter exhibits superior performance in terms of accuracy and mesh sensitivity compared to the cell-based or vertex-based bounds implementations.