New Unstructured-Grid Limiter Functions
Hiroaki Nishikawa
Abstract
View Video Presentation: https://doi.org/10.2514/6.2022-1374.vid In this paper, new unstructured-grid limiter functions are proposed that preserve up to fifth-order accuracy and serve as less-dissipative alternatives to the Venkatakrishnan limiter function for practical unstructured-grid solvers. The new limiters have the following desirable properties: (1) preserving up to fifth-order accuracy in smooth regions (as opposed to the Venkatakrishnan limiter preserving up to second-order accuracy and the Michalak- Ollivier-Gooch limiter preserving up to fourth-order accuracy), (2) completely differentiable, even in one dimension, (3) amenable to Venkatakrishnan’s modification to smoothy deactivate a limiter in nearly constant regions, (4) less dissipative than the Venkatakrishnan limiter, (5) keeping the original unlimited reconstruction whenever it is bounded (the Venkatakrishnan limiter does not). These properties are demonstrated theoretically and/or numerically for the Euler equations using a node-centered edge-based discretization on regular/irregular grids in one dimension and unstructured triangular grids in two dimensions.