A moving control volume approach to computing hydrodynamic forces and torques on immersed bodies
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 fluidstructure interface are avoided and farfield (smooth) velocity and pressure information is used. We revisit the approach to compute hydrodynamic forces and torques through force/torque balance equations in a Lagrangian frame that some of us took in a prior work (Bhalla et al., 2013 [13]). 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.
 Publication:

Journal of Computational Physics
 Pub Date:
 October 2017
 DOI:
 10.1016/j.jcp.2017.06.047
 arXiv:
 arXiv:1704.00239
 Bibcode:
 2017JCoPh.347..437N
 Keywords:

 Immersed boundary method;
 Spurious force oscillations;
 Reynolds transport theorem;
 Adaptive mesh refinement;
 Fictitious domain method;
 Lagrange multipliers;
 Mathematics  Numerical Analysis
 EPrint:
 doi:10.1016/j.jcp.2017.06.047