Mesh Curving and Refinement Based on Cubic Bézier Surface for High-Order Discontinuous Galerkin Methods

Abstract

In this paper, three-dimensional mesh curving and refinement methods are examined for high-order flow simulations with discontinuous Galerkin (DG) methods on hybrid grids. The mesh curving algorithm converts linear surface elements to quadratic ones with the cubic Bézier surface reconstruction. The effects of mesh curving on the impacts of DG solutions of the Euler and Navier–Stokes equations are investigated. Numerical results show that significant enhancements of accuracy and robustness can be gained for DG solutions of smooth and discontinuous flow fields. Additionally, a curved mesh refinement algorithm is also realized by inquiring the midpoints of edges and faces of the reconstructed quadratic elements. With this method, up to 0.9 billons curved elements are successfully generated around the DLR-F6 wing/body/nacelle/pylon configuration.