New Numerical Methods and Analysis for Navier Stokes Equations Involving Interfaces and Simulation of Electro-Migration of Voids

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This proposal is for the continuation of the PI's research toward thedevelopment, implementation, and application of efficient numerical methodsfor interface problems especially with moving interfaces and/or freeboundaries. Specific projects include development of the immersed interfacemethod for the Navier Stokes equations modeling incompressible viscous twophase flow with fixed or moving interfaces. Related to this topic, someimportant projects include development of new projection and/or gaugemethods so that the second order accuracy can be preserved even with thepresence of interfaces; second order elliptic solvers that can satisfy themaximum principle for interface problems in two and three dimensions; thefinite element methods using Cartesian and/or adaptive Cartesian grids forinterface problems. Another application which will be studied in depth isthe simulation of electro-migration of voids in integrated circuits withthe presence of grain boundaries.This proposal is about developing efficient (fast, accurate, and in realtime) methods to simulate some important moving interface/free boundary problems. Applications include the simulation of the interface between water and oil in petroleum industry; simulation of contaminated bubbles in water for environmental science; simulation of crystal growth of pattern formulation in material science; simulation of cell deformation and motion of biofilm in medical and biology sciences; and simulation of electro-migration of voids in an integrated circuit in semi-conductor industry. Over the years, we have developed advanced methods for solving these interface problems and we believe we are the leaders in this area. Therefore we are very confident in the success of the proposal and canmaintain the edge in this area over other countries. Economically, the success of this proposal can save millions of dollars that areneeded to carry out real experiments.