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.
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