Download or read book A Parallel High-order Discontinuous Galerkin Solver for the Unsteady Incompressible Navier-Stokes Equations in Complex Geometries written by Khosro Shahbazi and published by . This book was released on 2007 with total page 288 pages. Available in PDF, EPUB and Kindle. Book excerpt: We verify the accuracy and stability of the method on several two- and three-dimensional benchmarking problems. On the challenging Orr-Sommerfeld test problem, the equal-order polynomial approximation of the velocity and pressure (Pk - Pk) leads to a stable and accurate solution, while the mixed-order method (Pk - Pk-1) yields a non-physical instability. In simulating vortex shedding past a square cylinder at Re = 100 and in simulating a three-dimensional backward-facing step flow using the equal-order method, excellent agreement with other computational and experimental results are obtained. The developed solver is used to study flow through a two-dimensional bileaflet mechanical heart valve geometry. We conclude that the proposed discontinuous Galerkin method with the Pk - Pk formulation is a suitable scheme for simulations of flows through mechanical heart valve geometries. We develop a parallel method and corresponding code for the numerical solution of the unsteady incompressible Navier-Stokes equations, with application to the direct numerical simulation of transitional and turbulent flows through mechanical heart valves. The solver is based on a simple and efficient scheme, namely a high-order discontinuous Galerkin method on triangular and tetrahedral elements. Spatial discretization of the Stokes operator employed both equal-order (Pk - Pk) and mixed-order (Pk - Pk-1) velocity and pressure approximations. The interior penalty method and local Lax-Friedrichs fluxes are used for the discretizations of the viscous term and the nonlinear term in the divergence form, respectively. A second order approximate algebraic splitting is used to decouple the velocity and pressure calculations leading to an algebraic Helmholtz equation for each component of the velocity and a consistent Poisson equation for the pressure. The consistent Poisson operator is replaced by an equivalent operator, namely that arising from the interior penalty discretization of the standard Poisson operator with appropriate boundary conditions. An explicit lower bound is derived for the penalty parameter of the interior penalty method that ensures the coercivity of the bilinear form. Efficiency aspects of the scheme include knowing an explicit expression for the penalty parameter of the interior penalty method and compact stencil size for the discretizations of the velocity and pressure equations and the nonlinear term.