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
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Authors
Liu, Yingjie
Shu, Chi-Wang
Xu, Zhiliang
Shu, Chi-Wang
Xu, Zhiliang
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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
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