NUMERICAL METHODS FOR PROBLEMS W/ MOVING FRONTS

University Of Washington, Seattle WA

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Abstract

This section deals with the application of advanced numerical techniques to nonlinear mass transport and exchange problems. Mass transport and exchange in the micro circulation are driven by complex nonlinear phenomena. To investigate efficiently these phenomena, quick and accurate numerical solutions to large models are needed. To meet that requirement, we have applied specialized numerical techniques (namely random choice method, Euler-Lagrange method and MacCormack method with and without flux-correction) to a two-region blood-tissue exchange model which include carrier-mediated transport and nonlinear consumptions. The generality of the model has also been extended by allowing for non-uniform distribution of carrier sites and reaction sites along the capillary. To provide investigators with a robust package, stability conditions have been implemented and tested. Extension of the numerical techniques to more complicated models has started.