Toulorge, Thomas
[UCL]
Geuzaine, Christophe
[Universite de Liege]
Remacle, Jean-François
[UCL]
Lambrechts, Jonathan
[UCL]
In the recent years, high-order numerical methods have been shown to yield superior computational efficiency in problems with high resolution requirements, compared to standard second-order solvers based on Finite Volume technology. As the development of high-order schemes such as the Discontinuous Galerkin method is being brought to the level of practical application, many contributions show that the accuracy can be limited by the geometrical discretization. High-order meshes are thus necessary to fully benefit from the efficiency of high-order schemes. However, curvilinear mesh generation methods still suffer from major drawbacks in terms of robustness and computational efficiency. The first step in the creation of a high-order mesh consists in building a linear mesh, and then curving its boundaries to match the geometry. This often results in tangled elements, that can be identified by a change of sign in the Jacobian of the transformation from their straight-sided counterpart. In this talk, we propose a robust technique that allows to build a curvilinear mesh for which every element is guaranteed to be valid. It consists in solving a sequence of unconstrained optimization problems that progressively bring the Jacobian of each element within a user-defined range, through the use of moving log-barriers. A key ingredient of the method is the reliable estimation of the Jacobian bounds. The procedure is applied to patches of elements surrounding an invalid element, instead of the whole mesh, for the sake of computational efficiency. We demonstrate the benefits of our technique with several high-order meshes built for realistic applications. The time needed to curve them ranges from a split second to a few minutes. We also show how the method can be extended to control the numerical effects of the mesh in solvers, such as the time step allowed with explicit time integration.
Bibliographic reference |
Toulorge, Thomas ; Geuzaine, Christophe ; Remacle, Jean-François ; Lambrechts, Jonathan. Generation of Provably Correct High-Order meshes.Advances in Computational Mechanics (ACM 2013) - Finite Elements in Flow Problems (FEF 2013) (San Diego, USA, du 24/02/2013 au 27/06/2013). |
Permanent URL |
http://hdl.handle.net/2078.1/130557 |