Nesting an incompressible-flow code within a compressible-flow code: A two-dimensional study

We consider numerical algorithms appropriate for one- and two-way coupling between meso-scale and micro-scale fluid-dynamics codes for wind energy computing. At the meso-scale is a numerical weather-prediction code, which is typically based on the compressible-flow Euler equations. At the micro-scale, surrounding one or more wind turbines, is a computational fluid dynamics code, which is typically based on the incompressible-flow Navier-Stokes equations. When calculating short-duration flow around wind turbines, one-way coupling is sufficient, where the meso-scale computational model drives the micro-scale model. However, in long-duration simulations involving large wind farms, the influence of the wind farm on the meso-scale weather may no longer be insignificant and two-way coupling is warranted. In this study, we focus on a simple two-dimensional system, for which our goal is to devise one- and two-way coupling algorithms that can effectively transport a vortex propagating in laminar flow from one domain to the other. Two coupling schemes and their numerical implementation are described: partial-boundary coupling and projection coupling. In the former, the micro-scale-domain boundary is decomposed, based on the meso-scale solution, into sections corresponding to inflow and outflow. The micro-scale model has Dirichlet- and Neumann-type boundary conditions on these sections, respectively. In projection coupling, the meso-scale solution is projected onto the incompressible-flow solution space in the micro-scale domain, from which Dirichlet-type boundary conditions are derived. In these simulations, the uncoupled meso-scale solution is taken as the reference, and the best coupling method is that which produces solutions that deviate the least from the reference. In one-way coupling, under a simple two-dimensional laminar-flow test case, partial-boundary coupling was more effective than projection coupling. However, in two-way coupling, projection coupling was the best performer.