MACH-NUMBER UNIFORM ASYMPTOTIC-PRESERVING GAUGE SCHEMES FOR COMPRESSIBLE FLOWS
MACH-NUMBER UNIFORM ASYMPTOTIC-PRESERVING GAUGE SCHEMES FOR COMPRESSIBLE FLOWS
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发表时间：
2007
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通讯作者：
S. Jin;J.-G. Liu
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作者：
S. Jin;J.-G. Liu
我们提出了新的算法，可压缩流是有效的所有马赫数。该方法是基于几个成分：半隐式计划，规范分解的速度场和二阶制定的密度方程（在等熵的情况下）和能量方程（在充分的Navier-Stokes的情况下）。此外，我们表明，我们的方法对应于一个微观-宏观分解的模型，其中宏观场对应于不可压缩组件满足扰动低马赫数极限方程和微观场是速度的潜在组成部分。最后，我们还使用保守变量，以获得适当的保守列式的方程时，马赫数为单位阶。我们依次考虑等熵情形、全Navier-Stokes情形和等熵Navier-Stokes-Poisson情形。在这项工作中，我们只集中在时间离散的问题，并表明，所提出的方法导致渐近保持计划的可压缩流在低马赫数限制。2007年7月13日收到。AMS科目分类：65 N22、76 N15、76 R10、76 X 05。
We present novel algorithms for compressible flows that are efficient for all Mach numbers. The approach is based on several ingredients: semi-implicit schemes, the gauge decomposition of the velocity field and a second order formulation of the density equation (in the isentropic case) and of the energy equation (in the full Navier-Stokes case). Additionally, we show that our approach corresponds to a micro-macro decomposition of the model, where the macro field corresponds to the incompressible component satisfying a perturbed low Mach number limit equation and the micro field is the potential component of the velocity. Finally, we also use the conservative variables in order to obtain a proper conservative formulation of the equations when the Mach number is order unity. We successively consider the isentropic case, the full Navier-Stokes case, and the isentropic Navier-Stokes-Poisson case. In this work, we only concentrate on the question of the time discretization and show that the proposed method leads to Asymptotic Preserving schemes for compressible flows in the low Mach number limit. Received July 13, 2007. AMS Subject Classification: 65N22, 76N15, 76R10, 76X05.