  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.
