A Non-oscillatory Eulerian Approach to Interfaces in Multimaterial Flows (the Ghost Fluid Method)
A Non-oscillatory Eulerian Approach to Interfaces in Multimaterial Flows (the Ghost Fluid Method)
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DOI：
10.1006/jcph.1999.6236
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发表时间：
1999-07
影响因子：
4.1
通讯作者：
Ronald Fedkiw;T. Aslam;B. Merriman;S. Osher
中科院分区：
文献类型：
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作者：
Ronald Fedkiw;T. Aslam;B. Merriman;S. Osher
虽然欧拉格式对大多数气体流动都能很好地工作，但它们已被证明在某些材料界面附近存在非物理振荡。相比之下，拉格朗日格式在多材料界面上工作得很好，但在大多数气体流动的大变形和涡度特性问题上有其自身的困难。我们相信，最稳健的方案将结合联合收割机欧拉和拉格朗日方案的最佳性能。在本文中，我们提出了一种新的数值方法来处理界面的欧拉方案，保持了Heaviside的密度没有数值涂抹沿着线的早期工作和大多数拉格朗日计划。我们使用一个水平集函数来跟踪运动的多材料界面的欧拉框架。此外，鬼细胞（实际上是我们有限差分框架中的鬼节点）和新的等压固定技术的使用允许我们保持密度分布不模糊，同时仍然保持该方案的鲁棒性和易于编程，并简单扩展到多维和多级时间积分，例如，朗格？库塔方法。相比之下，以前的方法使用不明智的多维问题的维度分裂，并遭受了巨大的复杂性，当与多级时间积分器一起使用。
While Eulerian schemes work well for most gas flows, they have been shown to admit nonphysical oscillations near some material interfaces. In contrast, Lagrangian schemes work well at multimaterial interfaces, but suffer from their own difficulties in problems with large deformations and vorticity characteristic of most gas flows. We believe that the most robust schemes will combine the best properties of Eulerian and Lagrangian schemes. In this paper, we propose a new numerical method for treating interfaces in Eulerian schemes that maintains a Heaviside profile of the density with no numerical smearing along the lines of earlier work and most Lagrangian schemes. We use a level set function to track the motion of a multimaterial interface in an Eulerian framework. In addition, the use of ghost cells (actually ghost nodes in our finite difference framework) and a new isobaric fix technique allows us to keep the density profile from smearing out, while still keeping the scheme robust and easy to program with simple extensions to multidimensions and multilevel time integration, e.g., Runge?Kutta methods. In contrast, previous methods used ill-advised dimensional splitting for multidimensional problems and suffered from great complexity when used in conjunction with multilevel time integrators.