期刊
JOURNAL OF COMPUTATIONAL PHYSICS
卷 286, 期 -, 页码 172-193出版社
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jcp.2015.01.031
关键词
Stiff ODE/PDE/DAE time marching; Low-storage IMEXRK methods; SSP/TVD methods; L stability
资金
- AFOSR [FA9550-12-1-0046]
- NSF [CNS-1035828]
Implicit/explicit(IMEX) Runge-Kutta (RK) schemes are effective for time-marching ODE systems with both stiff and nonstiff terms on the RHS; such schemes implement an (often A-stable or better) implicit RK scheme for the stiff part of the ODE, which is often linear, and, simultaneously, a (more convenient) explicit RK scheme for the nonstiff part of the ODE, which is often nonlinear. Low-storageRK schemes are especially effective for timemarching high-dimensional ODE discretizations of PDE systems on modern (cache-based) computational hardware, in which memory management is often the most significant computational bottleneck. In this paper, we develop and characterize eight new low-storage implicit/explicitRK schemes which have higher accuracy and better stability properties than the only low-storage implicit/explicit RK scheme available previously, the venerable second-order Crank-Nicolson/Runge-Kutta-Wray (CN/RKW3) algorithm that has dominated the DNS/LES literature for the last 25 years, while requiring similar storage (two, three, or four registers of length N) and comparable floating-point operations per timestep. Published by Elsevier Inc.
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