Combined Immersed Boundary/Spectral Method for Large Eddy Simulation of Atmospheric Flows over Topography

Accurate modeling of atmospheric flows over topography plays an important role in the prediction of local weather in mountain areas and snow avalanche due to wind-induced snow redistribution. Large eddy simulation (LES) is a numerical technique in which only the large eddies of the turbulent motions are calculated and the net effect of the small eddies is modeled by a subgrid scale (SGS) model, hence practical grid sizes much larger than what is required to resolve all of the fluid motions can be used. The filtered Navier-Stokes and scalar transport equations are solved by spectral method due to its high-order accuracy. However, spectral method is limited to regular domain. With the help of terrain following coordinate transformation, it can be extended to handle topography with moderate slope. But the technique doesn’t work for topography with steep slope. In this work, we develop a Large Eddy Simulation code by combining Immersed Boundary Method (IBM) with Spectral Method. Without using fitted or unstructured grid, the influence of real topography on air flow is treated by the extended immersed boundary method [1], in which a body force is imposed to stop the flow inside the immersed boundary and additional treatment of wall modeling and turbulent stresses inside the solid body is implemented. The new-generation scale-dependent Lagrangian dynamic SGS model [2], which eliminates the need to specify tunable model coefficients, has been implemented together with IBM. The continuity equation is satisfied by the projection method. The resulting Poisson’s equation for pressure is coupled with the equation for immersed boundary force. They are solved iteratively, in which the solution of the Poisson’s equation is determined by a Fourier-based method. A cutting-cell approach without including the immersed boundary force explicitly is also considered and compared to the Fourier-based iterative method. When combining IBM with spectral-like methods, spurious oscillations occur in the calculated velocity derivatives near the immersed boundary. This is associated with the Gibbs phenomenon of spectral methods. A general smoothing technique based on radial basis function has been developed to reduce efficiently the Gibbs oscillation without affecting the flow field outside the body [3]. The developed code is validated against experimental results obtained from wind tunnels and field campaigns [4]. Numerical results and remaining challenges are discussed.