A new strategy for solving fluid-structure problems

A scheme for treating unsymmetrical coupled systems is outlined. Such systems occur naturally in connection with fluid–structure interaction, where an acoustic fluid is contained in an elastic structure. The discretization is performed by means of the finite element method, using displacement formulation in the structure and either pressure or displacement potential in the fluid. Based on the eigenvalues of each subdomain some simple steps give a standard eigenvalue problem. It might also be concluded that the unsymmetrical matrices have real eigenvalues.     

A new acoustic interface element for fluid-structure interaction problems

A new comprehensive acoustic 2-D interface element capable of coupling the boundary element (BE) and finite element (FE) discretizations has been formulated for fluid–structure interaction problems. The Helmholtz equation governing the acoustic pressure in a fluid is discretized using the BE method and coupled to the FE discretization of a vibrating structure that is in contact with the fluid. Since the BE method naturally maps the infinite fluid domain into finite node points on the fluid–structure interface, the formulation is especially useful for problems where the fluid domain extends to infinity. Details of the BE matrix computation process adapted to FE code architecture are included for easy incorporation of the interface element in FE codes. The interface element has been used to solve a few simple fluid–structure problems to demonstrate the validity of the formulation. Also, the vibration response of a submerged cylindrical shell has been computed and compared with the results from an entirely finite element formulation.     

Parallel block-preconditioned monolithic solvers for fluid-structure interaction problems

In this work, we consider the solution of fluid-structure interaction (FSI) problems using a monolithic approach for the coupling between fluid and solid subproblems. The coupling of both equations is realized by means of the arbitrary Lagrangian-Eulerian framework and a nonlinear harmonic mesh motion model. Monolithic approaches require the solution of large ill-conditioned linear systems of algebraic equations at every Newton step. Direct solvers tend to use too much memory even for a relatively small number of degrees of freedom and, in addition, exhibit superlinear growth in arithmetic complexity. Thus, iterative solvers are the only viable option. To ensure convergence of iterative methods within a reasonable amount of iterations, good and, at the same time, cheap preconditioners have to be developed. We study physics-based block preconditioners, which are derived from the block-LDU factorization of the FSI Jacobian, and their performance on distributed memory parallel computers in terms of two- and three-dimensional test cases permitting large deformations.     

Alternative graph formulation for solving complex factory-scheduling problems

The adaptation of the academic job shop scheduling model to industrial practice is well known to be rich of difficulties owing to the gap between scheduling theory and practice. On the other hand, several authors observed that the disjunctive graph formulation of Roy and Sussman was more robust than the job shop model itself. In fact, the disjunctive graph can be easily adapted to deal with many practical issues. This paper moves a step closer in the direction of generalizing the existing mathematical models in order to capture relevant aspects of complex factory scheduling problems. It considers an extension of the disjunctive graph, called an alternative graph, and allows it to be modelled in a precise way to solve effectively a number of complex practical scheduling problems for which there were no successful methodologies. Several examples are presented and a complex industrial application arising in the production of steel is provided. Finally, the performance of a new fast heuristic both on real data and several instances from the literature is discussed in relation to the job shop scheduling problem.     

一种局部形式的流固耦合界面插值方法

摘 要：提出了一种局部形式的流固耦合问题界面插值方法,并应用于机翼颤振计算的界面插值。用全局径向基函数和单项式基函数构造插值函数,插值定义域选择局部形式,使得气动节点的插值仅与其相邻的结构节点相关。给出局部形式定义域的设置方法,并确定出定义域的下界。按照插值过程的能量守恒原则推导出气动力的插值矩阵。三维变形球面的插值结果表明方法具有良好的精度和效率。将此方法应用于AGARD 445.6机翼跨音速颤振的界面插值,得到的颤振结果与实验值吻合。     

Non-linear approximation of weakly compressible fluids in fluid-structure interaction problems

A model for shock propagation in one-dimensional weakly compressible fluids is developed by assuming, for any instant, a step function for the fluid density. The resulting set of equations is reduced to a single first order ordinary differential equation for the density. Under simple assumptions this approach results in a novel non-linear interactive approximation for the fluid pressure on the structure's surface.     

An effective numerical method for solving viscous-inviscid interaction problems

This paper presents a new numerical method to solve the equations of the asymptotic theory of separated flows. A number of measures was taken to ensure fast convergence of the iteration procedure, which is employed to treat the nonlinear terms in the governing equations. Firstly, we selected carefully the set of variables for which the nonlinear finite difference equations were formulated. Secondly, a Newton-Raphson strategy was applied to these equations. Thirdly, the calculations were facilitated by utilizing linear approximation of the boundary-layer equations when calculating the corresponding Jacobi matrix.The performance of the method is illustrated, using as an example, the problem of laminar two-dimensional boundary-layer separation in the flow of an incompressible fluid near a corner point of a rigid body contour. The solution of this problem is non-unique in a certain parameter range where two solution branches are possible.     

A finite-element/boundary-element method for large-displacement fluid-structure interaction

We present a combined finite-element/boundary-element method to simulate inflation processes, characterized by a light, folded structure enveloping a viscous fluid. The application of the boundary-element method to approximate the flow allows for automatic evolution of the problem domain according to the kinematic condition. Moreover, it provides an intrinsic mechanism to treat the ubiquitous self-contact, common to inflation problems. We numerically verify that self-contact is indeed prevented and demonstrate the versatility and robustness of this method.     

A new 3-D finite element model to evaluate added mass for analysis of fluid-structure interaction problems

The paper presents the results of investigations conducted to evaluate the added mass to represent fluid-structure interaction effects in vibration/dynamic analysis of floating bodies such as ship hulls. While the structural plating is idealized by 9-noded plate/shell finite elements, the fluid domain is modelled by 20-noded/21-noded 3-D finite elements in the investigations conducted. A new 8-noded element has been developed to model the interface between the structure and the fluid. An efficient computational methodology has been used for computation of added mass. The finite element models are validated by comparing the results with those given by analytical solution for a submerged sphere. The efficacy of the finite element model is demonstrated through convergence of the results obtained for a floating barge problem. A better convergence rate and distribution of added mass in three orthogonal directions have been obtained.     

A frequency domain boundary element formulation for dynamic interaction problems in poroviscoelastic media

A unified formulation is presented, based on the boundary element method, to perform the interaction analysis for the problems involving poroviscoelastic media. The proposed formulation permits the evaluation of all the elements of impedance and input motion matrices at a single step in terms of system matrices of boundary element method without solving any special problem, such as, unit displacement or load problem, as required by conventional methods. It further eliminates the complicated procedure and the need for using scattering analysis in the evaluation of input motion functions. The formulation is explained by considering a simple interaction problem involving an inclusion embedded in an infinite poroviscoelastic medium, which is under the influence of a dynamic excitation induced by seismic waves. In the formulation, an impedance relation is established for this interaction problem, suitable for performing the interaction analysis by substructure method, which permits carrying out the analysis for inclusion and its surrounding medium separately. The inclusion is first treated as poroviscoelastic, then viscoelastic and finally rigid, where the formulation in each of these cases is obtained consecutively as a special case of the previous one. It is remarkable to note that, a cavity problem where there is a hole in place of inclusion can be also considered within the framework of the present formulation. The formulation is assessed by applying it to some sample problems. The extension of the formulation to other types of interaction problems, such as, multi-inclusion problems, the analyses of foundations supported by a poroviscoelastic medium, etc., will be the subject of a separate study.     

Modelling vortex-induced fluid-structure interaction

The principal goal of this research is developing physics-based, reduced-order, analytical models of nonlinear fluid-structure interactions associated with offshore structures. Our primary focus is to generalize the Hamilton's variational framework so that systems of flow-oscillator equations can be derived from first principles. This is an extension of earlier work that led to a single energy equation describing the fluid-structure interaction. It is demonstrated here that flow-oscillator models are a subclass of the general, physical-based framework. A flow-oscillator model is a reduced-order mechanical model, generally comprising two mechanical oscillators, one modelling the structural oscillation and the other a nonlinear oscillator representing the fluid behaviour coupled to the structural motion.Reduced-order analytical model development continues to be carried out using a Hamilton's principle-based variational approach. This provides flexibility in the long run for generalizing the modelling paradigm to complex, three-dimensional problems with multiple degrees of freedom, although such extension is very difficult. As both experimental and analytical capabilities advance, the critical research path to developing and implementing fluid-structure interaction models entails-formulating generalized equations of motion, as a superset of the flow-oscillator models; and-developing experimentally derived, semi-analytical functions to describe key terms in the governing equations of motion.The developed variational approach yields a system of governing equations. This will allow modelling of multiple d.f. systems. The extensions derived generalize the Hamilton's variational formulation for such problems. The Navier-Stokes equations are derived and coupled to the structural oscillator. This general model has been shown to be a superset of the flow-oscillator model. Based on different assumptions, one can derive a variety of flow-oscillator models.     

A mixed least squares method for solving problems in linear elasticity: formulation and initial results

In this paper a mixed least squares finite element method for solving problems in linear elasticity is proposed. The developed numerical technique allows the use of separate unknowns for displacements and stresses, discontinuous interpolation functions for displacements, and the resulting linear system has a symmetric and positive definite coefficient matrix. The approximate solution of the linear elasticity problem is obtained by minimization of a least squares functional based on the constitutive equations and equations of equilibrium. The proposed method is implemented in an original computer code written in C programming language. Its performance is tested on classical examples from theory of elasticity with well-known exact analytical solutions. Results from the implementation of a constant displacement-bilinear stress element and bilinear displacement-bilinear stress element are discussed.     

A variational formulation for convection-diffusion problems

A variational principle is proposed that under certain restrictions is shown to be equivalent to the advection-diffusion boundary value problem. Based on this variational principle, an upwind finite element method is derived that precludes spurious oscillations while possessing optimal convergence properties even in the multidimensional case. The formulation also points to a canonical choice of weighting functions for the Petrov-Galerkin method proposed by the Dundee and Swansea groups.     

Finite-element-based computational methods for cardiovascular fluid-structure interaction

In this paper a combined arbitrary Lagrange-Euler fictitious domain (ALE-FD) method for fluid-structure interaction problems in cardiovascular biomechanics is derived in terms of a weighted residual finite-element formulation. For both fluid flow of blood and solid mechanics of vascular tissue, the performance of tetrahedral and hexahedral Crouzeix-Raviart elements are evaluated. Comparable convergence results are found, although for the test cases considered the hexahedral elements are more accurate. The possibilities that are offered by the ALE-FD method are illustrated by means of a simulation of valve dynamics in a simplified left ventricular flow model.     

A unified approach for the formulation of interaction problems by the boundary element method

A unified formulation is presented, based on boundary element method, in a form suitable for performing the interaction analyses by substructure method for solid–solid and soil–structure problems. The proposed formulation permits the evaluation of all the elements of impedance and input motion matrices simultaneously at a single step in terms of system matrices of the boundary element method without solving any special problem, such as, unit displacement or load problem, as required in conventional methods. It eliminates further the complicated procedure and the need for using scattering analysis in the evaluation of input motion functions. To explain the formulation, it is first given for an inclusion interacting with an infinite surrounding medium under the influence of a seismic input, where both the inclusion and surrounding medium are treated as viscoelastic. It is shown that the formulation for a rigid inclusion may be obtained from that for flexible inclusion as a special case through a transformation. Then, the formulation is extended to other types of interaction problems: a multi‐inclusion problem and an interaction problem involving a foundation embedded in a viscoelastic half‐space. It is found that the proposed formulation remains essentially the same for all kinds of interaction problems and it can be used not only in regular interaction analysis, but also in the analysis involving diffraction of waves in a medium containing holes. Copyright © 2005 John Wiley & Sons, Ltd.     

A fully-coupled fluid-structure interaction simulation of cerebral aneurysms

This paper presents a computational vascular fluid-structure interaction (FSI) methodology and its application to patient-specific aneurysm models of the middle cerebral artery bifurcation. A fully coupled fluid-structural simulation approach is reviewed, and main aspects of mesh generation in support of patient-specific vascular FSI analyses are presented. Quantities of hemodynamic interest such as wall shear stress and wall tension are studied to examine the relevance of FSI modeling as compared to the rigid arterial wall assumption. We demonstrate the importance of including the flexible wall modeling in vascular blood flow simulations by performing a comparison study that involves four patient-specific models of cerebral aneurysms varying in shape and size.     

Parallel BDD-based monolithic approach for acoustic fluid-structure interaction

Parallel BDD-based monolithic algorithms for acoustic fluid-structure interaction problems are developed. In a previous study, two schemes, NN-I + CGC-FULL and NN-I + CGC-DIAG, have been proven to be efficient among several BDD-type schemes for one processor. Thus, the parallelization of these schemes is discussed in the present study. These BDD-type schemes consist of the operations of the Schur complement matrix-vector (Sv) product, Neumann-Neumann (NN) preconditioning, and the coarse problem. In the present study, the Sv product and NN preconditioning are parallelized for both schemes, and the parallel implementation of the solid and fluid parts of the coarse problem is considered for NN-I + CGC-DIAG. The results of numerical experiments indicate that both schemes exhibit performances that are almost as good as those of single solid and fluid analyses in the Sv product and NN preconditioning. Moreover, NN-I + CGC-DIAG appears to become more efficient as the problem size becomes large due to the parallel calculation of the coarse problem.     

Three-dimensional non-linear fluid-structure interaction problems: Formulation by the finite and infinite element method

Using the perturbation method, the non-linear exterior fluid-structure interaction problem is separated into first- and second-order problems. With the finite element method for the structure and the finite-infinite element method for the fluid, we obtain a first-order coupled matrix system and a second-order coupled matrix system. By determining the frequencies of resonance of the structure, comparison of numerical results for a vertical cylinder and a horizontal floating cylinder shows the validity of the presented method for the resolution of three-dimensional exterior hydroelastic problems.