Finite-Element Formulation for Advection-Reaction Equations with Change of Variable and Discontinuity Capturing

03/15/2020
by   Stefan Haßler, et al.
0

We propose a change of variable approach and discontinuity capturing methods to ensure physical constraints for advection-reaction equations discretized by the finite element method. This change of variable confines the concentration below an upper bound in a very natural way. For the non-negativity constraint, we propose to use a discontinuity capturing method defined on the reference element that is combined with an anisotropic crosswind-dissipation operator. This discontinuity capturing cannot completely eliminate negative values but effectively minimizes their occurrence. The proposed methods are applied to different biophysical models and show a good agreement with experimental results for the FDA benchmark blood pump for a physiological red blood cell pore formation model.

READ FULL TEXT

Please sign up or login with your details

Forgot password? Click here to reset