A fast BE‐FE coupling scheme for partly immersed bodies

Brunner, Dominik; Junge, Michael; Steinbach, Olaf; Gaul, Lothar

doi:10.1002/nme.2672

Cited by 29 publications

(24 citation statements)

References 42 publications

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“…4 HALF-SPACE BEM FORMULATION FOR THE ACOUSTIC DOMAIN As pointed out in [16], the fluid domain, which is bounded by the flat water surface, can be seen as semi-infinite half-space. For such a problem, the use of the special half-space fundamental solution …”

Section: Governing Equations Of the Coupled Problemmentioning

confidence: 99%

“…If P * (x,y) is plugged into eqns (8) and (9) it can be shown, that the integrals over the water surface vanish exactly. Thus, the boundary integral eqns (8) and (9) are applicable in the same way but this time P * (x,y) is used instead of P(x,y) and only G I has to be considered [16]. To obtain a Galerkin formulation, both boundary integral equations are weighted with linear functions n. Again a triangulation with piecewise linear shape functions for p and constant ones for q are applied, leading to 1 2…”

Section: Governing Equations Of the Coupled Problemmentioning

confidence: 99%

“…In case of the half-space problem, modifications are necessary for the near-field and the farfield [16]. The near-field also has to include the interaction to mirrored-clusters, which fulfil the near-field condition with a non-mirrored cluster.…”

Section: Fast Multipole Implementationmentioning

confidence: 99%

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Acoustic Fluid–Structure Interaction of Ships by Coupled Fast BE–FE Approaches

Gaul¹,

Brunner²,

Junge³

2017

Int. J. CMEM

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The vibration behaviour of ships is noticeably influenced by the surrounding water, which represents a fluid of high density. In this case, the feedback of the fluid pressure onto the structure cannot be neglected and a strong coupling scheme between the fluid domain and the structural domain is necessary. In this work, fast boundary element methods (BEMs) are used to model the semi-infinite fluid domain with the free water surface. Two approaches are compared: A symmetric mixed formulation is applied where a part of the water surface is discretized. The second approach is a formulation with a special half-space fundamental solution, which allows the exact representation of the Dirichlet boundary condition on the free water surface without its discretization. Furthermore, the influence of the compressibility of the water is investigated by comparing the solutions of the Helmholtz and the Laplace equation. The ship itself is modeled with the finite element method (FEM). A binary interface to the commercial finite element package ANSYS is used to import the mass matrix and the stiffness matrix. The coupled problems are formulated using Schur complements. To solve the resulting system of equations, a combination of a direct solver for the finite element matrix and a preconditioned GMRES for the overall Schur complement is chosen. The applicability of the approach is demonstrated using a realistic model problem.

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Section: Governing Equations Of the Coupled Problemmentioning

confidence: 99%

Section: Governing Equations Of the Coupled Problemmentioning

confidence: 99%

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Acoustic Fluid–Structure Interaction of Ships by Coupled Fast BE–FE Approaches

Gaul¹,

Brunner²,

Junge³

2017

Int. J. CMEM

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“…The second term in (6) accounts for the pressure-free boundary condition of the water surface [24,25,14]. Therefore, x  is mirrored on the water surface (see .…”

Section: The Normal On ) ( E Imentioning

confidence: 99%

“…Different solution strategies for multifield problems are compared in [13], where a Schur complement formulation working on the pressure DOFs turned out to be robust and fast. An extension of the above mentioned fast BE methods to partly immersed bodies is discussed in [14]. One major application of FE-BE coupled formulations is the prediction of the vibro-acoustic behavior of ship-like structures totally submerged or partly immersed in water.…”

Section: Introductionmentioning

confidence: 99%

Solution of the FE-BE Coupled Eigenvalue Problem for Immersed Ship-like Structures

2011

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-1-To predict the vibro-acoustic behavior of structures, both a structural problem and an acoustic problem have to be solved. For thin structures immersed in water a strong interaction between the structural domain and fluid domain occurs. This significantly alters the resonance frequencies. In this paper, the structure is modeled by the finite element method. The exterior acoustic problem is solved by a fast boundary element method employing hierarchical matrices. A FE-BE formulation is presented, which allows the solution of the coupled eigenvalue problem and thus the prediction of the coupled eigenfrequencies and mode shapes. It is based on a Schur complement formulation of the FE-BE system yielding a generalized eigenvalue problem. A Krylov-Schur solver is applied for its efficient solution. Hereby, the compressibility of the fluid is neglected. The applicability of the proposed formulation is demonstrated on a ship-like cylindrical test structure.

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Interface‐reduction for the Craig–Bampton and Rubin method applied to FE–BE coupling with a large fluid–structure interface

Junge

Brunner

Becker

et al. 2008

Numerical Meth Engineering

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SUMMARYComponent mode-based model-order reduction (MOR) methods like the Craig-Bampton method or the Rubin method are known to be limited to structures with small coupling interfaces. This paper investigates two interface-reduction methods for application of MOR to systems with large coupling interfaces: for the Craig-Bampton method a direct reduction method based on strain energy considerations is investigated. Additionally, for the Rubin method an iterative reduction scheme is proposed, which incrementally constructs the reduction basis. Hereby, attachment modes are tested if they sufficiently enlarge the spanned subspace of the current reduction basis. If so, the m-orthogonal part is used to augment the basis. The methods are applied to FE-BE coupled systems in order to predict the vibro-acoustic behavior of structures, which are partly immersed in water. Hereby, a strong coupling scheme is employed, since for dense fluids the feedback of the acoustic pressure onto the structure is not negligible. For two example structures, the efficiency of the reduction methods with respect to numerical effort, memory consumption and computation time is compared with the exact full-order solution.

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A fast BE‐FE coupling scheme for partly immersed bodies

Cited by 29 publications

References 42 publications

Acoustic Fluid–Structure Interaction of Ships by Coupled Fast BE–FE Approaches

Acoustic Fluid–Structure Interaction of Ships by Coupled Fast BE–FE Approaches

Solution of the FE-BE Coupled Eigenvalue Problem for Immersed Ship-like Structures

Interface‐reduction for the Craig–Bampton and Rubin method applied to FE–BE coupling with a large fluid–structure interface

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