CEE Seminar, Professor Annalisa Quaini, University of Houston, Dept. of Mathematics

Sep 14

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September 14, 2015 - 12:00pm to 1:00pm


Professor Annalisa Quaini

Speaker: Professor Annalisa Quaini, University of Houston, Department of Mathematics TITLE: CHALLENGES IN COMPUTATIONAL HEMODYNAMICS: MULTIPHYSICS AND COST REDUCTION ABSTRACT: Modeling and computational analysis play an increasingly important role in the investigation of blood flow problems. Significant challenges in the context of computational hemodynamics are the multiphysics nature of the problems (e.g., interaction of blood with artery walls or valve leaflets) and the associated high computational cost. We discuss efficient algorithms to simulate the interaction of blood (an incompressible fluid) and an elastic structure. Two cases are considered: 1. the elastic structure covers part of the fluid boundary and undergoes small displacement and 2. the elastic structure is immersed in the fluid and it features large displacement. For the first case, we propose an Arbitrary Lagrangian-Eulerian (ALE) method based on Lie¿s operator splitting. The resulting algorithm is unconditionally stable and weakly coupled: it requires the solution of one fluid subproblem and one structure subproblem per time step. Standard ALE methods fail when the structural displacement is large. Thus, for the second case we propose an extended ALE method that avoids remeshing and relies on a variational mesh optimization technique.