1. Efficient implementation of characteristic-based schemes on unstructured triangular grids
- Author
-
S. Cacace, R. Ferretti, Cacace, S., and Ferretti, R.
- Subjects
Computational Mathematics ,Applied Mathematics ,FOS: Mathematics ,Mathematics - Numerical Analysis ,Numerical Analysis (math.NA) ,65-04, 65D18, 65M06, 65M25 - Abstract
Using characteristics to treat advection terms in time-dependent PDEs leads to a class of schemes, e.g., semi-Lagrangian and Lagrange-Galerkin schemes, which preserve stability under large Courant numbers, and may therefore be appealing in many practical situations. Unfortunately, the need of locating the feet of characteristics may cause a serious drop of efficiency in the case of unstructured space grids, and thus prevent the use of large time-step schemes on complex geometries. In this paper, we perform an in-depth analysis of the main recipes available for characteristic location, and propose a technique to improve the efficiency of this phase, using additional information related to the advecting vector field. This results in a clear improvement of execution times in the unstructured case, thus extending the range of applicability of large time-step schemes.
- Published
- 2021