A stable partitioned FSI algorithm for rigid bodies and incompressible flow. Part I: Model problem analysis

TL;DR

This paper introduces a stable partitioned fluid-structure interaction algorithm that effectively handles added-mass and added-damping effects for rigid bodies in viscous incompressible flows, validated through analysis and simulations.

Contribution

The paper develops a novel AMP algorithm that remains stable without sub-iterations for light or zero mass rigid bodies, incorporating advanced Robin interface conditions and damping tensors.

Findings

The AMP scheme is stable for light and zero mass bodies.

Traditional schemes become unstable due to added-mass or damping effects.

Numerical simulations confirm second-order accuracy of the proposed method.

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 first part of a two-part series, the properties of the AMP scheme are motivated and evaluated through the development and analysis of some model problems. The analysis shows when and why the traditional partitioned scheme becomes unstable due to either added-mass or added-damping effects. The analysis also identifies the proper form of the added-damping which depends on the discrete time-step and the grid-spacing normal to the rigid body. The results of the analysis are confirmed with numerical simulations that also demonstrate a second-order accurate implementation of the AMP scheme.