We investigate a Cartesian-mesh immersed-boundary formulation within an incompressible flow solver to simulate laminar and turbulent katabatic slope flows. As a proof-of-concept study, we consider four different immersedboundary reconstruction schemes for imposing a Neumann-type boundary condition on the buoyancy field. Prandtl's laminar solution is used to demonstrate the second-order accuracy of the numerical solutions globally. Direct numerical simulation of a turbulent katabatic flow is then performed to investigate the applicability of the proposed schemes in the turbulent regime by analyzing both first-and second-order statistics of turbulence. First-order statistics show that turbulent katabatic flow simulations are noticeably sensitive to the specifics of the immersed-boundary formulation. We find reconstruction schemes that work well in the laminar regime may not perform as well when applied to a turbulent regime. Our proposed immersed-boundary reconstruction scheme agrees closely with the terrain-fitted reference solutions in both flow regimes.
Turbulent katabatic (downslope) flow under stable stratification over a cool surface remains a poorly understood subject, which finds application in geophysical flows. This work investigates an immersed boundary (IB) formulation within a multi-graphics-processing-unit (GPU) parallel incompressible flow solver to impose velocity and heat flux boundary conditions to simulate fundamental katabatic flows. Prandtl\u27s analytical solution for laminar katabatic flow is used to develop an IB formulation to impose heat flux boundary conditions, and to assess its formal order of accuracy. Direct numerical simulation of turbulent katabatic flow is then performed to investigate the applicability of proposed schemes in the turbulent regime. Results from first order statistics show that turbulent katabatic flow simulations are sensitive to the specifics of the IB formulation, and IB schemes that work well for the laminar regime do not readily apply to the turbulent regime. A reconstruction scheme is proposed that performs well in both the laminar and turbulent regime
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