Unified Analysis of Discontinuous Galerkin Methods for Elliptic Problems
SIAM Journal on Numerical Analysis
Adaptive discontinuous Galerkin finite element methods for the compressible Euler equations
Journal of Computational Physics
Anisotropic grid adaptation for functional outputs: application to two-dimensional viscous flows
Journal of Computational Physics
Metric tensors for anisotropic mesh generation
Journal of Computational Physics
Applied Numerical Mathematics - Applied scientific computing: Advances in grid generation, approximation and numerical modeling
Space-time discontinuous Galerkin method for the compressible Navier-Stokes equations
Journal of Computational Physics
deal.II—A general-purpose object-oriented finite element library
ACM Transactions on Mathematical Software (TOMS)
Journal of Computational Physics
Adjoint Consistency Analysis of Discontinuous Galerkin Discretizations
SIAM Journal on Numerical Analysis
Journal of Computational Physics
Multitarget Error Estimation and Adaptivity in Aerodynamic Flow Simulations
SIAM Journal on Scientific Computing
Fully anisotropic goal-oriented mesh adaptation for 3D steady Euler equations
Journal of Computational Physics
On the flexibility of agglomeration based physical space discontinuous Galerkin discretizations
Journal of Computational Physics
Time accurate anisotropic goal-oriented mesh adaptation for unsteady flows
Journal of Computational Physics
An optimization-based framework for anisotropic simplex mesh adaptation
Journal of Computational Physics
Hi-index | 31.46 |
This article considers a posteriori error estimation and anisotropic mesh refinement for three-dimensional laminar aerodynamic flow simulations. The optimal order symmetric interior penalty discontinuous Galerkin discretization which has previously been developed for the compressible Navier-Stokes equations in two dimensions is extended to three dimensions. Symmetry boundary conditions are given which allow to discretize and compute symmetric flows on the half model resulting in exactly the same flow solutions as if computed on the full model. Using duality arguments, an error estimation is derived for estimating the discretization error with respect to the aerodynamic force coefficients. Furthermore, residual-based indicators as well as adjoint-based indicators for goal-oriented refinement are derived. These refinement indicators are combined with anisotropy indicators which are particularly suited to the discontinuous Galerkin (DG) discretization. Two different approaches based on either a heuristic criterion or an anisotropic extension of the adjoint-based error estimation are presented. The performance of the proposed discretization, error estimation and adaptive mesh refinement algorithms is demonstrated for 3d aerodynamic flows.