High order explicit local time stepping methods for hyperbolic conservation laws

Journal Article · 28 January 2020 · Mathematics of Computation

DOI: https://doi.org/10.1090/mcom/3507 · OSTI ID:1594035

Hoang, Thi-Thao-Phuong ^[1]; Ju, Lili ^[2]; Leng, Wei ^[3]; Wang, Zhu ^[2]

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1. Auburn Univ., AL (United States); University of South Carolina
2. Univ. of South Carolina, Columbia, SC (United States)
3. Chinese Academy of Sciences (CAS), Beijing (China). State Key Lab. of Scientific and Engineering Computing

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.

• Research Organization: Univ. of South Carolina, Columbia, SC (United States)
• Sponsoring Organization: USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR) (SC-21); USDOE Office of Science (SC), Biological and Environmental Research (BER) (SC-23). Climate and Environmental Sciences Division
• Grant/Contract Number: SC0016540; SC0020270
• OSTI ID: 1594035
• Journal Information: Mathematics of Computation, Journal Name: Mathematics of Computation Vol. 89; ISSN 0025-5718
• Publisher: American Mathematical SocietyCopyright Statement
• Country of Publication: United States
• Language: English