High-Order Vertex-Centered U-MUSCL Schemes for Turbulent Flows (Communications in Computational Physics, 2018)
Many production and commercial unstructured CFD codes provide no better than 2nd-order spatial accuracy. Unlike structured grid procedures where thereis an implied structured connectivity between neighboring grid points, for unstructured grids, it is more difficult to compute higher derivatives due to a lack of explicitconnectivity beyond the first neighboring cells. Our goal is to develop a modular high-order scheme with low dissipation flux difference splitting that can be integrated intoexisting CFD codes for use in improving the solution accuracy and to enable betterprediction of complex physics and noise mechanisms and propagation. In a previousstudy, a 3rd-order U-MUSCL scheme using a successive differentiation method wasderived and implemented in FUN3D. Verification studies of the acoustic benchmarkproblems showed that the new scheme can achieve up to 4th-order accuracy. Application of the high-order scheme to acoustic transport and transition-to-turbulenceproblems demonstrated that with just 10% overhead, the solution accuracy can be dramatically improved by as much as a factor of eight. This paper examines the accuracyof the high-order scheme for turbulent flow over single and tandem cylinders. Considerably better agreement with experimental data is observed when using the new3rd-order U-MUSCL scheme.