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

North Carolina State University, Raleigh NC

Investigators

Abstract

This proposal is for the continuation of the PI's research toward the development, implementation, and application of efficient numerical methods for interface problems especially with moving interfaces and/or free boundaries. Specific projects include development of the immersed interface method for the Navier Stokes equations modeling incompressible viscous two phase flow with fixed or moving interfaces. Related to this topic, some important projects include development of new projection and/or gauge methods so that the second order accuracy can be preserved even with the presence of interfaces; second order elliptic solvers that can satisfy the maximum principle for interface problems in two and three dimensions; the finite element methods using Cartesian and/or adaptive Cartesian grids for interface problems. Another application which will be studied in depth is the simulation of electro-migration of voids in integrated circuits with the presence of grain boundaries. This proposal is about developing efficient (fast, accurate, and in real time) 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 can maintain the edge in this area over other countries. Economically, the success of this proposal can save millions of dollars that are needed to carry out real experiments.