title: Space-time least-squares finite element method for convection-reaction system with transformed variables.
abstract: We present a method to solve a convection-reaction system based on a least-squares finite element method (LSFEM). For steady-state computations, issues related to recirculation flow are stated and demonstrated with a simple example. The method can compute concentration profiles in open flow even when the generation term is small. This is the case for estimating hemolysis in blood. Time-dependent flows are computed with the space-time LSFEM discretization. We observe that the computed hemoglobin concentration can become negative in certain regions of the flow; it is a physically unacceptable result. To prevent this, we propose a quadratic transformation of variables. The transformed governing equation can be solved in a straightforward way by LSFEM with no sign of unphysical behavior. The effect of localized high shear on blood damage is shown in a circular Couette-flow-with-blade configuration, and a physiological condition is tested in an arterial graft flow.
authors.affiliation: Department of Chemical & Biomolecular Engineering and Ken Kennedy Institute for Information Technology Rice University, Houston, Texas 77005, USA.
authors.forename: Jaewook
authors.initials: J
authors.lastname: Nam
authors.forename: Marek
authors.initials: M
authors.lastname: Behr
authors.forename: Matteo
authors.initials: M
authors.lastname: Pasquali