Total-variation-diminishing implicit-explicit Runge-Kutta methods for the simulation of double-diffusive convection in astrophysics
Total-variation-diminishing implicit-explicit Runge-Kutta methods for the simulation of double-diffusive convection in astrophysics
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DOI：
10.1016/j.jcp.2011.12.031
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发表时间：
2012-05-01
影响因子：
4.1
通讯作者：
Koch, Othmar
中科院分区：
文献类型：
--
作者：
Kupka, Friedrich;Happenhofer, Natalie;Koch, Othmar
我们提出了用总变差递减法（或更一般地说，强稳定性保持法）隐式-显式龙格-库塔方法对恒星对流模拟中与半对流问题有关的运动方程进行时间积分。利用基本非振荡格式和耗散有限差分方法在空间上对全可压缩的Navier-Stokes方程和描述热力学量之间关系的状态方程进行半离散化。然后通过龙格-库塔方法对其进行时间积分，该方法的构造是为了保持空间离散与正演欧拉方法相结合所满足的总变差递减（或强稳定性）性质。我们分析了时间积分器的稳定性、精度和耗散性，并证明了与经典的显式龙格-库塔方法相比，最成功的方法在计算效率上有了实质性的提高。(C) 2012爱思唯尔公司版权所有。
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.