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

Abstract

Summary 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 use 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 remeshed 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.

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A moving control volume approach to computing hydrodynamic forces and torques on immersed bodies

“…Here we list a few of them. Verma et al [38] have recommended using a "lifted" surface: a surface two grid cell distance away from the actual interface to avoid choppy velocity gradients. This recommendation, based upon their empirical tests using a Brinkman penalization method, can change depending on the smoothness of the problem and the discrete delta function used in IB methods.…”

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“…Authors who have applied the DLM method within the immersed boundary or fictitious domain methods include Glowinski et al (1995), Glowinski et al (1997Glowinski et al ( , 1998, EC 38,4 Boffi et al (2015), Boffi and Gastaldi (2017), Kadapa et al (2016) and Sun (2019). Examples of the penalty approach being used within the immersed boundary or fictitious domain methods are Goldstein et al (1993), Khadra et al (2000), Viré et al (2012Viré et al ( , 2015, Viré et al (2016), Kim and Peskin (2016), Verma et al (2017) and Specklin and Delauré (2018).…”