Stability of Finite Difference Discretizations of Multi-Physics Interface Conditions
Stability of Finite Difference Discretizations of Multi-Physics Interface Conditions
复制标题
多物理场接口条件有限差分离散化的稳定性
DOI：
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发表时间：
2011
期刊：
影响因子：
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通讯作者：
J. Banks
中科院分区：
文献类型：
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作者：
B. Sjögreen;J. Banks
我们考虑多物理场计算，其中计算域的某些部分的可压缩流体流动的Navier-Stokes方程与计算域的其他部分的弹性方程耦合。不同的子域由定义良好的接口分隔。我们认为时间精确计算解决所有时间尺度。对于这样的计算，显式时间步进是非常有效的。我们解决了两个不同物理领域之间的离散界面条件问题，这些条件不会导致不稳定，也不会导致稳定时间步长显著减少。找到这样的接口条件是非常重要的。用局部边界闭合求和的方法对问题进行离散化。我们导出了线性化一维离散问题的l2稳定界面条件。此外，我们将界面条件推广到全非线性方程，并在一个简单的模型问题上用数值方法证明了其稳定和精确的性能。通过方程的对称化推导出的能量稳定界面条件包含了Banks和Sjogreen在[8]中作为特例通过正模分析得出的界面条件。
We consider multi-physics computations where the Navier-Stokes equations of compressible fluid flow on some parts of the computational domain are coupled to the equations of elasticity on other parts of the computational domain. The different subdomains are separated by well-defined interfaces. We consider time accurate computations resolving all time scales. For such computations, explicit time stepping is very efficient. We address the issue of discrete interface conditions between the two domains of different physics that do not lead to instability, or to a significant reduction of the stable time step size. Finding such interface conditions is non-trivial. We discretize the problem with high order centered difference approximations with summation by parts boundary closure. We derive L 2 stable interface conditions for the linearized one dimensional discretized problem. Furthermore, we generalize the interface conditions to the full non-linear equations and numerically demonstrate their stable and accurate performance on a simple model problem. The energy stable interface conditions derived here through symmetrization of the equations contain the interface conditions derived through normal mode analysis by Banks and Sjogreen in [8] as a special case.