A symmetric positive definite formulation for monolithic fluid structure interaction

Handle URI:
http://hdl.handle.net/10754/597419
Title:
A symmetric positive definite formulation for monolithic fluid structure interaction
Authors:
Robinson-Mosher, Avi; Schroeder, Craig; Fedkiw, Ronald
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.
Publisher:
Elsevier BV
Journal:
Journal of Computational Physics
KAUST Grant Number:
42959
Issue Date:
Feb-2011
DOI:
10.1016/j.jcp.2010.11.021
Type:
Article
ISSN:
0021-9991
Sponsors:
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.
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Publications Acknowledging KAUST Support

Full metadata record

DC FieldValue Language
dc.contributor.authorRobinson-Mosher, Avien
dc.contributor.authorSchroeder, Craigen
dc.contributor.authorFedkiw, Ronalden
dc.date.accessioned2016-02-25T12:32:51Zen
dc.date.available2016-02-25T12:32:51Zen
dc.date.issued2011-02en
dc.identifier.citationRobinson-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.en
dc.identifier.issn0021-9991en
dc.identifier.doi10.1016/j.jcp.2010.11.021en
dc.identifier.urihttp://hdl.handle.net/10754/597419en
dc.description.abstractIn 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.en
dc.description.sponsorshipResearch 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.en
dc.publisherElsevier BVen
dc.subjectFluid structure interactionen
dc.subjectIncompressible flowen
dc.titleA symmetric positive definite formulation for monolithic fluid structure interactionen
dc.typeArticleen
dc.identifier.journalJournal of Computational Physicsen
dc.contributor.institutionStanford University, Palo Alto, United Statesen
kaust.grant.number42959en
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