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

## TL;DR

This paper introduces a moving control volume method for accurately computing hydrodynamic forces and torques on complex bodies within an immersed boundary framework, improving robustness and applicability across flow regimes.

## Contribution

It presents a novel moving control volume approach that simplifies force computation in immersed boundary methods, avoiding noisy derivatives and enabling use with adaptive meshes.

## Key findings

- Method effectively suppresses force oscillations.
- Excellent agreement with previous force/torque balance approaches.
- Applicable across a range of flow regimes from Stokes to high Reynolds numbers.

## Abstract

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.