In this study, we present an adaptive anisotropic finite element method (FEM) and demonstrate how computational efficiency can be increased when applying the method to the simulation of blood flow in the cardiovascular system. We use the SUPG formulation for the transient 3D incompressible Navier-Stokes equations which are discretised by linear finite elements for both the pressure and the velocity field. Given the pulsatile nature of the flow in blood vessels we have pursued adaptivity based on the average flow over a cardiac cycle. Error indicators are derived to define an anisotropic mesh metric field. Mesh modification algorithms are used to anisotropically adapt the mesh according to the desired size field. We demonstrate the efficiency of the method by first applying it to pulsatile flow in a straight cylindrical vessel and then to a porcine aorta with a stenosis bypassed by a graft. We demonstrate that the use of an anisotropic adaptive FEM can result in an order of magnitude reduction in computing time with no loss of accuracy compared to analyses obtained with uniform meshes.
We describe procedures to model transient shock interaction problems using discontinuous Galerkin methods to solve the compressible Euler equations. The problems are motivated by blast flows surrounding cannons with perforated muzzle brakes. The goal is to predict shock strengths and blast over pressure. This application illustrates several computational difficulties. The software must handle complex geometries. The problems feature strong interacting shocks, with pressure ratios on the order of 1000 as well as weaker precursor shocks traveling rearward that also must be accurately captured. These aspects are addressed using anisotropic mesh adaptation. A shock detector is used to control the adaptation and limiting. We also describe procedures to track projectile motion in the flow by a level-set procedure.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.