Solution Of Fluid-structure Interaction Problems Research Articles

Asynchronous multi-splitting method for linear and pseudo-linear problems

This paper deals with the solution of fluid-structure interaction problems using an algorithm consisting in the coupling between two solvers, each one related to the fluid and the structure respectively. Due to the difficult decomposition of the domain into sub-domains, we consider for each environment a parallel multi-splitting algorithm which corresponds to an unified presentation of sub-domain methods with or without overlapping. Such method combines several contractant fixed point mappings and, we show that, under appropriate assumptions, each fixed point mapping are contractive in finite dimensional spaces normed by Hilbertian and non-Hilbertian norms. Moreover, we show in a novel way that such study is valid for the parallel synchronous and more generally asynchronous large scale linear systems arising in the solution of fluid-structure interaction problems and can be extended to the case where the displacement of the structure is submitted to some constraints. We perform parallel simulations for a fluid-structure test case on different clusters, considering blocking and non-blocking communications. The performances of the parallel simulations are presented and analyzed.

Numerical solution of fluid-structure interaction problems by means of a high order Discontinuous Galerkin method on polygonal grids

We consider the two-dimensional numerical approximation of the fluid-structure interaction problem over unfitted fluid and structure meshes. In particular, we consider a method where the fluid mesh (on the background) is fixed, apart from the interface with the moving immersed structure, where general polygonal elements of arbitrary shape and changing in time are generated. The new idea of this work is to handle the discretization on such polygons by using the Discontinuous Galerkin method on polyhedral grids (PolyDG), which has been recently developed for different differential equations and here adapted for the first time to a heterogeneous problem. We prove a stability result of the proposed semi-discrete formulation and discuss how to deal with the partial or total covering of a fluid mesh element due to the structure movement. We finally present some numerical results with the aim of showing the effectiveness of the proposed method.

Pressure-Based and Potential-Based Differential Quadrature Procedures for Free Vibration of Circular Plates in Contact with Fluid

The differential quadrature method (DQM) has been so far applied to a wide variety of fluid and/or structural problems. The results of many researchers reveal that the DQM is computationally efficient and is applicable to a large class of boundary value problems. However, there is little information about its applications to fluid-structure interaction problems. Therefore, the purpose of this paper is to provide some information in this area and to develop procedures based on the DQM for the numerical solution of fluid-structure interaction problems. First, the governing partial differential equations of motion of the structure and fluid are discretized separately using the DQM. Then, by applying the boundary condition at fluid-structure interface, the governing eigenvalue equations of the coupled system are obtained which can then be solved for the eigenvalues of the system. The applicability of the proposed procedures is shown herein through the free vibration analysis of thin circular plates in contact with a cylindrical fluid-filled cavity. Issues related to the implementation of the regularity conditions at the center of the circular plate and the central line of the cylindrical cavity are addressed. Two new regularity conditions are proposed for the circular cylindrical fluid domain. The accuracy and efficiency of the proposed procedures are demonstrated by comparing the obtained results with those available in the literature. It is shown that highly accurate converged results can be obtained by the proposed procedures using a small number of grid points. Three new dimensionless parameters and variables are also introduced for the free vibration of the coupled system. The influences of these parameters on dynamic behavior of the system are studied.

A cut-cell finite volume – finite element coupling approach for fluid–structure interaction in compressible flow

We present a loosely coupled approach for the solution of fluid-structure interaction problems between a compressible flow and a deformable structure. The method is based on staggered Dirichlet-Neumann partitioning. The interface motion in the Eulerian frame is accounted for by a conservative cut-cell Immersed Boundary method. The present approach enables sub-cell resolution by considering individual cut-elements within a single fluid cell, which guarantees an accurate representation of the time-varying solid interface. The cut-cell procedure inevitably leads to non-matching interfaces, demanding for a special treatment. A Mortar method is chosen in order to obtain a conservative and consistent load transfer. We validate our method by investigating two-dimensional test cases comprising a shock-loaded rigid cylinder and a deformable panel. Moreover, the aeroelastic instability of a thin plate structure is studied with a focus on the prediction of flutter onset. Finally, we propose a three-dimensional fluid-structure interaction test case of a flexible inflated thin shell interacting with a shock wave involving large and complex structural deformations.

Second-Order Pure Lagrange--Galerkin Methods for Fluid-Structure Interaction Problems

In this paper, we propose a second-order (both in time and in space) pure Lagrange--Galerkin method for the numerical solution of fluid-structure interaction problems. The proposed scheme is written in material coordinates and in terms of displacements in the structure and of displacements and pressures in the fluid. Pure-Lagrangian displacement methods are useful for solving free surface problems and fluid-structure interaction problems because the computational domain is independent of time, and fluid-structure coupling at the interphase is straightforward. Unfortunately, for moderate- to high-Reynolds number flows, pure-Lagrangian methods can lead to high distortion of the mesh elements, and as a consequence inaccurate approximations can be obtained. Before this happens, it is necessary to remesh and reinitialize the motion. In the present paper, we also deal with this problem by proposing a method to be combined with the pure Lagrange--Galerkin method we introduce that preserves the order. In order to...

On the similarity between Dirichlet–Neumann with interface artificial compressibility and Robin–Neumann schemes for the solution of fluid-structure interaction problems

In this note, the similarity between two implicit, partitioned solution techniques for fluidstructure interaction (FSI) problems is analyzed using finite volume discretization of the flow equations. Fluid-structure interaction refers to the mutual interaction between a fluid flow and a flexible structure. Partitioned solution techniques solve the flow equations and the structural equations separately. These techniques are classified as implicit (or strongly coupled) if they satisfy the interaction conditions on the fluid-structure interface in each time step and as explicit (or loosely coupled) if they do not. Both techniques analyzed in this note use block Gauss-Seidel (GS) iterations, meaning that the flow equations and the structural equations are solved consecutively within a time step until some convergence tolerance is reached. As the flow and structural equations are solved separately, the interaction conditions on the fluid-structure interface have to be converted into boundary conditions on the common boundary of the fluid and structure subdomains. Several types of boundary conditions can be applied, resulting in different decompositions. In the case of Dirichlet-Neumann (DN) decomposition, the flow equations are solved with a Dirichlet boundary condition (given velocity) on the fluid-structure interface, while the structural equations are solved with a Neumann boundary condition (given stress) on the interface. Conversely, RobinNeumann (RN) decomposition, introduced in [1], denotes a Robin boundary condition on the fluid side of the interface and a Neumann boundary condition on the structure side. The first technique in this comparison is block Gauss-Seidel iterations applied to the monolithic system previously multiplied by a suitable permutation matrix, leading to a Robin-Neumann decomposition (GS-RN). This first technique includes a simplified version of the structural model in the flow equations by means of a Robin boundary condition to accelerate the convergence of the GS iterations [1, 2]. The second technique is block Gauss-Seidel iterations with DirichletNeumann decomposition and Interface Artificial Compressibility (GS-DN-IAC). This second

Immersed finite element method for fluid-structure interactions

In this paper, we present a detailed derivation of the numerical method, Immersed Finite Element Method (IFEM), for the solution of fluid-structure interaction problems. This method is developed based on the Immersed Boundary (IB) method that was initiated by Peskin, with additional capabilities in handling nonuniform and independent meshes and applying arbitrary boundary conditions on both fluid and solid domains. A higher order interpolation function is adopted from one of the mesh-free methods, the Reproducing Kernel Particle Method (RKPM), which relieves the uniformity constraint of fluid meshes. Two 2-D example problems are presented to illustrate the capabilities of the algorithm. The accuracy in the numerical analysis demonstrates that the IFEM algorithm is a reliable and robust numerical approach to solve fluid and deformable solid interactions.

Least squares finite element methods for fluid-structure interaction problems

The first order least squares finite element method is an alternative numerical procedure to standard Galerkin methods for the solution of partial differential equations. Its advantages are mainly the resulting symmetric positive definite matrices and the inherent numerical stability. Several first order formulations were proposed for the incompressible Navier–Stokes equations and for the equations of linear elasticity. Here we analyse which of these methods could provide an efficient and accurate tool for the solution of fluid-structure interaction problems. It seems that the combination of inherent least squares stability and high order ansatz functions is very promising.

Acceleration of a fixed point algorithm for fluid-structure interaction using transpiration conditions

In this work, we address the numerical solution of fluid-structure interaction problems. This issue is particularly difficulty to tackle when the fluid and the solid densities are of the same order, for instance as it happens in hemodynamic applications, since fully implicit coupling schemes are required to ensure stability of the resulting method. Thus, at each time step, we have to solve a highly non-linear coupled system, since the fluid domain depends on the unknown displacement of the structure. Standard strategies for solving this non-linear problems, are fixed point based methods such as Block-Gauss-Seidel (BGS) iterations. Unfortunately, these methods are very CPU time consuming and usually show slow convergence. We propose a modified fixed-point algorithm which combines the standard BGS iterations with a transpiration formulation. Numerical experiments show the great improvement in computing time with respect to the standard BGS method.

An application of ADINA to the solution of fluid-structure interaction problems

ADINA is employed to solve the lowest natural frequencies and corresponding mode shapes of a plate and turbine blade when submerged in water. Finite element solution parameters such as integration order of elements, mass matrix, flow around edges, and other modelling considerations are reported. The performance of the present solution algorithms and comparisons with experimentally obtained results are also presented. The experience reported can be useful for the analysis of problems involving an elastic structure immersed in an acoustic fluid (exterior problems) and problems involving an acoustic fluid within elastic structures (interior problems).