(untitled) (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 on stretched and curvilinear meshes. Although the conception of HILES is similar to that of monotone integrated LES (MILES), i.e., truncation error of the discretization scheme itself is employed to model the effects of unresolved scales, HDCS-E8T7 is a new high-order finite difference scheme, which can eliminate the surface conservation law (SCL) errors and has inherent dissipation. The capability of HILES is tested by solving several benchmark cases. In the case of flow past a circular cylinder, the solutions of HILES fulfilling the SCL have good agreement with the corresponding experiment data, however, the flow field is gradually contaminated when the SCL error is enlarged. With the help 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 of HILES in simulating turbulent flow on complex configuration.