John C. Hart, Michael T. Heath, Xiangmin Jiao, and John M. Sullivan
This collaborative project funded under DMS-0310642 and DMS-0310354 is a CARGO full team award made under solicitation www.nsf.gov/pubs/2002/nsf02155/nsf02155.htm.
Level sets represent a moving interface surface implicitly, which naturally accommodates singularities and topology changes, but at the expense of a wasteful volumetric Eulerian representation that provides no control over the topology of the level set. Our project will develop new methods for tracking interfaces using a more efficient Lagrangian surface mesh. Through careful prediction of instabilities and topology changes, we will address the numerical, geometric, and topological difficulties that have plagued previous Lagrangian approaches to interface propagation. The result will be faster and more compact simulations of the motion of interface surfaces, as well as the ability to detect and control changes in their topology.
Moving boundary or interface surfaces are an integral part of a wide variety of physical phenomena, such as solidification, extrusion, multiphase flow, and fluid-solid interaction. Numerical simulations of such phenomena require reliable and efficient methods for propagating and tracking such moving surfaces. The focus of our project is to develop new methods that provide greater control over surface propagation while also attaining greater computational efficiency than existing methods. One specific application we will consider is the simulation of combustion in solid propellant rocket motors, which is the primary focus of UIUC's Center for Simulation of Advanced Rockets (CSAR). This work will result in more efficient and more accurate virtual prototyping of rocket motor designs, leading to safer and more efficient solid rocket boosters, such as those powering the U.S. Space Shuttle.
