Robust Lagrangian Surface Propagation with Topological Control

DMS-0310446John C. Hart, Michael T. Heath, Xiangmin Jiao, and John M. sulvan这个由DMS-0310642和DMS-0310354资助的合作项目是CARGO团队在征求下获得的奖励http://www.nsf.gov/pubs/2002/nsf02155/nsf02155.htm.Level集合隐含地表示一个移动的界面表面，它自然地适应了奇点和拓扑变化，但代价是浪费体积欧拉表示，无法控制水平集的拓扑结构。我们的项目将开发使用更有效的拉格朗日曲面网格跟踪界面的新方法。通过对不稳定性和拓扑变化的仔细预测，我们将解决数值、几何和拓扑方面的困难，这些困难一直困扰着以前的拉格朗日界面传播方法。结果将是更快，更紧凑的模拟界面表面的运动，以及检测和控制其拓扑变化的能力。移动的边界或界面表面是各种物理现象的一个组成部分，如凝固、挤压、多相流和流固相互作用。这种现象的数值模拟需要可靠和有效的方法来传播和跟踪这种移动表面。我们项目的重点是开发新的方法，提供更好的控制表面传播，同时获得比现有方法更高的计算效率。我们将考虑的一个具体应用是固体推进剂火箭发动机燃烧的模拟，这是UIUC先进火箭模拟中心（CSAR）的主要重点。这项工作将产生更高效、更精确的火箭发动机虚拟原型设计，从而产生更安全、更高效的固体火箭助推器，例如为美国航天飞机提供动力的助推器。

DMS-0310446John C. Hart, Michael T. Heath, Xiangmin Jiao, and John M. SullivanThis collaborative project funded under DMS-0310642 and DMS-0310354 is a CARGO full team award made under solicitation http://www.nsf.gov/pubs/2002/nsf02155/nsf02155.htm.Level sets represent a moving interface surface implicitly, whichnaturally accommodates singularities and topology changes, but at theexpense of a wasteful volumetric Eulerian representation that provides nocontrol over the topology of the level set. Our project will develop newmethods for tracking interfaces using a more efficient Lagrangian surfacemesh. Through careful prediction of instabilities and topology changes,we will address the numerical, geometric, and topological difficultiesthat have plagued previous Lagrangian approaches to interface propagation.The result will be faster and more compact simulations of the motion ofinterface surfaces, as well as the ability to detect and control changesin their topology.Moving boundary or interface surfaces are an integral part of a widevariety of physical phenomena, such as solidification, extrusion,multiphase flow, and fluid-solid interaction. Numerical simulations ofsuch phenomena require reliable and efficient methods for propagating andtracking such moving surfaces. The focus of our project is to developnew methods that provide greater control over surface propagation whilealso attaining greater computational efficiency than existing methods.One specific application we will consider is the simulation of combustionin solid propellant rocket motors, which is the primary focus of UIUC'sCenter for Simulation of Advanced Rockets (CSAR). This work will resultin more efficient and more accurate virtual prototyping of rocket motordesigns, leading to safer and more efficient solid rocket boosters,such as those powering the U.S. Space Shuttle.