Efficient implementation of characteristic-based schemes on unstructured triangular grids
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.
Cite
@article{arxiv.2104.09189,
title = {Efficient implementation of characteristic-based schemes on unstructured triangular grids},
author = {Simone Cacace and Roberto Ferretti},
journal= {arXiv preprint arXiv:2104.09189},
year = {2021}
}