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
| dc.contributor.author | Liu, Yingjie | |
| dc.contributor.author | Shu, Chi-Wang | |
| dc.contributor.author | Xu, Zhiliang | |
| dc.contributor.corporatename | Georgia Institute of Technology. School of Mathematics | |
| dc.contributor.corporatename | Brown University. Division of Applied Mathematics | |
| dc.contributor.corporatename | University of Notre Dame. Dept. of Mathematics | |
| dc.date.accessioned | 2009-08-04T15:13:13Z | |
| dc.date.available | 2009-08-04T15:13:13Z | |
| dc.date.issued | 2009-07-31 | |
| dc.description.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. | en |
| dc.description.sponsorship | NSF grant DMS-0810913; ARO grant W911NF-08-1-0520; NSF grant DMS-0809086; NSF grant DMS-0800612 | en |
| dc.identifier.uri | http://hdl.handle.net/1853/29403 | |
| dc.language.iso | en_US | en |
| dc.publisher | Georgia Institute of Technology | en |
| dc.relation.ispartofseries | CDSNS2009-419 | en |
| dc.subject | Hierarchical reconstruction | en |
| dc.subject | Nonlinear conservation laws | en |
| dc.subject | Discontinuous solutions | en |
| dc.title | Hierarchical Reconstruction with up to Second Degree Remainder for Solving Nonlinear Conservation Laws | en |
| dc.type | Text | |
| dc.type.genre | Pre-print | |
| dspace.entity.type | Publication | |
| local.contributor.author | Liu, Yingjie | |
| local.contributor.corporatename | College of Sciences | |
| local.contributor.corporatename | School of Mathematics | |
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