Donald W. Schwendeman

Daniel A. Serino, Jeffrey W. Banks, William D. Henshaw et al.

A stable added-mass partitioned (AMP) algorithm is developed for fluid-structure interaction (FSI) problems involving viscous incompressible flow and compressible elastic solids. Deforming composite grids are used to effectively handle the evolving geometry and large deformations. The fluid is updated with an implicit-explicit (IMEX) fractional-step scheme whereby the velocity is advanced in one step, treating the viscous terms implicitly, and the pressure is computed in a second step. The AMP interface conditions for the fluid arise from the outgoing characteristic variables in the solid and are partitioned into a Robin (mixed) interface condition for the pressure, and interface conditions for the velocity. The latter conditions include an impedance-weighted average between fluid and solid velocities using a fluid impedance of a special form. A similar impedance-weighted average is used to define interface values for the solid. The new algorithm is verified for accuracy and stability on a number of useful benchmark problems including a radial-piston problem where exact solutions for radial and azimuthal motions are found and tested. Traveling wave exact solutions are also derived and numerically verified for a solid disk surrounded by an annulus of fluid. Fluid flow in a channel past a deformable solid annulus is computed and errors are estimated from a self-convergence grid refinement study. The AMP scheme is found to be stable and second-order accurate even for very difficult cases of very light solids.

Daniel A. Serino, Jeffrey W. Banks, William D. Henshaw et al.

A stable added-mass partitioned (AMP) algorithm is developed for fluid-structure interaction (FSI) problems involving viscous incompressible flow and compressible elastic-solids. The AMP scheme remains stable and second-order accurate even when added-mass and added-damping effects are large. The fluid is updated with an implicit-explicit (IMEX) fractional-step scheme whereby the velocity is advanced in one step, treating the viscous terms implicitly, and the pressure is computed in a second step. The AMP interface conditions for the fluid arise from the outgoing characteristic variables in the solid and are partitioned into a Robin (mixed) interface condition for the pressure, and interface conditions for the velocity. The latter conditions include an impedance-weighted average between fluid and solid velocities using a fluid impedance of a special form. A similar impedance-weighted average is used to define interface values for the solid. The fluid impedance is defined using material and discretization parameters and follows from a careful analysis of the discretization of the governing equations and coupling conditions near the interface. A normal mode analysis is performed to show that the AMP scheme is stable for a few carefully-selected model problems. Two extensions of the analysis in Banks et al. are considered, including a first-order accurate discretization of a viscous model problem and a second-order accurate discretization of an inviscid model problem. The AMP algorithm is shown to be stable for any ratio of solid and fluid densities, including when added-mass effects are large. The algorithm is verified for accuracy and stability for a set of new exact benchmark solutions where finite interface deformations are permitted. The AMP scheme is found to be stable and second-order accurate even for very difficult cases of very light solids.