A symmetric positive definite formulation for monolithic fluid structure interaction

Robinson-Mosher, Avi; Schroeder, Craig; Fedkiw, Ronald

A symmetric positive definite formulation for monolithic fluid structure interaction

Type

Article

Authors

Robinson-Mosher, Avi
Schroeder, Craig
Fedkiw, Ronald

KAUST Grant Number

42959

Date

2011-02

Abstract

In this paper we consider a strongly coupled (monolithic) fluid structure interaction framework for incompressible flow, as opposed to a loosely coupled (partitioned) method. This requires solving a single linear system that combines the unknown velocities of the structure with the unknown pressures of the fluid. In our previous work, we were able to obtain a symmetric formulation of this coupled system; however, it was also indefinite, making it more difficult to solve. In fact in practice there have been cases where we have been unable to invert the system. In this paper we take a novel approach that consists of factoring the damping matrix of deformable structures and show that this can be used to obtain a symmetric positive definite system, at least to the extent that the uncoupled systems were symmetric positive definite. We use a traditional MAC grid discretization of the fluid and a fully Lagrangian discretization of the structures for the sake of exposition, noting that our procedure can be generalized to other scenarios. For the special case of rigid bodies, where there are no internal damping forces, we exactly recover the system of Batty et al. (2007) [4]. © 2010 Elsevier Inc.

Citation

Robinson-Mosher A, Schroeder C, Fedkiw R (2011) A symmetric positive definite formulation for monolithic fluid structure interaction. Journal of Computational Physics 230: 1547–1566. Available: http://dx.doi.org/10.1016/j.jcp.2010.11.021.

Acknowledgements

Research supported in part by a Packard Foundation Fellowship, an Okawa Foundation Research Grant, ONR N0014-06-1-0393, ONR N00014-06-1-0505, ONR N00014-05-1-0479 for a computing cluster, NIH U54-GM072970, NSF ACI-0323866, NSF IIS-0326388, and King Abdullah University of Science and Technology (KAUST) 42959. C.S. was supported in part by a Stanford Graduate Fellowship.