Analysis of some partitioned algorithms for fluid-structure interaction (original) (raw)
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An Algorithm for the Strong-Coupling of the Fluid-Structure Interaction Using a Staggered Approach
We present a staggered approach for the solution of the piston fluid-structure problem in a timedependent domain. The one-dimensional fluid flow is modelled using the nonlinear Euler equations. We investigate the time marching fluid-structure interaction and integrate the fluid and structure equations alternately using separate solvers. The Euler equations are written in moving mesh coordinates using the arbitrary Lagrangian-Eulerian ALE approach and discretised in space using the finite element method while the structure is integrated in time using an implicit finite difference Newmark-Wilson scheme. The influence of the time lag is studied by comparing two different structural predictors.
Fluid–structure interaction with a staged algorithm
A common approach to solving fluid-structure interaction problems is to solve each subproblem in a partitioned procedure where time and space discretization methods could be different. Such a scheme simplifies explicit/implicit integration and it is in favor of the use of different codes specialized on each sub-area. In this work a staggered fluid-structure coupling algorithm is considered. For each time step a "stage-loop" is performed. In the first stage a high order predictor is used for the structure state, then the fluid and the structure systems are advanced in that order. In subsequent stages of the loop each system uses the previously computed state of the other system until convergence. For weakly coupled problems a stable and efficient algorithm is obtained using one stage and an accurate enough predictor. For strongly coupled problems, stability is enhanced by increasing the number of stages in the loop. If the stage loop is iterated until convergence, a monolithic scheme is recovered. In addition, two items that are specially important in fluid structure problems are discussed, namely invariance of the stabilization terms and dynamic absorbing boundary conditions. Finally, numerical examples are presented.
Time marching for simulation of fluid–structure interaction problems
Journal of Fluids and Structures, 2009
Numerical simulation of industrial multi-physics problems is still a challenge. It generally requires large computational resources. It may involve complex code coupling techniques. It also relies on appropriate numerical methods making data transfer possible, quick and accurate. In the framework of partitioned procedures, multi-physics computations require the right choice of code coupling schemes, because several physical mechanisms are involved. Numerical simulation of fluid-structure interactions is one of these issues. It is investigated in this paper. First the computational process involving a code coupling procedure is presented. Then, applications and test cases involving fluid structure interactions are investigated using several examples. A partitioned procedure involves several operators ensuring code coupling. A special attention must be paid to energy conservation at the fluid-structure interface, especially when it is moving and when strong non-linear behaviour occurs in both fluid and structure systems. In the present work, several fluid-structure code-coupling schemes are compared and discussed in terms of stability and energy conservation properties. The criteria are based on the evaluation of the energy that is numerically created at the fluid-structure interface. This is achieved by considering the staggering process due to the time lag between the fluid and structure solvers. Comparisons are made, and finally the article gives recommendations for creating a tool devoted to coupled simulations of fluid structure interactions. r (E. Longatte).
ABSTRACT:The interaction between fluid and structure may appear in many problems of Engineering. These problems related differential equations are very difficult to solve analytically and hence solved generally by numerical approximations. There is, however, a computational difficulty always arises to yield a desired convergence due to convoluted geometries, complicated physics of the fluids, structural deformations, and complex fluid-structure interactions. This computational complexity can be reduced by setting the interactional behaviour between fluid and structure. In this paper, several approaches have been discussed in order to reduce computational effort with a desired accuracy
Strong Coupling Algorithm to Solve Fluid-Structure-Interaction Problems with a Staggered Approach
2011
During the last decades, numerical analysis of mult i-physics problems has been increasingly used, espe cially for space applications. A particularly challenging problem is the FSI (Fluid-Structure Interaction), where a flu id flow (liquid or gas) induces forces and thermal fluxes on a solid s tructure, which modifies in return the fluid domain , the velocities and the temperature fields at the fluid-structure inter faces.
Stable and accurate loosely-coupled scheme for unsteady fluid-structure interaction
AIAA Paper, 2007
This paper presents a new loosely-coupled partitioned procedure for modeling fluid-structure interaction. The procedure relies on a higher-order Combined Interface Boundary Condition (CIBC) treatment for improved accuracy and stability of fluid-structure coupling. Traditionally, continuity of velocity and momentum flux along interfaces are satisfied through algebraic interface conditions applied in a sequential fashion, which is often referred to staggered computation. In existing staggered procedures, the interface conditions undermine stability and accuracy of coupled fluid-structure simulations. By utilizing the CIBC technique on the velocity and momentum flux boundary conditions, a staggered coupling procedure can be constructed with similar order of accuracy and stability of standalone computations. Introduced correction terms for velocity and momentum flux transfer can be explicitly added to the standard staggered time-stepping stencils so that the discretization is well-defined across the deformable interface. The new formulation involves a coupling parameter, which has an interval of well-performing values for both classical 1D closed-and open-elastic piston problems. The technique is also demonstrated in 2D in conjunction with the common refinement method for subsonic flow over a thin-shell structure.
Adaptive time stepping for fluid-structure interaction solvers
Finite Elements in Analysis and Design
A novel adaptive time stepping scheme for fluid-structure interaction (FSI) problems is proposed that allows for controlling the accuracy of the time-discrete solution. Furthermore, it eases practical computations by providing an efficient and very robust time step size selection. This has proven to be very useful, especially when addressing new physical problems, where no educated guess for an appropriate time step size is available. The fluid and the structure field, but also the fluid-structure interface are taken into account for the purpose of a posteriori error estimation, rendering it easy to implement and only adding negligible additional cost. The adaptive time stepping scheme is incorporated into a monolithic solution framework, but can straightforwardly be applied to partitioned solvers as well. The basic idea can be extended to the coupling of an arbitrary number of physical models. Accuracy and efficiency of the proposed method are studied in a variety of numerical examples ranging from academic benchmark tests to complex biomedical applications like the pulsatile blood flow through an abdominal aortic aneurysm. The demonstrated accuracy of the time-discrete solution in combination with reduced computational cost make this algorithm very appealing in all kinds of FSI applications.
A comparative study of time-marching schemes for fluid-structure interactions
2014
Four types of partitioned time-marching schemes, namely the iterative staggered serial (ISS) scheme, the conventional serial staggered serial (CSS) scheme, the generalized serial staggered scheme (GSS), and the serial staggered scheme with fluid loads predictions (FPSS), are presented for accuracy comparisons of nonlinear fluid-structure interactions (FSI). A 2-DOF aeroelastic model for an airfoil is used as an example to illustrate the effects of different control parameters of the schemes. Some modifications are made to the schemes to improve the FSI simulation accuracy. The numerical results show that the GSS and FPSS are accurate and robust if the default parameters are adopted. Moreover, the accuracy of FPSS can be further improved by simply tuning the control parameters.
International Journal for Numerical Methods in Fluids, 2010
This work investigates the effect of employing different time integration schemes in the sub-domains of a coupled problem, such as fluid-structure interaction. On the basis of a one-dimensional model problem and the two versions of the generalized-method developed for first-and second-order systems, it is shown that the overall problem is likely to be less stable and less accurate than the individual sub-problems unless special measures are taken. The benchmark problem of the oscillating flexible beam is used to demonstrate that these findings also apply to full computational fluid-structure interaction.
Journal of Applied Mathematics, 2011
The interaction between fluid and structure occurs in a wide range of engineering problems. The solution for such problems is based on the relations of continuum mechanics and is mostly solved with numerical methods. It is a computational challenge to solve such problems because of the complex geometries, intricate physics of fluids, and complicated fluid-structure interactions. The way in which the interaction between fluid and solid is described gives the largest opportunity for reducing the computational effort. One possibility for reducing the computational effort of fluid-structure simulations is the use of one-way coupled simulations. In this paper, different problems are investigated with one-way and two-way coupled methods. After an explanation of the solution strategy for both models, a closer look at the differences between these methods will be provided, and it will be shown under what conditions a one-way coupling solution gives plausible results.