Student Posters Repository

The Navier-Stokes Equations, incompressible or compressible, are a set of non-linear partial differential equations used to model important phenomena, e.g. fluid flow around ship hulls, wind turbine simulations, blood flow inside the body. We employ a finite element method called Hybridizable Discontinuous Galerkin method to reduce the continuous problem into successive solutions of linear systems of equations. The size of this linear system depends on the required fidelity of the solution. The size can easily grow to millions and we need highly parallelizable and efficient methods to solve them. For those sizes, it is either impossible or incredibly infeasible to use direct methods, like Gaussian elimination, and we would like to use the so-called Krylov subspace methods. However, the performance of these methods highly depends on the size of the problem and the speed of the fluid. The idea is to improve the performance by using a preconditioner. We generalized the Pressure Convection-Diffusion preconditioner which was developed for another finite element method and we are going to show the results of our investigation for three test problems.