CSAR Seminar
SPEAKER: Saikrishna Marella, University of Iowa
TITLE:
A Parallelized Sharp-Interface, Fixed Grid Method for Moving Boundary Problems
DATE: Monday, March 6, 2006
TIME: 12:00 Noon
PLACE: 2240 DCL
1304 W. Springfield Ave., Urbana, IL
ABSTRACT
A parallelized sharp-interface computational method applicable to
moving boundary problems is presented. The method relies on a
Cartesian grid with objects/structures being represented on the mesh
using level-sets. A second-order accurate finite-difference
formulation is implemented for the incompressible fluid flow
equations. The level-set method in conjunction with finite-differences
for the flow equations eases the implementation for three-dimensional
problems. A sharp interface method is implemented for the
computational points adjoining the interface to ensure proper
imposition of boundary conditions. The above method has been
parallelized using MPI to perform large-scale calculations on a
distributed memory systems. Domain decomposition is used for
load-balancing and an efficient communication protocol has been
developed to ensure good scalability and speedup.
The methodology is used to simulate the dynamics of a bi-leaflet
mechanical heart valve. Since one of the main reasons for the failure
of mechanical heart valves is thrombus formation, numerical simulation
of the blood flow through the valve chamber is carried out to gain
better insight into the mechanics of the valve closure phase. The
challenges in studying the dynamics of the heart valve are (a)
simulating flow around complicated valve geometry and (b) resolving the
flow features in the closure phase. The valve geometry is represented
as a level-set on the Cartesian mesh and is modeled as a hinged rigid
body rotating with fluid dynamic forces. The level-set algorithm
enables interface-tracking as the valve moves. In the valve chamber,
the blood flow is driven by a pressure pulse applied across the valve.
During this pulse, the valve moves from fully open to fully closed
position. In the closure phase, the clearance region between the valve
and valve chamber is extremely small, thereby creating high pressure