An adaptive mesh refinement approach for high Reynolds number flows over immersed bodies

The Lattice Green's Function (LGF) has been fruitfully combined with the immersed-boundary (IB) method for efficient, scalable simulation of incompressible, external flows. A significant source of computational savings is the snug domain enabled by only requiring grid cells in vortical flow regions and truncating them in the far wake. However, at high Reynolds numbers, the uniform grid required by the LGF is inefficient for resolving thin boundary layers. To alleviate this constraint, we develop an adaptive mesh refinement method compatible with the LGF and IB formulations. We perform accurate DNS of flows over immersed bodies of arbitrary shape and complexity at Reynolds numbers on the order of 10000 while reducing the number of computational cells by 99.5% compared to a non-adaptive method. The framework is also efficient for simulating the effects of gusts on immersed bodies, particularly when they are represented as unsteady potential flows which can be imposed in our method without resolving the potential flow region. We demonstrate both steady and gusting flows over airfoils and compare our results with companion experiments in the IIT unsteady wind tunnel.