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Efficient numerical simulation and optimization of fluid-structure interaction 1

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1st International Workshop on computational engineering - Fluid-Structure Interactions, FSI 2009

作者： Schäfer, M. Sternel, D.C. Becker, G. Pironkov, P. Institute of Numerical Methods in Mechanical Engineering Technische Universität Darmstadt Dolivostr. 15 64293 Darmstadt Germany

ISBN: (数字)9783642142062

ISBN: (纸本)9783642142055

The paper concerns the efficient numerical simulation and optimization of fluid-structure interaction (FSI) problems. The basis is an implicit partitioned solution approach involving the finite-volume flow solver FASTEST, the finite-element structural solver FEAP, and the coupling interface MpCCI. Special emphasis is given to the grid moving techniques for which algebraic and elliptic approaches are considered. The possibilities for accelerating the computations by the usage of multigrid methods, adaptive underrelaxation, and displacement prediction are discussed. A concept for integrating the FSI solver into an optimization procedure for FSI problems is presented. Numerical results are given to illustrate the capabilities of the approaches considered. © 2011 Springer.

关键词： Fluid structure interaction

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Experimental benchmark: Self-excited fluid-structure interaction test cases 1

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1st International Workshop on computational engineering - Fluid-Structure Interactions, FSI 2009

作者： Gomes, J. Pereira Lienhart, H. Institute of Fluid Mechanics Erlangen Graduate School in Advanced Optical Technologies University of Erlangen-Nürnberg Cauerstr. 4 91058 Erlangen Germany

ISBN: (数字)9783642142062

ISBN: (纸本)9783642142055

The swivelling motion of a flexible structure immersed in a flow can become self-excited as a result of different fluid-structure interaction mechanisms. The accurate simulation of these mechanisms still constitutes a challenge with respect to mathematical modelling, numerical discretization, solution techniques, and implementation as software tools on modern computer architectures. Thus, to support the development of numerical codes for fluid structure interaction computations, in the present work an experimental investigation on the two-dimensional self-excited periodic swivelling motion of flexible structures in both laminar and turbulent uniform flows was performed. The investigated structural model consisted of a stainless-steel flexible sheet attached to a cylindrical front body. At the trailing edge of the flexible sheet, a rectangular mass was considered. The entire structure model was free to rotate around an axle located in the central point of the front body. During the experimental investigation, the general character of the elastic-dynamic response of the structure model was studied first. The tests in laminar flows were performed in a polyglycol syrup (dynamic viscosity: 1.64 ×10 -4 m2/s) for a Reynolds number smaller than 270, whereas the tests in turbulent flows were conducted in water for Reynolds numbers up to 44000. In both cases, the maximum incoming velocity tested was about 2 m/s. Subsequently, three specific test cases were selected and characterized in more detail as far as the flow velocity field and structure mechanical behavior are concerned. Thus, the present contribution presents the detailed results obtained at 1.07 m/s and at 1.45 m/s in laminar and at 0.68 m/s in turbulent flows. It also compares the experimental data with numerical results obtained for the same conditions using different simulating approaches. They revealed very good agreement in some of the fluid-structure interaction modes whereas in others deficiencies were observ

关键词： Fluid structure interaction

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Numerical simulation and benchmarking of a monolithic multigrid solver for fluid-structure interaction problems with application to hemodynamics 1

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1st International Workshop on computational engineering - Fluid-Structure Interactions, FSI 2009

作者： Turek, S. Hron, J. Mádlík, M. Razzaq, M. Wobker, H. Acker, J.F. Institute for Applied Mathematics TU Dortmund Vogelpothsweg 87 44227 Dortmund Germany Mathematical Institute Charles University Prague Sokolovska 83 18675 Prague Czech Republic

ISBN: (数字)9783642142062

ISBN: (纸本)9783642142055

An Arbitrary Lagrangian-Eulerian (ALE) formulation is applied in a fully coupled monolithic way, considering the fluid-structure interaction (FSI) problem as one continuum. The mathematical description and the numerical schemes are designed in such a way that general constitutive relations (which are realistic for biomechanics applications) for the fluid as well as for the structural part can be easily incorporated. We utilize the LBB-stable finite element pairs Q 2 P 1 and P 2+ P 1 for discretization in space to gain high accuracy and perform as time-stepping the 2nd order Crank-Nicholson, respectively, a new modified Fractional-Step-θ-scheme for both solid and fluid parts. The resulting discretized nonlinear algebraic system is solved by a Newton method which approximates the Jacobian matrices by a divided differences approach, and the resulting linear systems are solved by direct or iterative solvers, preferably of Krylov-multigrid type. For validation and evaluation of the accuracy and performance of the proposed methodology, we present corresponding results for a new set of FSI benchmark configurations which describe the self-induced elastic deformation of a beam attached to a cylinder in laminar channel flow, allowing stationary as well as periodically oscillating deformations. Then, as an example of FSI in biomedical problems, the influence of endovascular stent implantation on cerebral aneurysm hemodynamics is numerically investigated. The aim is to study the interaction of the elastic walls of the aneurysm with the geometrical shape of the implanted stent structure for prototypical 2D configurations. This study can be seen as a basic step towards the understanding of the resulting complex flow phenomena so that in future aneurysm rupture shall be suppressed by an optimal setting of the implanted stent geometry. © 2011 Springer.

关键词： Fluid structure interaction

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Multi-level accelerated sub-iterations for fluid-structure interaction 1

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1st International Workshop on computational engineering - Fluid-Structure Interactions, FSI 2009

作者： Van Zuijlen, A.H. Bijl, H. Delft University of Technology Kluyverweg 1 2629HS Delft Netherlands

ISBN: (数字)9783642142062

ISBN: (纸本)9783642142055

computational fluid-structure interaction is most commonly performed using a partitioned approach. For strongly coupled problems sub-iterations are required, increasing computational time as flow and structure have to be resolved multiple times every time step. Many sub-iteration techniques exist that improve robustness and convergence, although still flow and structure problems have to be solved a number of times every time step. In this paper we apply a multilevel acceleration technique, which is based on the presumed existing multigrid solver for the flow domain, to a two-dimensional strongly coupled laminar and turbulent problem and investigate the combination of multilevel acceleration with the Aitken underrelaxtion technique. It is found that the value for the under-relaxation parameter is not significantly different when performing sub-iterations purely on the coarse level or purely on the fine level. Therefore coarse and fine level sub-iterations are used alternately, where it is found that performing 3 or 4 coarse level sub-iterations followed by 1 fine level sub-iteration resulted in the highest gain in efficiency. Although the total number of sub-iterations increases slightly by 30%, the number of fine grid iterations can be decreased by as much as 65-70%. © 2011 Springer.

关键词： Fluid structure interaction

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Stability issues in partitioned FSI calculations 1

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1st International Workshop on computational engineering - Fluid-Structure Interactions, FSI 2009

作者： Vierendeels, J. Degroote, J. Annerel, S. Haelterman, R. Ghent University Department of Flow Heat and Combustion Mechanics Sint-Pietersnieuwstraat 41 9000 Gent Belgium Royal Military Academy Department of Mathematics Renaissancelaan 30 1000 Brussels Belgium

ISBN: (数字)9783642142062

ISBN: (纸本)9783642142055

In this chapter a short review will be given on stability issues for fluid-structure interaction (FSI) problems we encountered and studied in the last decade. Based on this, the ideas behind two implicit coupling algorithms, developed in the department, will be explained. The first algorithm is the Interface Quasi-Newton coupling method and the second is the Interface Artificial Compressibility coupling method. Most of the applications that are shown are in the biomechanical field. These are representative for more general strongly coupled problems with incompressible fluids and flexible structures. © 2011 Springer.

关键词： Flexible structures

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Parallel computational fluid dynamics 2008 : parallel numerical methods, software development and ap

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2010年

作者： Parallel CFD Conference

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Accomodating Irregular Subdomains in Domain Decomposition Theory

Accomodating Irregular Subdomains in Domain Decomposition Th...

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18th International Conference on Domain Decomposition Methods

作者： Widlund, Olof B. NYU Courant Inst New York NY 10012 USA

ISBN: (纸本)9783642026775;9783642026768

In the theory for domain decomposition methods, it has previously often been assumed that each subdomain is the union of a small set of coarse shape-regular triangles or tetrahedra. Recent progress is reported, which makes it possible to analyze cases with irregular subdomains such as those produced by mesh partitioners. The goal is to extend the analytic tools so that they work for problems on subdomains that might not even be Lipschitz and to characterize the rates of convergence of domain decomposition methods in terms of a few, easy to understand, geometric parameters of the subregions. For two dimensions, some best possible results have already been obtained for scalar elliptic and compressible and almost incompressible linear elasticity problems;the subdomains should be John or Jones domains and the rates of convergence are determined by parameters that characterize such domains and that of an isoperimetric inequality. Technical issues for three dimensional problems are also discussed.

关键词： Domain decomposition methods

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The Development of Coarse Spaces for Domain Decomposition Algorithms

The Development of Coarse Spaces for Domain Decomposition Al...

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18th International Conference on Domain Decomposition Methods

作者： Widlund, Olof B. Courant Inst New York NY 10012 USA

ISBN: (纸本)9783642026775;9783642026768

The importance of using coarse components, and thus at least one additional level, in the design of domain decomposition methods has been understood for at least twenty years. For many problems of interest, such a device, which provides at least a minimal amount of global transfer of information in each step, is necessary in order to obtain convergence rates which are independent of the number of subdomains. An historical overview, colored by the scientific history of its author, is given of the development of such coarse components of the domain decomposition algorithms. These algorithms are all preconditioned conjugate gradient methods or they are accelerated by using some alternative Krylov space method. The preconditioners are built from solvers of the given problem restricted to subdomains and a coarse approximation which often can be quite exotic.

关键词： Domain decomposition methods

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A Recursive Trust-Region Method for Non-Convex Constrained Minimization

A Recursive Trust-Region Method for Non-Convex Constrained M...

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18th International Conference on Domain Decomposition Methods

作者： Gross, Christian Krause, Rolf Univ Bonn Inst Numer Simulat Bonn Germany

ISBN: (纸本)9783642026775

The mathematical modelling of mechanical or biomechanical problems involving large deformations or biological materials often leads to highly nonlinear and constrained minimization problems. For instance, the simulation of soft-tissues, as the deformation of skin, gives rise to a highly non-linear PDE with constraints, which constitutes the first order condition for a minimizer of the corresponding non-linear energy functional. Besides of the pure deformation of the tissue, bones and muscles have a restricting effect on the deformation of the considered material, leading to additional constraints. Although PDEs are usually formulated in the context of Sobolev spaces, their numerical solution is carried out using discretizations as, e.g., finite elements. Thus, in the present work we consider the following finite dimensional constrained minimization problem: u ε B : J (u) =min! where B= {v ε ℝ ⁿ | Q ≤ v ≤ Q̄} and Q < Q̄ ε ℝ ⁿ and the possibly nonconvex, but differentiable, objective function J : ℝ ⁿ → ℝ . Here, the occurring inequalities are to be understood pointwise. In the context of discretized PDEs, n corresponds to the dimension of the finite element space and may therefore be very large. © 2009 Springer-Verlag Berlin Heidelberg.

关键词： Deformation

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Linearly Implicit Domain Decomposition Methods for Nonlinear Time-Dependent Reaction-Diffusion Problems

Linearly Implicit Domain Decomposition Methods for Nonlinear...

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18th International Conference on Domain Decomposition Methods

作者： Arraras, A. Portero, L. Jorge, J. C. Univ Publ Navarra Dpto Ingn Matemat & Informat Pamplona 31006 Spain

ISBN: (纸本)9783642026775;9783642026768

A new family of linearly implicit fractional step methods is proposed for the efficient numerical solution of a class of nonlinear time-dependent reaction-diffusion equations. By using the method of lines, the original problem is first discretized in space via a mimetic finite difference technique. The resulting differential system of stiff nonlinear equations is locally decomposed by suitable Taylor expansions and a domain decomposition splitting for the linear terms. This splitting is then combined with a linearly implicit one-step scheme belonging to the class of so-called fractional step Runge-Kutta methods. In this way, the original problem is reduced to the solution of several linear systems per time step which can be trivially decomposed into a set of uncoupled subsystems. As compared to classical domain decomposition techniques, our proposal does not require any Schwarz iterative procedure. The convergence of the designed method is illustrated by numerical experiments.

关键词： Domain decomposition methods

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