Total-variation-diminishing implicit-explicit Runge-Kutta methods for the simulation of double-diffusive convection in astrophysics

JOURNAL OF COMPUTATIONAL PHYSICS

卷:231

Article

Kupka, Friedrich¹  Happenhofer, Natalie¹  Higueras, Inmaculada²  Koch, Othmar^1,3 

[1] Univ Vienna, Fac Math, A-1090 Vienna, Austria

[2] Univ Publ Navarra, Dept Ingn Matemat & Informat, Pamplona 31006, Spain

[3] Vienna Univ Technol, Inst Anal & Sci Comp, A-1040 Vienna, Austria

关键词: Hydrodynamics;    Stellar convection and pulsation;    Double-diffusive convection;    Numerical methods;    Total-variation-diminishing;    Strong stability preserving;    TVD;    SSP;   

DOI  :  10.1016/j.jcp.2011.12.031

来源: Elsevier

【 摘 要 】

We put forward the use of total-variation-diminishing (or more generally, strong stability preserving) implicit-explicit Runge-Kutta methods for the time integration of the equations of motion associated with the semiconvection problem in the simulation of stellar convection. The fully compressible Navier-Stokes equation, augmented by continuity and total energy equations, and an equation of state describing the relation between the thermodynamic quantities, is semi-discretized in space by essentially non-oscillatory schemes and dissipative finite difference methods. It is subsequently integrated in time by Runge-Kutta methods which are constructed such as to preserve the total variation diminishing (or strong stability) property satisfied by the spatial discretization coupled with the forward Euler method. We analyse the stability, accuracy and dissipativity of the time integrators and demonstrate that the most successful methods yield a substantial gain in computational efficiency as compared to classical explicit Runge-Kutta methods. (C) 2012 Elsevier Inc. All rights reserved.

【 授权许可】

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