A continuous-mesh optimization technique for piecewise polynomial approximation on tetrahedral grids

• ID: 2816, RIV: 10384600
• ISSN: not specified, ISBN: 978-1-5108-6886-1
• source: 48th AIAA Fluid Dynamics Conference 2018
• keywords: continuous-mesh optimization technique; piecewise polynomial approximation; tetrahedral grids
• authors: Ajay Rangarajan, Ankii Chakraborry, Georg May, Vít Dolejší
• authors from KNM: Dolejší Vít

Abstract

Building on previous research we present a three-dimensional formulation of a metricbased mesh optimization scheme. The intended application area is higher order (discontinuous) Galerkin schemes for convection-diffusion problems. Ultimately, as in our previous two-dimensional formulation, the aim is to use the method for compressible flow simulation. Similar to the two-dimensional formulation, we combine a local (analytical) optimization of the anisotropy with an ensuing global optimization of the mesh density distribution. In particular the local optimization of the mesh anisotropy is a non-trivial extension of the two-dimensional case. Both optimization steps are built on a suitable continuous-mesh error estimate. The scheme is parameter-free, using only the total integrated mesh density as a constraint. We present the derivation of the method, as well as numerical experiments using model problems.