A moving control volume approach to computing hydrodynamic forces and torques on immersed bodies
This work provides a robust force/torque computation method for immersed boundary methods, reducing numerical noise for researchers simulating fluid-structure interactions.
The authors present a moving control volume approach for computing hydrodynamic forces and torques on immersed bodies, which avoids noisy derivatives at fluid-structure interfaces by using far-field velocity and pressure. The method is validated across Stokes to high Reynolds number regimes, showing suppression of spurious force oscillations and excellent agreement with prior work.
We present a moving control volume (CV) approach to computing hydrodynamic forces and torques on complex geometries. The method requires surface and volumetric integrals over a simple and regular Cartesian box that moves with an arbitrary velocity to enclose the body at all times. The moving box is aligned with Cartesian grid faces, which makes the integral evaluation straightforward in an immersed boundary (IB) framework. Discontinuous and noisy derivatives of velocity and pressure at the fluid-structure interface are avoided and far-field (smooth) velocity and pressure information is used. We re-visit the approach to compute hydrodynamic forces and torques through force/torque balance equation in a Lagrangian frame that some of us took in a prior work (Bhalla et al., J Comp Phys, 2013). We prove the equivalence of the two approaches for IB methods, thanks to the use of Peskin's delta functions. Both approaches are able to suppress spurious force oscillations and are in excellent agreement, as expected theoretically. Test cases ranging from Stokes to high Reynolds number regimes are considered. We discuss regridding issues for the moving CV method in an adaptive mesh refinement (AMR) context. The proposed moving CV method is not limited to a specific IB method and can also be used, for example, with embedded boundary methods.