A Class of High Resolution Difference Schemes Based on Non-Uniformly Cell Averaged-Solution Reconstruction

DOI

10.2991/snce-18.2018.151How to use a DOI?

Keywords

Hyperbolic conservation laws; High-order accuracy; Difference scheme; Euler equations

Abstract

Based on non-uniformly cell averaged-solution reconstruction, a class of high-order accuracy and high resolution conservative difference schemes is obtained for one-dimensional nonlinear hyperbolic conservation laws in this paper. Its idea is the following. The First, the computational interval is divided into pieces of nonoverlapping sub-intervals, and then each sub-interval is further subdivided into small-intervals by using Gauss-Lobatto and Gauss-Chebyshev partitions according to required accuracy. Cell averaged-solutions from these small-intervals are used to reconstruct solutions at small-interval boundaries. Furthermore the correction is introduced. The second, the approximate Riemann solver is used to compute numerical fluxs at small-intervals boundaries, and a high-order accurate fully discretization method is obtained by applying high-order Runge-Kutta TVD time discretization. Moreover, the non-oscillatory property of the scheme is proved. The extension to systems is implemented. Finally, several typical numerical experients are given. The numerical results verify high accuracy and high resolution of the resulting schemes.

Copyright

© 2018, the Authors. Published by Atlantis Press.

Open Access

This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

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TY  - CONF
AU  - Chongkun Xu
AU  - Yuting Xu
PY  - 2018/05
DA  - 2018/05
TI  - A Class of High Resolution Difference Schemes Based on Non-Uniformly Cell Averaged-Solution Reconstruction
BT  - Proceedings of the 8th International Conference on Social Network, Communication and Education (SNCE 2018)
PB  - Atlantis Press
SP  - 738
EP  - 743
SN  - 2352-538X
UR  - https://doi.org/10.2991/snce-18.2018.151
DO  - 10.2991/snce-18.2018.151
ID  - Xu2018/05
ER  -