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

Abstract

A stable partitioned algorithm is developed for fluid-structure interaction (FSI) problems involving viscous incompressible flow and rigid bodies. This 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 basedmore » on a fractional-step method for the incompressible Navier-Stokes equations using finite difference methods and overlapping grids to handle the moving geometry. Here, the numerical scheme is verified on a number of difficult benchmark problems.« less

Authors:
 [1];  [1];  [1];  [1]
  1. Rensselaer Polytechnic Inst., Troy, NY (United States)
Publication Date:
Research Org.:
Rensselaer Polytechnic Inst., Troy, NY (United States)
Sponsoring Org.:
USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR) (SC-21)
OSTI Identifier:
1353365
Grant/Contract Number:
AC52-07NA27344
Resource Type:
Journal Article: Accepted Manuscript
Journal Name:
Journal of Computational Physics
Additional Journal Information:
Journal Volume: 343; Journal Issue: C; Journal ID: ISSN 0021-9991
Publisher:
Elsevier
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICS AND COMPUTING; fluid-structure interaction; moving overlapping; grids; incompressible Navier-Stokes; partitioned schemes; added-mass; added-damping; rigid bodies

Citation Formats

Banks, J. W., Henshaw, W. D., Schwendeman, D. W., and Tang, Qi. A stable partitioned FSI algorithm for rigid bodies and incompressible flow. Part I: Model problem analysis. United States: N. p., 2017. Web. doi:10.1016/j.jcp.2017.01.015.
Banks, J. W., Henshaw, W. D., Schwendeman, D. W., & Tang, Qi. A stable partitioned FSI algorithm for rigid bodies and incompressible flow. Part I: Model problem analysis. United States. doi:10.1016/j.jcp.2017.01.015.
Banks, J. W., Henshaw, W. D., Schwendeman, D. W., and Tang, Qi. Fri . "A stable partitioned FSI algorithm for rigid bodies and incompressible flow. Part I: Model problem analysis". United States. doi:10.1016/j.jcp.2017.01.015. https://www.osti.gov/servlets/purl/1353365.
@article{osti_1353365,
title = {A stable partitioned FSI algorithm for rigid bodies and incompressible flow. Part I: Model problem analysis},
author = {Banks, J. W. and Henshaw, W. D. and Schwendeman, D. W. and Tang, Qi},
abstractNote = {A stable partitioned algorithm is developed for fluid-structure interaction (FSI) problems involving viscous incompressible flow and rigid bodies. This 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. Here, the numerical scheme is verified on a number of difficult benchmark problems.},
doi = {10.1016/j.jcp.2017.01.015},
journal = {Journal of Computational Physics},
number = C,
volume = 343,
place = {United States},
year = {Fri Jan 20 00:00:00 EST 2017},
month = {Fri Jan 20 00:00:00 EST 2017}
}

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  • An added-mass partitioned (AMP) algorithm is described for solving fluid–structure interaction (FSI) problems coupling incompressible flows with thin elastic structures undergoing finite deformations. The new AMP scheme is fully second-order accurate and stable, without sub-time-step iterations, even for very light structures when added-mass effects are strong. The fluid, governed by the incompressible Navier–Stokes equations, is solved in velocity-pressure form using a fractional-step method; large deformations are treated with a mixed Eulerian-Lagrangian approach on deforming composite grids. The motion of the thin structure is governed by a generalized Euler–Bernoulli beam model, and these equations are solved in a Lagrangian frame usingmore » two approaches, one based on finite differences and the other on finite elements. The key AMP interface condition is a generalized Robin (mixed) condition on the fluid pressure. This condition, which is derived at a continuous level, has no adjustable parameters and is applied at the discrete level to couple the partitioned domain solvers. Special treatment of the AMP condition is required to couple the finite-element beam solver with the finite-difference-based fluid solver, and two coupling approaches are described. A normal-mode stability analysis is performed for a linearized model problem involving a beam separating two fluid domains, and it is shown that the AMP scheme is stable independent of the ratio of the mass of the fluid to that of the structure. A traditional partitioned (TP) scheme using a Dirichlet–Neumann coupling for the same model problem is shown to be unconditionally unstable if the added mass of the fluid is too large. A series of benchmark problems of increasing complexity are considered to illustrate the behavior of the AMP algorithm, and to compare the behavior with that of the TP scheme. The results of all these benchmark problems verify the stability and accuracy of the AMP scheme. Results for one benchmark problem modeling blood flow in a deforming artery are also compared with corresponding results available in the literature.« less
  • A class of solutions of the steady-state hydrodynamic equations of an incompressible liquid has been considered in the Euler approximation when the pressure field is described by an additive function of the form P(x;y) = F(x) + G(y). It turns out that this class of solutions includes potential flows such as wave motion of a liquid with a finite depth, a flow inside a right angle, and a hyersonic gas flow around a sphere in the approximation of constant density near the stagnation point. Among nonpotential flows, this class includes, in particular, a hyersonic flow around a cylinder. The resultsmore » obtained are used to construct a model of a flow around convex symmetric bodies with suction or injection. This model can be of interest in solving some problems of physicochemical technology, for example, separation of gas mixtures and isotopes.« less
  • We describe a new partitioned approach for solving conjugate heat transfer (CHT) problems where the governing temperature equations in different material domains are time-stepped in a implicit manner, but where the interface coupling is explicit. The new approach, called the CHAMP scheme (Conjugate Heat transfer Advanced Multi-domain Partitioned), is based on a discretization of the interface coupling conditions using a generalized Robin (mixed) condition. The weights in the Robin condition are determined from the optimization of a condition derived from a local stability analysis of the coupling scheme. The interface treatment combines ideas from optimized-Schwarz methods for domain-decomposition problems togethermore » with the interface jump conditions and additional compatibility jump conditions derived from the governing equations. For many problems (i.e. for a wide range of material properties, grid-spacings and time-steps) the CHAMP algorithm is stable and second-order accurate using no sub-time-step iterations (i.e. a single implicit solve of the temperature equation in each domain). In extreme cases (e.g. very fine grids with very large time-steps) it may be necessary to perform one or more sub-iterations. Each sub-iteration generally increases the range of stability substantially and thus one sub-iteration is likely sufficient for the vast majority of practical problems. The CHAMP algorithm is developed first for a model problem and analyzed using normal-mode the- ory. The theory provides a mechanism for choosing optimal parameters in the mixed interface condition. A comparison is made to the classical Dirichlet-Neumann (DN) method and, where applicable, to the optimized- Schwarz (OS) domain-decomposition method. For problems with different thermal conductivities and dif- fusivities, the CHAMP algorithm outperforms the DN scheme. For domain-decomposition problems with uniform conductivities and diffusivities, the CHAMP algorithm performs better than the typical OS scheme with one grid-cell overlap. Lastly, the CHAMP scheme is also developed for general curvilinear grids and CHT ex- amples are presented using composite overset grids that confirm the theory and demonstrate the effectiveness of the approach.« less