Accurate Cartesian-grid simulations of near-body flows at intermediate Reynolds numbers

An accurate Cartesian-grid treatment for intermediate Reynolds number fluid-solid interaction problems is described. We first identify the inability of existing immersed boundary methods to handle intermediate Reynolds number flows to be the discontinuity of the velocity gradient at the interface. We address this issue by generalizing the Boundary Data Immersion Method (BDIM, Weymouth and Yue, J. Comp. Phys., vol. 230, 2011), in which the field equations of each domain are combined analytically, through the addition of a higher order term to the integral formulation. The new method, featuring a second-order convolution, retains the desirable simplicity of direct forcing methods and smoothes the velocity field at the fluid-solid interface while removing its bias. This results in accurate flow predictions and pressure fields without spurious fluctuations, even at high Reynolds number where the method is second order in the L2 norm. A treatment for sharp corners is also derived that significantly improves the flow predictions near the trailing edge of thin airfoils. The second-order BDIM is applied to unsteady problems relevant to ocean energy extraction as well as animal and vehicle locomotion for Reynolds numbers up to 10.