A diffuse interface method for complex three-dimensional free surface flows
A diffuse interface method for complex three-dimensional free surface flows
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DOI：
10.1016/j.cma.2013.01.006
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发表时间：
2013-04
影响因子：
7.2
通讯作者：
M. Dumbser
中科院分区：
文献类型：
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作者：
M. Dumbser
本文将Dumber在[24]中提出的用于模拟复杂二维非静力自由表面流动的弱可压缩两相扩散界面方法(DIM)推广到三维非结构四面体网格。与2D情况一样，使用了可压缩多相流的Baer-Nunziato模型的简化版本。物理模型由水的Tait状态方程封闭，可以很容易地在现有的基于高分辨率激波捕捉有限体积格式的可压缩程序中实现。由于所提出的模型是完全三维的，它考虑了流体在重力方向上的加速度，因此不像经典的浅水方程那样假定静水压力分布。此外，三维两相模型还可以自然地处理破碎波。为了求解质量守恒定律和动量守恒定律以及流体体积分数的非保守演化方程，在单元界面采用高精度路径守恒的一步WENO有限体积格式和一种新的广义Osher型Riemann求解器。精确的黎曼解算器与高阶有限体积法相结合，可获得简单但精确的自由面分辨率。实验参考数据与大量三维试验算例计算结果的比较表明，该方法适用于复杂三维自由表面流动的精确模拟。可压缩流动模型的使用允许该方法模拟低速和高速自由面流动问题，这使得该方法适用于非常广泛的环境和工业自由面流动问题。
In this article the weakly compressible two-phase diffuse interface method (DIM) for the simulation of complex two-dimensional non-hydrostatic free surface flows proposed by Dumbser in [24] is extended to three-dimensional unstructured tetrahedral meshes. As in the 2D case, a reduced version of the Baer–Nunziato model for compressible multiphase flows is used. The physical model is closed by the Tait equation of state for water and can be implemented easily into existing compressible codes based on high resolution shock capturing finite volume schemes. Since the proposed model is fully three-dimensional, it includes the fluid accelerations in gravity direction and hence does not assume a hydrostatic pressure distribution, like the classical shallow water equations. Furthermore, the 3D two-phase model can naturally deal also with breaking waves. To solve the system of conservation laws of mass and momentum coupled with the non-conservative evolution equation of the fluid volume fraction, a high order path-conservative one-step WENO finite volume scheme is applied, together with a new generalized Osher-type Riemann solver at the element interfaces. The accurate Riemann solver in combination with a high order finite volume approach leads to a simple but sharp resolution of the free surface. A thorough comparison of experimental reference data with the computational results obtained for a large set of three-dimensional test cases shows the suitability of the present approach for the accurate simulation of complex three-dimensional free surface flows. The use of a compressible flow model allows the method to simulate both, low speed and high speed free surface flow problems, which makes the approach applicable to a very wide class of environmental and industrial free surface flow problems.