High Performance Computing in Free Surface Fluid Flows

拟议的研究包括几个相互关联的活动领域。其中首先是对存在运动边界的不可压缩流体流动的一般稳定有限元方法的持续发展，特别强调自由表面和两相流动。该方法基于一种稳定的时空公式，能够处理区域的大变形。速度-压力-应力公式将并行发展。它是一种适用于粘弹性流体的新型不可压缩流稳定公式。这一研究领域将并入时空方法的发展，以允许在存在移动边界的粘弹性流体的数值处理。提出的有限元公式导致了大型线性方程组。这些系统将使用GMRES迭代法隐式求解。为了提高收敛速度，需要设计和测试有效的预处理技术。除此之外，还将研究结合逐元素聚类和多网格方法的技术。所有的实现工作都将集中在大规模并行架构上。

The proposed research includes several interconnected areas of activity. First among them is the continuing developments of a general stabilized finite element method for incompressible fluid flows in the presence of moving boundaries, with particular emphasis on free surface and two-phase flows. The method is based on a stabilized space-time formulation, and is capable of handling large deformations of the domain. The velocity- pressure-stress formulation will be developed in parallel. It is a novel stabilized formulation for incompressible flows which is applicable to viscoelastic fluids. This research area will be merged into the space-time method development, to allow for numerical treatment of viscoelastic fluids in the presence of moving boundaries. Proposed finite element formulations result in large linear systems of equations. These systems will be solved implicitly using a GMRES iterative method. To improve the rate of convergence, efficient preconditioning techniques will be designed and test. Among others, techniques combining the Clustered Element-By-Element and Multigrid approaches will be examined. All implementation work will concentrate on massively parallel architectures.