A Space-Time Finite Element Approach to the Numerical Simulation of Vascular Fluid-Solid Interaction

A Space-Time Finite Element Approach to the Numerical Simulation of Vascular Fluid-Solid Interaction

Vlijm, E.J.
Van Brummelen, E.H.

Aerospace Engineering

Aerospace Materials & Manufacturing

2008-07-01

Numerical studies of cardiovascular diseases like arteriosclerosis have gained increasing attention the last decade. The modeling of blood, blood vessel and their coupling, shows to be a challenging problem. In this thesis a two-dimensional model has been constructed and its behaviour has been investigated. We model the blood vessel by a linear elastic continuum and blood by an incompressible Newtonian fluid. The coupled system is solved with a space-time discontinuous Galerkin method. The solution is allowed to be discontinuous over the discrete time level, but continuity in space is enforced. We calculate the movement of the fluid domain by the equations of linear elasticity, which results in a so-called ’pseudo solid’ mapping. The coupled system is solved with a strongly-coupled solution method. The subiteration procedure occurring within each time step is accelerated by relaxation. Relaxation shows to be necessary when the density of the structure approaches the density of the fluid. The number of iteration steps needed within a time step shows to be quite large and the need for better acceleration becomes apparent. Although the relaxation technique offers some improvement of the subiteration procedure, better techniques are necessary for three-dimensional simulations.

http://resolver.tudelft.nl/uuid:1fbba63b-f1e2-411e-bf29-47241ee63565

Delft Aerospace Computational Science

1574-6992

Report DACS-08-002

Institutional Repository

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(c) 2008 The Author(s)