Efficiency of high-order elements for continuous and discontinuous Galerkin methods

High-Order Discontinuous Galerkin Methods for CFD

In recent years it has become clear that the current computational methods for scientific and engineering phenomena are inadequate for many challenging problems. Examples of these problems are wave propagation, turbulent fluid flow, as well as problems involving nonlinear interactions and multiple scales. This has resulted in a significant interest in so-called high-order accurate methods, whic...

High-Order Discontinuous Galerkin Method on Hexahedral Elements for Aeroacoustics High-Order Discontinuous Galerkin Method on Hexahedral Elements for Aeroacoustics

High-Order Discontinuous Galerkin Methods for Turbulent High-lift Flows

In this work a robust discontinuous Galerkin (DG) solver for turbulent high-lift aerodynamic flows using the turbulence model of Spalart and Allmaras (SA) is developed. The application of DG discretizations to turbulent RANS flows is one of the most pressing issues facing high-order methods on unstructured grids. The issue is the result of non-smooth behavior of the turbulence model equation, w...

Unified Hybridization of Discontinuous Galerkin, Mixed, and Continuous Galerkin Methods for Second Order Elliptic Problems

We introduce a unifying framework for hybridization of finite element methods for second order elliptic problems. The methods fitting in the framework are a general class of mixed-dual finite element methods including hybridized mixed, continuous Galerkin, nonconforming, and a new, wide class of hybridizable discontinuous Galerkin methods. The distinctive feature of the methods in this framewor...

High-order Discontinuous Galerkin Methods for Incompressible Flows

Abstract. The spatial discretization of the unsteady incompressible Navier-Stokes equations is stated as a system of Differential Algebraic Equations (DAEs), corresponding to the conservation of momentum equation plus the constraint due to the incompressibility condition. Runge-Kutta methods applied to the solution of the resulting index-2 DAE system are analyzed, allowing a critical comparison...