A fully-coupled discontinuous Galerkin method for two-phase flow in porous media with discontinuous capillary pressure
A fully-coupled discontinuous Galerkin method for two-phase flow in porous media with discontinuous capillary pressure
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DOI：
10.1007/s10596-014-9426-y
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发表时间：
2013-09
影响因子：
2.5
通讯作者：
P. Bastian
中科院分区：
文献类型：
--
作者：
P. Bastian
在本文中，我们制定和数值试验的完全耦合间断伽辽金（DG）方法不可压缩两相流与间断毛细管压力。空间离散化使用的对称内部惩罚DG制定加权平均值，是基于润湿相电位/毛细管电位制定的两相流系统。对角隐式Runge-Kutta格式在时间上离散后，用牛顿法求解所产生的非线性代数方程组，用代数多重网格法高效并行地求解所产生的线性方程组。新的计划进行了研究，从文献中的各种测试问题，并进行了比较，以细胞为中心的有限体积计划的精度和时间的解决方案。我们发现，该方法是准确的，强大的，和有效的。特别是，没有后处理的DG速度场是必要的，相反，由几个作者报告的解耦计划的结果。此外，求解器的并行和三维问题的规模高达近1亿度的自由度，每一个时间步已计算在1,000个处理器。
In this paper, we formulate and test numerically a fully-coupled discontinuous Galerkin (DG) method for incompressible two-phase flow with discontinuous capillary pressure. The spatial discretization uses the symmetric interior penalty DG formulation with weighted averages and is based on a wetting-phase potential/capillary potential formulation of the two-phase flow system. After discretizing in time with diagonally implicit Runge-Kutta schemes, the resulting systems of nonlinear algebraic equations are solved with Newton’s method and the arising systems of linear equations are solved efficiently and in parallel with an algebraic multigrid method. The new scheme is investigated for various test problems from the literature and is also compared to a cell-centered finite volume scheme in terms of accuracy and time to solution. We find that the method is accurate, robust, and efficient. In particular, no postprocessing of the DG velocity field is necessary in contrast to results reported by several authors for decoupled schemes. Moreover, the solver scales well in parallel and three-dimensional problems with up to nearly 100 million degrees of freedom per time step have been computed on 1,000 processors.