Extending Seventh-Order Dissipative Compact Scheme Satisfying Geometric Conservation Law to Large Eddy Simulation on Curvilinear Grids (Advances in Applied Mathematics and Mechanics, 2018)
Seventh-order hybrid cell-edge and cell-node dissipative compact scheme(HDCS-E8T7) is extended to a new implicit large eddy simulation named HILES onstretched and curvilinear meshes. Although the conception of HILES is similar to thatof monotone integrated LES (MILES), i.e., truncation error of the discretization schemeitself is employed to model the effects of unresolved scales, HDCS-E8T7 is a new high-orderfinite difference scheme, which can eliminate the surface conservation law (SCL)errors and has inherent dissipation. The capability of HILES is tested by solving severalbenchmark cases. In the case of flow past a circular cylinder, the solutions of HILESfulfilling the SCL have good agreement with the corresponding experiment data, however,the flow field is gradually contaminated when the SCL error is enlarged. With thehelp of fulling the SCL, ability of HILES for handling complex geometry has been enhanced.The numerical solutions of flow over delta wing demonstrate the potential ofHILES in simulating turbulent flow on complex configuration.