A New Physics-Based Method for Simulation of Free-Surface Fluid Phenomena

这项研究涉及一种新的跟踪动态界面的3D方法，在精度和实用性方面取代了复杂流体现象的模拟技术。这种新的3D方法被称为标记水平集(MLS)方法，它为当前流体方法的几个挑战提供了一个综合的解决方案。它是精确的，具有处理二维或三维拓扑变化的能力，具有良好的体积守恒性质，提供界面切向动力学，并且是高效的。现有的界面跟踪方法中没有一种将所有这些特性结合在同一个公式中。这项研究的理论、算法、系统和应用对计算机图形学和医学应用以及与计算流体力学相关的领域都很有用。标记水平集方法结合了水平集和只沿界面放置标记的使用。这在计算上是高效和准确的，因为标记提供了特征曲面信息。此外，MLS方法自然提供了切线曲面动力学，这是其他基于水平集的方法所缺少的。此属性对于图形和可视化领域中的平流纹理非常有用。最后，MLS允许对流体与变形体的相互作用进行建模。

This research involves a new 3D method for tracking dynamic interfaces that supersedes the state of the art in the simulation of complex fluid phenomena in terms of accuracy and utility. This new 3D method, termed the Marker Level Set (MLS) method, provides an integrated solution to several challenges of the present fluid methodologies. It is accurate, has the ability to easily deal with topology changes in two or three dimensions, has good volume conservation properties, provides interfacial tangential dynamics and is efficient. None of the existing interface tracking methods combine all these qualities in the same formulation. The theories, algorithms, systems and applications derived from this research are useful to both computer graphics and medical applications, as well as to fields related to computational fluid dynamics.The Marker Level Set method combines the use of level sets and markers placed only along the interface. This is computationally efficient and accurate since the markers provide characteristic surface information. In addition, the MLS method naturally provides tangential surface dynamics, something missing from the other level set based methods. This property is very useful for advecting textures in the fields of graphics and visualization. Finally, MLS allows modeling the interaction of fluids with deformable bodies.