A stable partitioned FSI algorithm for rigid bodies and incompressible flow. Part II: General formulation

TL;DR

This paper introduces a stable, non-iterative partitioned fluid-structure interaction algorithm for rigid bodies and incompressible flow, capable of handling light or zero mass bodies with large added-mass and damping effects, verified through benchmark tests.

Contribution

It presents a general formulation of the added-mass partitioned (AMP) scheme with interface conditions and damping tensors for complex geometries, advancing stability and accuracy in FSI simulations.

Findings

The AMP scheme remains stable without sub-iterations for light and zero mass bodies.

The scheme achieves second-order accuracy in two-dimensional simulations.

Numerical verification confirms robustness on challenging benchmark problems.

Abstract

A stable partitioned algorithm is developed for fluid-structure interaction (FSI) problems involving viscous incompressible flow and rigid bodies. This {\em added-mass partitioned} (AMP) algorithm remains stable, without sub-iterations, for light and even zero mass rigid bodies when added-mass and viscous added-damping effects are large. The scheme is based on a generalized Robin interface condition for the fluid pressure that includes terms involving the linear acceleration and angular acceleration of the rigid body. Added mass effects are handled in the Robin condition by inclusion of a boundary integral term that depends on the pressure. Added-damping effects due to the viscous shear forces on the body are treated by inclusion of added-damping tensors that are derived through a linearization of the integrals defining the force and torque. Added-damping effects may be important at low Reynolds number, or, for example, in the case of a rotating cylinder or rotating sphere when the rotational moments of inertia are small. In this second part of a two-part series, the general formulation of the AMP scheme is presented including the form of the AMP interface conditions and added-damping tensors for general geometries. A fully second-order accurate implementation of the AMP scheme is developed in two dimensions based on a fractional-step method for the incompressible Navier-Stokes equations using finite difference methods and overlapping grids to handle the moving geometry. The numerical scheme is verified on a number of difficult benchmark problems.