Reconsidering remap methods
Abstract
Methods for discretizing remap are often based on algorithms developed for hyperbolic conservation laws. Because its introduction in 1977 Van Leer's monotonicity‐preserving piecewise linear method and its extensions have been ubiquitous in remap “Van Leer's fourth paper in his series “Towards the Ultimate””. In that 1977 paper, Van Leer introduced another five algorithms, which largely have not been used for remap despite the observation that the piecewise linear method had the least favorable theoretical properties. This adoption parallels the algorithmic choices in other related fields. Two factors have led to the lack of attraction to the five algorithms: the simplicity and effectiveness of the piecewise linear method and complications in practical implementation of the other methods. Plainly stated, Van Leer's piecewise linear method enabled ALE methods to move forward by providing a high‐resolution, monotonicity‐preserving remap. As a cell‐centered scheme, the extension to remap was straightforward. Several factors may be conspiring to reconsider these methods anew: computing architectures are more favorable toward more floating point intensive methods, methods lacking data movement, and 30 years of experience in devising nonlinear stability mechanisms (i.e., limiters). In particular, one of the methods blends characteristics of finite volume and finite difference methods together in an ingenious manner that has exceptional numerical properties and should be considered as a viable alternative to the ubiquitous piecewise linear method. Published 2014. This article is a U.S. Government work and is in the public domain in the USA.
Document Details
- Document Type
- Pub Defense Publication
- Publication Date
- Sep 03, 2014
- Source ID
- 10.1002/fld.3950
Entities
People
- William J. Rider
Organizations
- Sandia National Laboratories
- United States Army Research Laboratory