University of Copenhagen, Copenhagen.
IEEE Trans Vis Comput Graph. 2014 Jan;20(1):4-16. doi: 10.1109/TVCG.2013.97.
In this paper, we present a method for animating multiphase flow of immiscible fluids using unstructured moving meshes. Our underlying discretization is an unstructured tetrahedral mesh, the deformable simplicial complex (DSC), that moves with the flow in a Lagrangian manner. Mesh optimization operations improve element quality and avoid element inversion. In the context of multiphase flow, we guarantee that every element is occupied by a single fluid and, consequently, the interface between fluids is represented by a set of faces in the simplicial complex. This approach ensures that the underlying discretization matches the physics and avoids the additional book-keeping required in grid-based methods where multiple fluids may occupy the same cell. Our Lagrangian approach naturally leads us to adopt a finite element approach to simulation, in contrast to the finite volume approaches adopted by a majority of fluid simulation techniques that use tetrahedral meshes. We characterize fluid simulation as an optimization problem allowing for full coupling of the pressure and velocity fields and the incorporation of a second-order surface energy. We introduce a preconditioner based on the diagonal Schur complement and solve our optimization on the GPU. We provide the results of parameter studies as well as a performance analysis of our method, together with suggestions for performance optimization.
在本文中，我们提出了一种使用非结构动网格动画不可混溶流体多相流的方法。我们的基本离散是一个非结构的四面体网格，可变形单纯复形（DSC），以拉格朗日方式随流移动。网格优化操作可提高元素质量并避免元素反转。在多相流的情况下，我们保证每个元素仅被一种流体占据，因此，流体之间的界面由单纯复形中的一组面表示。这种方法确保了底层离散化与物理相符，并避免了基于网格的方法中所需的额外簿记，在基于网格的方法中，多个流体可能占据同一单元。我们的拉格朗日方法自然导致我们采用有限元方法进行模拟，这与大多数使用四面体网格的流体模拟技术采用的有限体积方法形成对比。我们将流体模拟特征化为一个允许压力和速度场完全耦合并纳入二阶表面能的优化问题。我们基于对角 Schur 补引入了一个预条件器，并在 GPU 上求解我们的优化问题。我们提供了参数研究的结果以及我们方法的性能分析，并提出了性能优化的建议。
