High Order Discontinuous Galerkin Methods with Differential Transform Strategy

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 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...

Bridging the Hybrid High-Order and Hybridizable Discontinuous Galerkin Methods

We build a bridge between the hybrid high-order (HHO) and the hybridizable discontinuous Galerkin (HDG) methods in the setting of a model diffusion problem. First, we briefly recall the construction of HHO methods and derive some new variants. Then, by casting the HHO method in mixed form, we identify the numerical flux so that the HHO method can be compared to HDG methods. In turn, the incorpo...

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...

High-Order Discontinuous Galerkin Methods using a Spectral Multigrid Approach