Fluid Structure Interaction
We develop novel computational methods for fluid-structure interaction (FSI) to simulate the cardiovascular system, including vascular, ventricular, and heart valve dynamics. We study, expand and apply FSI techniques in both major categories of method: fitted and unfitted discretizations. Arbitrary Lagrangian-Eulerian (ALE) methods, which use a fitted or conforming discretization, need re-meshing algorithms to deal with large displacements and special treatment of contact. With fitted ALE, we have also proposed an alternative novel unified formulation for handling compressible and incompressible solids. Unfitted or immersed methods, which use non-conforming discretization, include the classical immersed boundary method, the immersed finite element method, and Nitsche-based finite element methods. These methods are used in our application research, including studies of aortic dissection, tissue-engineered vascular grafts, and congenital valve defects.