A face-centred finite volume method for high-contrast Stokes interface problems
A face-centred finite volume method for high-contrast Stokes interface problems
复制标题
高对比度斯托克斯接口问题的面心有限体积法
DOI：
10.1002/nme.7294
复制
发表时间：
2023
影响因子：
2.9
通讯作者：
Sevilla R
中科院分区：
文献类型：
--
作者：
Sevilla R
提出了一种求解尖锐界面Stokes问题的面心有限体积法（FCFV）.两个配方，基于两个强形式的斯托克斯问题，并使用不同的混合变量，提出。特别注意由此产生的全局方程组的对称性，并提出了界面边界条件的简单重写，以确保其中一个公式保留线性系统的对称性，而这种对称性在考虑材料界面时通常会丢失。四个数值例子被认为是测试实施数值网格收敛的研究，在二维和三维。这些例子说明了不连续粘度以及表面张力的影响。结果表明，其中一种公式对FCFV方法中的数值稳定化不太敏感，但不保持全局系统的对称性，而另一种公式对数值稳定化更敏感，但保持了所得方程组的对称性. FCFV方法作为一种很有前途的替代方案，在共形网格上模拟粘性流动，包括内部边界。讨论了FCFV方法在地球动力学建模中的潜在应用。
A new face‐centred finite volume method (FCFV) for Stokes problems involving sharp interfaces is proposed. Two formulations, based on two strong forms of the Stokes problem, and using different mixed variables, are presented. Particular attention is paid to the symmetry of the resulting system of global equations, and a simple rewriting of the interface boundary condition is proposed to ensure that one of the formulations preserves the symmetry of the linear system that is usually lost when considering material interfaces. Four numerical examples are considered to test the implementation numerically by performing mesh convergence studies, in two and three dimensions. The examples account for discontinuous viscosity as well as the effect of surface tension. The results show that one of the formulations is less sensitive to the numerical stabilisation used in FCFV methods but does not preserve the symmetry of the global system, whereas the other formulation is more sensitive to the stabilisation, but preserves the symmetry of the resulting system of equations. The FCFV method appears as a promising alternative for the simulation of viscous flow involving internal boundaries on conformal meshes. The potential application of the FCFV method for the purpose of geodynamic modelling is discussed.