Numerical Simulations of Stably Stratified Flows around Complex Terrain using the Immersed Boundary Method

The Immersed Boundary (IB) method, integrated with the large-eddy simulation technique, has been developed further to model neutrally stratified atmospheric flows over complex terrains. This advancement involves a logarithmic IB reconstruction scheme that accounts for surface parameterization of momentum flux and enhances the subgrid-scale viscosity using a Reynolds-averaged Navier-Stokes (RANS)-based eddy viscosity model. Extending this approach to stably stratified atmospheric flows, however, presents challenges due to the need for simultaneous representation of both momentum and temperature fields using the IB method. In this study, we introduce an IB reconstruction scheme based on an extended version of the Monin-Obukhov Similarity Theory (MOST) and propose a stability-dependent correction to the eddy viscosity model, particularly near the surface. We validate our model against direct numerical simulations of stably stratified flows over both a periodic hill and flat terrain.