Title:
Hierarchical Reconstruction with up to Second Degree Remainder for Solving Nonlinear Conservation Laws
Hierarchical Reconstruction with up to Second Degree Remainder for Solving Nonlinear Conservation Laws
Files
Author(s)
Liu, Yingjie
Shu, Chi-Wang
Xu, Zhiliang
Shu, Chi-Wang
Xu, Zhiliang
Advisor(s)
Editor(s)
Collections
Supplementary to
Permanent Link
Abstract
The hierarchical reconstruction (HR) [Liu, Shu, Tadmor and Zhang, SINUM ’07] can effectively reduce spurious oscillations without local characteristic decomposition
for numerical capturing of discontinuous solutions. However, there are still small re-
maining overshoots/undershoots in the vicinity of discontinuities. HR with partial
neighboring cells [Xu, Liu and Shu, JCP ’09] essentially overcomes this drawback for
the third order case, and in the mean time further improves the resolution of the numer-
ical solution. Extending the technique to higher order cases we observe the returning of overshoots/undershoots. In this paper, we introduce a new technique to work with HR
on partial neighboring cells, which lowers the order of the remainder while maintaining
the theoretical order of accuracy, essentially eliminates overshoots/undershoots for the fourth and fifth order cases (in one dimensional numerical examples) and reduces the
numerical cost.
Sponsor
NSF grant DMS-0810913; ARO grant W911NF-08-1-0520; NSF grant DMS-0809086; NSF grant DMS-0800612
Date Issued
2009-07-31
Extent
Resource Type
Text
Resource Subtype
Pre-print