KMS Of Academy of mathematics and systems sciences, CAS
| HIGH ORDER EXPLICIT LOCAL TIME STEPPING METHODS FOR HYPERBOLIC CONSERVATION LAWS | |
| Thi-Thao-Phuong Hoang1; Ju, Lili2; Leng, Wei3; Wang, Zhu2 | |
| 2020-07-01 | |
| Source Publication | MATHEMATICS OF COMPUTATION
 |
| ISSN | 0025-5718 |
| Volume | 89Issue:324Pages:1807-1842 |
| Abstract | In this paper we present and analyze a general framework for constructing high order explicit local time stepping (LTS) methods for hyperbolic conservation laws. In particular, we consider the model problem discretized by Runge-Kutta discontinuous Galerkin (RK-DG) methods and design LTS algorithms based on the strong stability preserving Runge-Kutta (SSP-RK) schemes, that allow spatially variable time step sizes to be used for time integration in different regions of the computational domain. The proposed algorithms are of predictor-corrector-type, in which the interface information along the time direction is first predicted based on the SSP-RK approximations and Taylor expansions, and then the fluxes over the region of the interface are corrected to conserve mass exactly at each time step. Following the proposed framework, we detail the corresponding LTS schemes with accuracy up to the fourth order, and prove their conservation property and nonlinear stability for the scalar conservation laws. Numerical experiments are also presented to demonstrate excellent performance of the proposed LTS algorithms. |
| DOI | 10.1090/mcom/3507 |
| Indexed By | SCI |
| Language | 英语 |
| Funding Project | U.S. Department of Energy[DESC0016540] ; U.S. Department of Energy[DE-SC0020270] ; U.S. National Science Foundation[DMS-1818438] ; U.S. National Science Foundation[DMS-1913073] |
| WOS Research Area | Mathematics |
| WOS Subject | Mathematics, Applied |
| WOS ID | WOS:000525355900009 |
| Publisher | AMER MATHEMATICAL SOC |
| Citation statistics | |
| Document Type | 期刊论文 |
| Identifier | http://ir.amss.ac.cn/handle/2S8OKBNM/51098 |
| Collection | 中国科学院数学与系统科学研究院 |
| Corresponding Author | Thi-Thao-Phuong Hoang |
| Affiliation | 1.Auburn Univ, Dept Math & Stat, Auburn, AL 36849 USA 2.Univ South Carolina, Dept Math, Columbia, SC 29208 USA 3.Chinese Acad Sci, State Key Lab Sci & Engn Comp, Beijing 100190, Peoples R China |
| Recommended Citation GB/T 7714 | Thi-Thao-Phuong Hoang,Ju, Lili,Leng, Wei,et al. HIGH ORDER EXPLICIT LOCAL TIME STEPPING METHODS FOR HYPERBOLIC CONSERVATION LAWS[J]. MATHEMATICS OF COMPUTATION,2020,89(324):1807-1842. |
| APA | Thi-Thao-Phuong Hoang,Ju, Lili,Leng, Wei,&Wang, Zhu.(2020).HIGH ORDER EXPLICIT LOCAL TIME STEPPING METHODS FOR HYPERBOLIC CONSERVATION LAWS.MATHEMATICS OF COMPUTATION,89(324),1807-1842. |
| MLA | Thi-Thao-Phuong Hoang,et al."HIGH ORDER EXPLICIT LOCAL TIME STEPPING METHODS FOR HYPERBOLIC CONSERVATION LAWS".MATHEMATICS OF COMPUTATION 89.324(2020):1807-1842. |
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