Anisotropic goal‐oriented error analysis for a third‐order accurate CENO Euler discretization |
| |
Authors: | A Carabias A Belme A Loseille A Dervieux |
| |
Institution: | 1. Université C?te d'Azur, Biot 06410, France;2. Sorbonne Universités, UPMC Univ PAris 06, F‐75005 Paris, France;3. Inria Saclay Ile‐de‐France, Projet Gamma3, Palaiseau 91126, France |
| |
Abstract: | In this paper, a central essentially non‐oscillatory approximation based on a quadratic polynomial reconstruction is considered for solving the unsteady 2D Euler equations. The scheme is third‐order accurate on irregular unstructured meshes. The paper concentrates on a method for a metric‐based goal‐oriented mesh adaptation. For this purpose, an a priori error analysis for this central essentially non‐oscillatory scheme is proposed. It allows us to get an estimate depending on the polynomial reconstruction error. As a third‐order error is not naturally expressed in terms of a metric, we propose a least‐square method to approach a third‐order error by a quadratic term. Then an optimization problem for the best mesh metric is obtained and analytically solved. The resulting mesh optimality system is discretized and solved using a global unsteady fixed‐point algorithm. The method is applied to an acoustic propagation benchmark. |
| |
Keywords: | compressible flow error estimation Euler flow finite volume hyperbolic mesh adaptation |
|
|