High-order methods and mesh adaptation for Euler equations

• Published in: International journal for numerical methods in fluids Vol. 56; no. 8; pp. 1069 - 1076
• Main Author: Alauzet, F.
• Format: Journal Article Conference Proceeding
• Language: English
• Published: Chichester, UK John Wiley & Sons, Ltd 20-03-2008; Wiley
• Subjects: anisotropic mesh adaptation; Computational methods in fluid dynamics; Euler equations; Exact sciences and technology; Fluid dynamics; Fundamental areas of phenomenology (including applications); high-order method; Physics; unstructured meshes; Three dimensional flow; Computational fluid dynamics; Anisotropy; Digital simulation; anisotropic mesh adaptation; Modelling; Euler equations; Adaptive method; Numerical convergence; Mesh generation; high-order method; unstructured meshes
• ISSN: 0271-2091; 1097-0363
• DOI: 10.1002/fld.1739

In this paper, we point out a novel contribution of mesh adaptation to high‐order methods for stationary and time‐dependent problems. From theoretical results, we exhibit that mesh adaptation, based on an adjoint‐free method, achieves a global second‐order mesh convergence for numerical solutions with discontinuities in Lp norm. To attain this result, it is mandatory to combine together all mesh adaptive methods developed in the previous work. This theoretical result is validated on 2D and 3D examples for stationary and time‐dependent simulations. Copyright © 2008 John Wiley & Sons, Ltd.