A moving control volume approach to computing hydrodynamic forces and torques on immersed bodies. (English) Zbl 1380.76106

Nangia, Nishant; Johansen, Hans; Patankar, Neelesh A.; Bhalla, Amneet Pal Singh

J. Comput. Phys. 347, 437-462 (2017).

Summary: 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 equations in a Lagrangian frame that some of us took in a prior work [the last author et al., ibid. 250, 446–476 (2013; Zbl 1349.65403)]. 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.

MSC:

76M25	Other numerical methods (fluid mechanics) (MSC2010)
65M85	Fictitious domain methods for initial value and initial-boundary value problems involving PDEs
65M50	Mesh generation, refinement, and adaptive methods for the numerical solution of initial value and initial-boundary value problems involving PDEs

Keywords:

immersed boundary method; spurious force oscillations; Reynolds transport theorem; adaptive mesh refinement; fictitious domain method; Lagrange multipliers

Citations:

Zbl 1349.65403

Software:

PETSc; SAMRAI

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