Grid adaptation for functional outputs: application to two-dimensional inviscid flows
Journal of Computational Physics
SIAM Journal on Scientific Computing
Anisotropic grid adaptation for functional outputs: application to two-dimensional viscous flows
Journal of Computational Physics
Iterative Methods for Sparse Linear Systems
Iterative Methods for Sparse Linear Systems
Mesh Generation: Application to Finite Elements
Mesh Generation: Application to Finite Elements
Applied Numerical Mathematics - Applied scientific computing: Advances in grid generation, approximation and numerical modeling
3D transient fixed point mesh adaptation for time-dependent problems: Application to CFD simulations
Journal of Computational Physics
Optimization Algorithms on Matrix Manifolds
Optimization Algorithms on Matrix Manifolds
Size gradation control of anisotropic meshes
Finite Elements in Analysis and Design
High-order sonic boom modeling based on adaptive methods
Journal of Computational Physics
Error estimation and anisotropic mesh refinement for 3d laminar aerodynamic flow simulations
Journal of Computational Physics
Original Articles: 3D Metric-based anisotropic mesh adaptation for vortex capture
Mathematics and Computers in Simulation
Continuous Mesh Framework Part II: Validations and Applications
SIAM Journal on Numerical Analysis
Time accurate anisotropic goal-oriented mesh adaptation for unsteady flows
Journal of Computational Physics
Hi-index | 31.46 |
This paper studies the coupling between anisotropic mesh adaptation and goal-oriented error estimate. The former is very well suited to the control of the interpolation error. It is generally interpreted as a local geometric error estimate. On the contrary, the latter is preferred when studying approximation errors for PDEs. It generally involves non local error contributions. Consequently, a full and strong coupling between both is hard to achieve due to this apparent incompatibility. This paper shows how to achieve this coupling in three steps. First, a new a priori error estimate is proved in a formal framework adapted to goal-oriented mesh adaptation for output functionals. This estimate is based on a careful analysis of the contributions of the implicit error and of the interpolation error. Second, the error estimate is applied to the set of steady compressible Euler equations which are solved by a stabilized Galerkin finite element discretization. A goal-oriented error estimation is derived. It involves the interpolation error of the Euler fluxes weighted by the gradient of the adjoint state associated with the observed functional. Third, rewritten in the continuous mesh framework, the previous estimate is minimized on the set of continuous meshes thanks to a calculus of variations. The optimal continuous mesh is then derived analytically. Thus, it can be used as a metric tensor field to drive the mesh adaptation. From a numerical point of view, this method is completely automatic, intrinsically anisotropic, and does not depend on any a priori choice of variables to perform the adaptation. 3D examples of steady flows around supersonic and transsonic jets are presented to validate the current approach and to demonstrate its efficiency.