High-Order Numerical Simulation of Turbulent Flow Over a Wall-Mounted Hump

Abstract

The development of a high-order spatial discretization for a k-e turbulence model and its application to flow over a wall-mounted hump is described. The high-order implementation is validated for a flat plate and subsequently applied to the more complex wall-mounted hump for conditions with and without flow control. Results for the hump flow are compared to experimental data. The turbulence model is incorporated in an implicit parallel flow solver that is based on an approximately factored time-integration method coupled with spatially fourth- and sixth-order compact-difference formulations and a high-order filtering strategy. Both second-order and high-order discretizations of the k-e turbulence equations were included in the compact solver. Validation using flow over a flat plate demonstrated that use of a second-order scheme for the k-∈ turbulence equations dominates the solution even when high-order compact differencing is used for the flow equations. This validation also demonstrated that significant computational savings are possible because less mesh resolution is required when using a high-order discretization of the k-e turbulence equations. Comparison of the high-order and second-order solutions was also performed for the wall-mounted hump. Qualitative agreement was achieved with experimental data for both high-and low-order schemes. High-order solutions on a coarse grid agreed very well with second-order solutions on a considerably finer grid.