Anisotropic Goal‐oriented error analysis for a third‐order accurate CENO Euler discretization

Alexandre Carabias 1 Anca Belme 2 Adrien Loseille 3 Alain Dervieux 4
1 SCIPORT - Program transformations for scientific computing
CRISAM - Inria Sophia Antipolis - Méditerranée
2 IJLRDA-FCIH - Fluides Complexes et Instabilités Hydrodynamiques
DALEMBERT - Institut Jean Le Rond d'Alembert
3 Gamma3 - Automatic mesh generation and advanced methods
Inria Paris-Rocquencourt, ICD - Institut Charles Delaunay
Abstract : In this paper a central-ENO 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 CENO 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 discretised and solved using a global unsteady fixed point algorithm. The method is applied to an acoustic propagation benchmark.
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https://hal.sorbonne-universite.fr/hal-01579998
Contributor : Anca Belme <>
Submitted on : Thursday, August 31, 2017 - 9:54:23 PM
Last modification on : Monday, July 8, 2019 - 4:52:02 PM

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Alexandre Carabias, Anca Belme, Adrien Loseille, Alain Dervieux. Anisotropic Goal‐oriented error analysis for a third‐order accurate CENO Euler discretization. International Journal for Numerical Methods in Fluids, Wiley, 2017, 86 (6), pp.392-413. ⟨10.1002/fld.4423⟩. ⟨hal-01579998⟩

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