Seventh Mississippi State - UAB Conference on Differential Equations and Computational Simulations. Electron. J. Diff. Eqns., Conference 17 (2009), pp. 171-184.

Finite difference methods for coupled flow interaction transport models

Shelly McGee, Padmanabhan Seshaiyer

Understanding chemical transport in blood flow involves coupling the chemical transport process with flow equations describing the blood and plasma in the membrane wall. In this work, we consider a coupled two-dimensional model with transient Navier-Stokes equation to model the blood flow in the vessel and Darcy's flow to model the plasma flow through the vessel wall. The advection-diffusion equation is coupled with the velocities from the flows in the vessel and wall, respectively to model the transport of the chemical. The coupled chemical transport equations are discretized by the finite difference method and the resulting system is solved using the additive Schwarz method. Development of the model and related analytical and numerical results are presented in this work.

Published April 15, 2009.
Math Subject Classifications: 65N30, 65N15.
Key Words: Finite difference; coupled; flow-transport.

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Shelly McGee
Department of Mathematics, University of Findlay
Findlay, OH 45840, USA
Padmanabhan Seshaiyer
Mathematical Sciences, George Mason University
Fairfax, VA 22030, USA

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