A massively parallel adaptive sharp interface solver with application to mechanical heart valve simulations

This thesis presents a framework for simulating the fluid dynamical behavior of complex moving boundary problems in a high-performance computing environment. The framework is implemented in the pELAFINT3D software package. Moving boundaries are evolved in a seamless fashion through the use of distributed narrow band level set methods and the effect of moving boundaries is incorporated into the flow solution by a novel Cartesian grid method. The proposed Cartesian grid approach builds on the concept of a ghost fluid method where boundary conditions are applied through least-squares polynomial extrapolations. The method is hybridized such that computational cells adjacent to moving boundaries change discretization schemes smoothly in time to avoid the introduction of strong oscillations in the pressure field. The hybridization is shown to have minimal effect on accuracy while significantly suppressing pressure oscillations.;The computational capability of the Cartesian grid approach is enhanced with a massively parallel adaptive meshing algorithm. Local mesh enrichment is effected through the use of octree refinement, and a scalable mesh pruning algorithm is used to reduce the memory footprint of the Cartesian grid for geometries which are not well bounded by a rectangular cuboid. The computational work is kept in a well-balanced state through the use of an adaptive repartitioning strategy. The numerical scheme is validated against many benchmark problems and the composite approach is demonstrated to work well on tens of thousands of computational cores. A simulation of the closure phase of a mechanical heart valve was carried out to demonstrate the ability of the pELAFINT3D package to compute high Reynolds number flows with complex moving boundaries and a wide disparity in length scales. Finally, a novel image-to-computation algorithm was implemented to demonstrate the flexibility the current method allows in designing new applications.