Paper Info
Title
A new type of multi-resolution WENO schemes with increasingly higher order of accuracy on triangular meshes
Abstract
In this paper, we continue our work in [46] and propose a new type of high-order finite volume multi-resolution weighted essentially non-oscillatory (WENO) schemes to solve hyperbolic conservation laws on triangular meshes. Although termed “multi-resolution WENO schemes”, we only use the information defined on a hierarchy of nested central spatial stencils and do not introduce any equivalent multi-resolution representation. We construct new third-order, fourth-order, and fifth-order WENO schemes using three or four unequal-sized central spatial stencils, different from the classical WENO procedure using equal-sized biased/central spatial stencils for the spatial reconstruction. The new WENO schemes could obtain the optimal order of accuracy in smooth regions, and could degrade gradually to first-order of accuracy so as to suppress spurious oscillations near strong discontinuities. This is the first time that only a series of unequal-sized hierarchical central spatial stencils are used in designing arbitrary high-order finite volume WENO schemes on triangular meshes. The main advantages of these schemes are their compactness, robustness, and their ability to maintain good convergence property for steady-state computation. The linear weights of such WENO schemes can be any positive numbers on the condition that they sum to one. Extensive numerical results are provided to illustrate the good performance of these new finite volume WENO schemes.
Year
DOI
Venue
2019
10.1016/j.jcp.2019.04.027
Journal of Computational Physics
Keywords
Field
DocType
Multi-resolution scheme,Weighted essentially non-oscillatory scheme,Triangular mesh,Finite volume,High-order accuracy,Steady-state problem
Convergence (routing),Applied mathematics,Order of accuracy,Polygon mesh,Mathematical analysis,Compact space,Robustness (computer science),Finite volume method,Conservation law,Mathematics,Computation
Journal
Volume
ISSN
Citations 
392
0021-9991
0
PageRank 
References 
Authors
0.34
0
2
Name
Order
Citations
PageRank
Jun Zhu111410.88
Chi-Wang Shu24053540.35