Commun. Comput. Phys., 5 (2009), pp. 620-634.


Analysis and Computation for a Fluid Mixture Model

Qunlei Jiang 1, Zhilin Li 1*, Sharon R. Lubkin 1

1 Department of Mathematics and Center for Scientific Computations, North Carolina State University, Raleigh, NC 27695, USA.

Received 30 September 2007; Accepted (in revised version) 18 January 2008
Available online 1 August 2008

Abstract

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.

AMS subject classifications: 65N06, 65N12, 65M06, 76M20

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Key words: Tissue deformations, immersed interface method, linear stability analysis, finite difference method.

*Corresponding author.
Email: qjiang2@gmail.com (Q. Jiang), zhilin@math.ncsu.edu (Z. Li), lubkin@math.ncsu.edu (S. R. Lubkin)
 

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