Asymptotic preserving IMEX finite volume schemes for low Mach number Euler equations with gravitation
Asymptotic preserving IMEX finite volume schemes for low Mach number Euler equations with gravitation
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DOI：
10.1016/j.jcp.2017.01.020
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发表时间：
2017-04
期刊：
影响因子：
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通讯作者：
Georgij Bispen;M. Lukáčová-Medvid’ová;L. Yelash
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文献类型：
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作者：
Georgij Bispen;M. Lukáčová-Medvid’ová;L. Yelash
本文给出并分析了一类新的具有重力源项的欧拉方程的IMEX有限体积格式。我们将特别关注马赫数M≪1时弱可压缩流的奇异极限。为了有效地解决慢动力学问题，我们将整个非线性系统拆分为控制声波和重力波的刚性线性部分和模拟非线性平流效应的非刚性非线性部分。对于时间离散，我们使用一类特殊的全局刚性精确IMEX格式，隐式逼近刚性线性算子和显式逼近非刚性非线性算子。对于空间离散化，分别对线性子系统和非线性子系统采用中心通量和鲁萨诺夫/拉克斯-弗里德里希数值通量的有限体积近似。在背景势温恒定的情况下，从理论上证明了该方法对于小马赫数是渐近一致和均匀稳定的。实验分析了马赫数趋于零的奇异极限下的收敛速率。
In this paper we will present and analyze a new class of the IMEX finite volume schemes for the Euler equations with a gravity source term. We will in particular concentrate on a singular limit of weakly compressible flows when the Mach number M≪ 1. In order to efficiently resolve slow dynamics we split the whole nonlinear system in a stiff linear part governing the acoustic and gravity waves and a non-stiff nonlinear part that models nonlinear advection effects. For time discretization we use a special class of the so-called globally stiffly accurate IMEX schemes and approximate the stiff linear operator implicitly and the non-stiff nonlinear operator explicitly. For spatial discretization the finite volume approximation is used with the central and Rusanov/Lax–Friedrichs numerical fluxes for the linear and nonlinear subsystem, respectively. In the case of a constant background potential temperature we prove theoretically that the method is asymptotically consistent and asymptotically stable uniformly with respect to small Mach number. We also analyze experimentally convergence rates in the singular limit when the Mach number tends to zero.