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

Banks, Jeffrey W.; Henshaw, William D.; Schwendeman, Donald W.; Tang, Qi

doi:10.1016/j.jcp.2017.01.015

Cited by 24 publications

(52 citation statements)

References 38 publications

(114 reference statements)

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“…For the present model problem with the the pseudo-spectral approximation (4.2), for example, we have |k x | ≤ π/∆x, while a second-order difference approximation would roughly imply |k x | ≤ 2/∆x. Experience [19] shows that added-damping instabilities are generally caused by relatively high-frequency modes on the grid, and this suggests taking k x = 1/h which leads to a definition of the fluid impedance of the form…”

Section: Velocity Boundary Conditions On ∂ωmentioning

confidence: 99%

A Stable Added-Mass Partitioned (AMP) Algorithm for Elastic Solids and Incompressible Flow: Model Problem Analysis

Serino¹,

Banks²,

Henshaw³

et al. 2019

SIAM J. Sci. Comput.

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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) fractionalstep 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 [1] 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. On the other hand, the traditional algorithm involving a Dirichlet-Neumann coupling is shown to be unconditionally unstable as added-mass effects become large with grid refinement. The algorithm is verified for accuracy and stability for set of new exact benchmark solutions. These new solutions are elastic piston problems, 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.

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Section: Velocity Boundary Conditions On ∂ωmentioning

confidence: 99%

A Stable Added-Mass Partitioned (AMP) Algorithm for Elastic Solids and Incompressible Flow: Model Problem Analysis

Serino¹,

Banks²,

Henshaw³

et al. 2019

SIAM J. Sci. Comput.

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“…Algorithm 1 provides the details of the AMP-RB time-stepping scheme used for the calculations presented in this paper. The algorithm given here follows the ones discussed in our previous work [1,2], but extended to three dimensions. It is a predictor-corrector-type fractional-step scheme that advances the solution from the time step t n to t n+1 .…”

Section: Time-stepping Algorithmmentioning

confidence: 99%

“…In recent work [1,2], a new partitioned scheme was developed and shown, in two-dimensions, to be accurate and stable for any mass of the solid, including the extreme case of a solid with zero mass, thus overcoming instabilities due to added-mass effects. The key development for this new scheme, referred to as the AMP-RB scheme, was the treatment of the interface coupling.…”

Section: Introductionmentioning

confidence: 99%

“…This is the first partitioned algorithm that remains stable and second-order accurate, without sub-time-step iterations, for very light, and even zero-mass, bodies in three dimensions. This new added-mass partitioned (AMP) algorithm extends the previous developments in [1,2] by generalizing the added-damping tensors to account for arbitrary three-dimensional rotations, and by employing a general quadrature for the surface integral over a rigid body to derive the discrete AMP interface condition for the fluid pressure. Stability analyses for two three-dimensional model problems show that the algorithm remains stable for bodies of any mass when applied to the relevant model problems.…”

mentioning

confidence: 99%

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A stable partitioned FSI algorithm for rigid bodies and incompressible flow in three dimensions

Banks

Henshaw

Schwendeman

et al. 2018

Journal of Computational Physics

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This paper describes a novel partitioned algorithm for fluid-structure interaction (FSI) problems that couples the motion of rigid bodies and incompressible flow. This is the first partitioned algorithm that remains stable and second-order accurate, without sub-time-step iterations, for very light, and even zero-mass, bodies in three dimensions. This new added-mass partitioned (AMP) algorithm extends the previous developments in [1,2] by generalizing the added-damping tensors to account for arbitrary three-dimensional rotations, and by employing a general quadrature for the surface integral over a rigid body to derive the discrete AMP interface condition for the fluid pressure. Stability analyses for two three-dimensional model problems show that the algorithm remains stable for bodies of any mass when applied to the relevant model problems. The resulting AMP algorithm is implemented in parallel using a moving composite grid framework to treat one or more rigid bodies in complex three-dimensional configurations. The new three-dimensional algorithm is verified and validated though several benchmark problems, including the motion of a sphere in a viscous incompressible fluid and the interaction of a bi-leaflet mechanical heart valve and a pulsating fluid. Numerical simulations confirm the predictions of the stability analysis even for complex problems, and show that the AMP algorithm remains stable, without sub-iterations, for light and even zero-mass three-dimensional rigid bodies of general shape. These benchmark problems are further used to examine the parallel performance of the algorithm and to investigate the conditioning of the linear system for the pressure including the newly derived AMP interface conditions.

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“…Proof. By solving equation (30) with the assumption (s) > 0, we know the root with magnitude less one is of the following form:…”

Section: Local Stability and Accuracymentioning

confidence: 99%

A split-step finite-element method for incompressible Navier-Stokes equations with high-order accuracy up-to the boundary

2020

Journal of Computational Physics

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An efficient and accurate finite-element algorithm is described for the numerical solution of the incompressible Navier-Stokes (INS) equations. The new algorithm that solves the INS equations in a velocity-pressure reformulation is based on a split-step scheme in conjunction with the standard finite-element method. The split-step scheme employed for the temporal discretization of our algorithm completely separates the pressure updates from the solution of velocity variables. When the pressure equation is formed explicitly, the algorithm avoids solving a saddle-point problem; therefore, our algorithm has more flexibility in choosing finite-element spaces. In contrast, popular mixed finite-element methods that solve the INS equations in the primitive variables (or velocity-divergence formulation) lead to discrete saddle-point problems whose solution depends on the choice of finite-element spaces for velocity and pressure that is subject to the wellknown Ladyzenskaja-Babuška-Brezzi (LBB) (or inf-sup) condition. For efficiency and robustness, Lagrange (piecewise-polynomial) finite elements of equal order for both velocity and pressure are used. Accurate numerical boundary condition for the pressure equation is also investigated. Motivated by a post-processing technique that calculates derivatives of a finite element solution with super-convergent error estimates, an alternative numerical boundary condition is proposed for the pressure equation at the discrete level. The new numerical pressure boundary condition that can be regarded as a better implementation of the compatibility boundary condition improves the boundary-layer errors of the pressure solution. A normal-mode analysis is performed using a simplified model problem on a uniform mesh to demonstrate the numerical properties of our methods. Convergence studies using P 1 elements support the analytical results and demonstrates that our algorithm with the new numerical boundary condition achieves the optimal second-order accuracy for both velocity and pressure up-to the boundary. Benchmark problems are also computed and carefully compared with existing studies. Finally, as an example to illustrate that our approach can be easily adapted for higher-order finite elements, we solve the classical flow-past-a-cylinder problem using P n finite elements with n ≥ 1.

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

Cited by 24 publications

References 38 publications

A Stable Added-Mass Partitioned (AMP) Algorithm for Elastic Solids and Incompressible Flow: Model Problem Analysis

A Stable Added-Mass Partitioned (AMP) Algorithm for Elastic Solids and Incompressible Flow: Model Problem Analysis

A stable partitioned FSI algorithm for rigid bodies and incompressible flow in three dimensions

A split-step finite-element method for incompressible Navier-Stokes equations with high-order accuracy up-to the boundary

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