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An immersed boundary method wall model for high-Reynolds-number channel flow over complex topography


Correspondence to: William Anderson, Mechanical Engineering Department, Baylor University, One Bear Place #97356, Waco, Texas 76798-7356, USA.



High-Reynolds-number channel flows regularly encounter topographies composed of multiple length scales and that protrude into the boundary layer. Physically, the presence of immersed obstacles leads to increased velocity gradients, turbulence production, and manifestation of wakes. Considerable challenges are associated with numerically describing the presence of obstacles in channel flows. Common approaches include generation of a computational mesh that is uniquely designed for the flow and obstacle, the immersed boundary method, and terrain-following coordinates. There are challenges and limitations associated with each of these techniques. Specification of boundary conditions representing the perimeter of solid obstacles is a primary challenge of the immersed boundary method. In this document, a simplistic canopy stress-like wall model is used to impose boundary conditions. The model isolates aerodynamically relevant local frontal areas through evaluation of the gradient of the topographic height field. The gradient of the height field describes both the surface-normal direction and the frontal area, making it ideal for detecting areas on which the flow impinges. The model is tested in numerical simulations of turbulent half-channel flow over topographies with different obstacles affixed–right prisms, rectangular prisms, ellipsoidal mounds, and sinusoids. In all cases, the performance is strong relative to datasets presented in the literature. Results are finally presented for numerical simulation of flow over complex synthetic fractal-like topography and a synthetic city. These results show interesting trends in how the turbulent multiscale flow field responds to multiscale topography. Copyright © 2012 John Wiley & Sons, Ltd.

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