Semi-implicit extension of a Godunov-type scheme based on low Mach number asymptotics
Semi-implicit extension of a Godunov-type scheme based on low Mach number asymptotics
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DOI：
10.1016/s0021-9991(95)90034-9
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发表时间：
1995-10
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影响因子：
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通讯作者：
R. Klein
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文献类型：
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作者：
R. Klein
单尺度、多空间尺度渐近分析提供了可压缩欧拉方程解的低马赫数极限行为的详细见解。我们使用渐近性作为指导方针，发展一个显式高阶激波捕捉方案的低马赫数扩展。这种半隐式格式涉及多个压力变量、大尺度差分和平均程序，这些程序是多尺度渐近分析中标准操作的离散化版本。对流和声波传播显式离散和迎风，只有一个标量椭圆方程是隐式求解在每个时间步。该方程是马赫数为零时不可压缩流的压力修正方程。在低马赫数限制下，时间步长受基本上基于最大流速的柯朗数限制。对于中等马赫数和大马赫数，该格式简化为基本的显式高阶激波捕捉算法。
A single scale, multiple space scale asymptotic analysis provides detailed insight into the low Mach number limit behavior of solutions of the compressible Euler equations. We use the asymptotics as a guideline for developing a low Mach number extension of an explicit higher order shock-capturing scheme. This semi-implicit scheme involves multiple pressure variables, large scale differencing and averaging procedures that are discretized versions of standard operations in multiple scales asymptotic analysis. Advection and acoustic wave propagation are discretized explicitly and upwind and only one scalar elliptic equation is to be solved implicitly at each time step. This equation is a pressure correction equation for incompressible flows when the Mach number is zero. In the low Mach number limit, the time step is restricted by a Courant number based essentially on the maximum flow velocity. For moderate and large Mach numbers the scheme reduces to the underlying explicit higher order shock capturing algorithm.