Validations of flux reconstruction CFD on hybrid unstructured grids and application to low-Reynolds number transitional flow

Abstract

The flux reconstruction (FR) method, a high-order accurate solution method for unstructured grid CFD, is known as a method with a smaller computational load than the traditional discontinuous Galerkin method. It also contains other discrete spectral element methods by properly selecting the flux correction function. The 1D and tensor-product FR method is intuitively easy to understand, but the general-purpose automatic computational grid generation also requires tetrahedral, prism, and pyramid elements, which are not yet in general use for high-order CFD due to the complexity of their formulation and implementation. In this study, we extended an in-house FR CFD to hybrid elements, verified the accuracy in benchmark problems, and confirmed its applicability to low Reynolds number separated flows around an airfoil. The detailed formula for the pyramid are rarely found and they are elaborated in this study. For all types of elements mentioned above, we confirmed that the ideal accuracies (mesh convergence of errors) are achieved. For the application to a low-Reynolds-number transitional flows around an airfoil, the results well agreed with other high-order CFD results with more degrees of freedom.