Development of a High-Order Flux Reconstruction Scheme for Body-Fitted Cartesian Unstructured Grids

Abstract

A high-order flux reconstruction (FR) scheme on unstructured hexahedral grids is developed for aerospace flow simulation. In order to use computational grids generated by the body-fitted Cartesian (BFC) method, the grid which contains polyhedral cells with hanging nodes are subdivide into hexahedral cells first. Then, to perform computation by the FR scheme on the non-conformal hexahedral grid, the mortal element method (MEM) is employed to determine the numerical flux at cell interface. As a shock capturing scheme, the localized artificial diffusivity (LAD) method is developed for the FR scheme. The developed scheme is tested for typical benchmark problems including smooth and shocked flows. I. Introduction HE use of CFD in designing aerospace vehicles has been growing over the past decades. Commercial CFD software can be effectively used for early stage of the design process with the reasonable accuracy in quick turn around time. The finite volume methods (FVM) are widely used for the commercial and industrial CFD solvers, but the spatial order of accuracy is remained less than 2 nd -order due to several reasons mainly related to the robustness. In order to tackle more complicated flowfields and to improve the prediction accuracy by CFD, employing highorder methods is one of the prospective directions. It is well known that high-order methods can give the numerical solution more efficiently than the low-order methods with the same level of accuracy if the flowfield is sufficiently smooth. High-order methods were developed and investigated first in the context of the structured or multi-block structured grids. The formal order of accuracy can be retained with the relatively better quality mesh in contrast to the case with unstructured grids. A main drawback with structured grids is the difficulty in the mesh generation around complex geometries. Therefore, unstructured methods are often used in the production codes. Automated processes in the unstructured grid generation has facilitated the routinely works in the design cycle and has gained more users in the wide engineering areas. A criticism for this approach is related to the solution accuracy especially on the dirty grid around real complicated configurations. Recent research for the reconstruction of the solution gradient