Adaptive mesh refinement with an enhanced velocity mixed finite element method on semi-structured grids using a fully coupled solver
Adaptive mesh refinement with an enhanced velocity mixed finite element method on semi-structured grids using a fully coupled solver
复制标题
使用全耦合求解器在半结构化网格上采用增强速度混合有限元方法进行自适应网格细化
DOI：
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发表时间：
2018
影响因子：
2.5
通讯作者：
M. Wheeler
中科院分区：
文献类型：
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作者：
B. Ganis;G. Pencheva;M. Wheeler
我们描述了一种使用混合有限元对多孔介质中的流动进行自适应网格加密的新方法。采用增强型速度(EV)混合有限元方法，构造了非匹配子域网格间的强通量连续速度近似。在这项工作中，最初的EV实现被推广到允许在邻近非活动单元的子域内部的接口，并允许动态自适应网格加密(AMR)。在新的实现中，具有不同空间分辨率的子域被堆叠在彼此的顶部以产生非常通用的半结构网格。分解是不重叠的，但现在子域可以有洞，有参差不齐的边，并且相互嵌套。给出了两维和三维自适应网格加密的算例；先验指标用于适应多相流组成模型的网格，后验指标用于适应单相流模型的网格。此外，本文还实现了一种新的EV方法的全耦合线性求解器，与以前实现的非线性块Jacobi求解器相比，它的牛顿迭代次数显著减少，特别是当系统具有强椭圆分量时。
We describe a novel approach for performing adaptive mesh refinement using mixed finite elements for flow in porous media applications. The enhanced velocity (EV) mixed finite element method is used to construct a strongly flux-continuous velocity approximation between non-matching subdomain grids. In this work, the original EV implementation was generalized to allow interfaces in the interior of subdomains adjacent to inactive cells and to allow dynamic adaptive mesh refinement (AMR). In the new implementation, subdomains with different spatial resolutions are stacked on top of each other to produce a very general semi-structured grid. The decomposition is non-overlapping, but now the subdomains can have holes, have ragged edges, and be nested within each other. Several examples with adaptive mesh refinement are demonstrated in two and three spatial dimensions; a priori indicators are used to adapt the grid for a multiphase compositional flow model, and a posteriori indicators are used to adapt the grid for a single-phase flow model. Moreover, a new fully coupled linear solver for the EV method is also implemented in this work, which shows a dramatic reduction in the number of Newton iterations versus the previously implemented nonlinear block Jacobi solver, especially when systems have a strong elliptic component.