A Reduced Dissipation Approach for Unsteady Flows on

A reduced dissipation approach is developed for and studied on unstructured grids using the BCFD code. The approach, termed bounded central dierencing, or BCD, acts in two ways to reduce the inherent dissipation in the Roe scheme on arbitrary meshes. The proposed BCD approach blends several recent low dissipation approaches and adjusts them for a greater deal of robustness on unstructured grids of arbitrary element type. BCFD typically uses least squares cell-based gradients whose stencil involves all node neighbors. These gradients have been shown to be overly dissipative for unsteady simulations. To lessen the dissipation in the BCD approach, the component of the derivative in the edge direction is replaced with 50% of the central dierence derivative based on the cell center data of the parent and face neighbor cells. Second, the Roe dissipation term is allowed to be decreased by an amount determined from the parameter fd from the Delayed Detached Eddy Simulation (DDES) method in combination with a wiggle detector and grid quality metric. This approach ensures that the simulation recovers the full Roe scheme in the RANS region, while allowing a more central-dierence -like behavior far from the walls where typically it is desired to resolve eddy structures. An important distinguishing factor of the current method is its attention to regions of poor grid quality. Performance of the approach is tested in decaying isotropic turbulence for dierent grid resolutions and two topologies, on a NACA 0021 airfoil, and on a typical commercial aircraft flap edge where acoustics are of concern. All test cases are compared to experimental data when available. In all cases, the BCD approach delivered favorable results and was shown to be robust across many grid types/resolutions.