A scalable exponential-DG approach for nonlinear conservation laws: With application to Burger and Euler equations

Kang, Shinhoo; Bui-Thanh, Tan

doi:10.1016/j.cma.2021.114031

Title: A scalable exponential-DG approach for nonlinear conservation laws: With application to Burger and Euler equations

Journal Article · Thu Jul 29 00:00:00 EDT 2021 · Computer Methods in Applied Mechanics and Engineering

DOI:https://doi.org/10.1016/j.cma.2021.114031· OSTI ID:1883229

^[1]; Bui-Thanh, Tan ^[2]

Argonne National Lab. (ANL), Argonne, IL (United States)
Univ. of Texas, Austin, TX (United States)

In this work, we propose an Exponential DG framework for partial differential equations. We decompose 7 governing equations into linear and nonlinear parts to which we apply the discontinuous Galerkin 8 (DG) spatial discretization. In particular, we construct the linear part using Jacobian that effectively 9 capture stiff characteristics in the system. The former is integrated analytically, whereas the latter 10 is approximated. This approach i) is stable with a large Courant number (Cr > 1); ii) supports 11 high-order solutions both in time and space; iii) is computationally favorable compared to IMEX 12 DG methods with no preconditioner; iv) becomes comparable to explicit RKDG methods on uniform 13 mesh and beneficial on non-uniform grid for Euler equations; v) is scalable in a modern massively 14 parallel computing architecture due to its explicit nature of exponential time integrators and com15 pact communication stencil of DG method. Numerical results demonstrate the performance of our 16 proposed methods through various examples. We also discuss the stability and convergence analysis 17 for our exponential DG scheme in the context of Burgers equation.

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Research Organization:: Argonne National Laboratory (ANL), Argonne, IL (United States)

Sponsoring Organization:: USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR); National Science Foundation (NSF)

Grant/Contract Number:: AC02-06CH11357; SC0010518; SC0011118; DMS1620352; NSF-DMS1620352

OSTI ID:: 1883229

Alternate ID(s):: OSTI ID: 1817923

Journal Information:: Computer Methods in Applied Mechanics and Engineering, Vol. 385; ISSN 0045-7825

Publisher:: ElsevierCopyright Statement

Country of Publication:: United States

Language:: English

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Exponential integrators
Discontinuous Galerkin methods
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Title: A scalable exponential-DG approach for nonlinear conservation laws: With application to Burger and Euler equations

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