Efficient Algorithms for Complex Multiphase Physics

许多问题涉及多个连接的移动界面，包括液体和固体泡沫，材料的粗化，流体中的复杂混合，以及生物学中的细胞结构。这些问题有多个域，这些域共享在多个结中相遇的公共壁。 边界移动的力量，这取决于局部和全局的几何属性，如表面张力和体积约束，以及长期的物理力，包括不可压缩流，膜渗透性，和elastic forces.This建议的目的是发展，实施和应用新的数值方法传播多相界面在复杂的物理设置。中央计算工具之一将是最近开发的Voronoi隐式接口方法，这是一个数学的角度和相关的数值方法跟踪接口在一般多相问题。这些方法为多维耦合多相提供了准确，一致和有效的方案，这些方案处理复杂的三重接头/结，拓扑变化，并自然地耦合到复杂的物理。 研究人员和他的同事们将开发新的算法工具，用于多相耦合传输问题，并将这些技术应用于计算固体和液体泡沫，以及新材料的制造技术，提供新的方法来计算，改进和优化复杂材料的设计和性能。

Many problems involve multiply-connected moving interfaces, including liquid and solid foams, coarsening in materials, complex mixing in fluids, and evolving cell structures in biology. These problems have multiple domains which share common walls meeting in multiple junctions. Boundaries move under forces which depend on both local and global geometric properties, such as surface tension and volume constraints, as well long-range physical forces, including incompressible flow, membrane permeability, and elastic forces.This proposal is aimed toward developing, implementing, and applying new numerical methods for propagating multiphase interfaces in a complex physical settings. One of the central computational tools will be the recently developed Voronoi Implicit Interface Methods, which is a mathematical perspective and associated numerical methodology for tracking interfaces in general multiphase problems. These methods offer accurate, consistent, and efficient schemes for multi-dimensional coupled multiphase, which handle complex triple joints/junction, topological change, and naturally couple to complex physics. The investigator and his colleagues will develop new algorithmic tools for multiphase coupled transport problems, and will apply these techniques to computing solid and liquid foams, as well as manufacturing techniques for new materials, providing new methods to compute, refine, and optimize the design and performance cf complex materials.