Goal-oriented adaptive composite discontinuous Galerkin methods for incompressible flows

Goal-oriented adaptive composite discontinuous Galerkin methods for incompressible flows

In this article we consider the application of goal–oriented mesh adaptation to problems posed on complicated domains which may contain a huge number of local geometrical features, or micro-structures. Here, we exploit the composite variant of the discontinuous Galerkin finite element method based on exploiting finite element meshes consisting of arbitrarily shaped element domains. Adaptive mes...

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...

Adaptive Discontinuous Galerkin Methods for Eigenvalue Problems Arising in Incompressible Fluid Flows

In this article we consider the a posteriori error estimation and adaptive mesh refinement of discontinuous Galerkin finite element approximations of the hydrodynamic stability problem associated with the incompressible Navier–Stokes equations. Particular attention is given to the reliable error estimation of the eigenvalue problem in channel and pipe geometries. Here, computable a posteriori e...

Adaptive Discontinuous Galerkin Finite Element Methods for Compressible Fluid Flows

Anisotropic adaptive simulation of transient flows using discontinuous Galerkin methods

An anisotropic adaptive analysis procedure based on a discontinuous Galerkin finite element discretization and local mesh modification of simplex elements is presented. The procedure is applied to transient 2and 3dimensional problems governed by Euler’s equation. A smoothness indicator is used to isolate jump features where an aligned mesh metric field in specified. The mesh metric field in smo...