Computing the force distribution on the surface of complex, deforming geometries using vortex methods and Brinkman penalization

Abstract

The distribution of forces on the surface of complex, deforming geometries is an invaluable output of flow simulations. One particular example of such geometries involves self-propelled swimmers. Surface forces can provide significant information about the flow field sensed by the swimmers, and are difficult to obtain experimentally. At the same time, simulations of flow around complex, deforming shapes can be computationally prohibitive when body-fitted grids are used. Alternatively, such simulations may employ penalization techniques. Penalization methods rely on simple Cartesian grids to discretize the governing equations, which are enhanced by a penalty term to account for the boundary conditions. They have been shown to provide a robust estimation of mean quantities, such as drag and propulsion velocity, but the computation of surface force distribution remains a challenge. We present a method for determining flow- induced forces on the surface of both rigid and deforming bodies, in simulations using re-meshed vortex methods and Brinkman penalization. The pressure field is recovered from the velocity by solving a Poisson's equation using the Green's function approach, augmented with a fast multipole expansion and a tree- code algorithm. The viscous forces are determined by evaluating the strain-rate tensor on the surface of deforming bodies, and on a 'lifted' surface in simulations involving rigid objects. We present results for benchmark flows demonstrating that we can obtain an accurate distribution of flow-induced surface-forces. The capabilities of our method are demonstrated using simulations of self-propelled swimmers, where we obtain the pressure and shear distribution on their deforming surfaces.