Analysis and Computation for a Fluid Mixture Model

A fluid mixture model of tissue deformations has been studied in this paper.The model is a mixed system of nonlinear hyperbolic and elliptic partial differential equations.Both theoretical linear stability and numerical analysis are presented.Comparisons between standard numerical methods that utilize Runge-Kutta methods coupled with the WENO scheme and the immersed interface methods are given.Numerical examples are also presented.