An eXtended Finite Element Method based approach for large deformation fluid-structure interaction

This paper illustrates aspects of an ongoing effort to develop a fixed grid fluid-structure interaction scheme that can be applied to the interaction of most general structures with incompressible flow. After presenting a list of requirements for future fixed grid methods, an eXtended Finite Element Method (XFEM) based fixed grid method is proposed. The extended Eulerian fluid field and the Lagrangian structural field are coupled using an partitioned, iterative approach. It will allow the simulation of large deformations of thin and bulky structures. Finally, first results illustrating the essential capabilities are presented

An ALE-Chimera method for large deformation fluid structure interaction

This note discusses a combination of the Chimera fixed grid approach and Arbitrary Lagrangean Eulerian ('ALE') based methods for large deformation fluid structure interaction ('FSI'). The governing equations for incompressible flows in an Eulerian framework, a rotating frame of reference and an ALE-setting are discussed in order to point out the relatedness of these approaches. An algorithm to solve the Navier-Stokes-equations on domains with large deformations in an ALE-Chimera framework is derived from these equations. Some remarks on the implementation of the method are made, and in the end the theory is illustrated by small numerical examples

Efficient approaches for fluid structure interaction with fully enclosed incompressible flow domains

Many popular partitioned approaches to fluid-structure interaction (FSI) problems fail to work for an interesting subset of problems if highly deformable structures are interacting with incompressible flows. This is particularly true for coupling approaches based on Dirichlet-Neumann substructuring, both for weak and strong coupling schemes. The subset is characterized by the absence of any unconstrained out flow boundary at the fluid field, that is the fluid domain is entirely enclosed by Dirichlet boundary conditions. The inflating of a balloon with prescribed in flow rate constitutes a simple problem of that kind. The commonly used coupling algorithms will not satisfy the fluid's incompressibility during the FSI iterations in such cases. That is because the structure part determines the interface displacements and the structural solver does not know about the constraint on the fluid field. To overcome this deficiency of partitioned algorithms a small augmentation is proposed that consists in introducing the fluid volume constraint on the structural system of equations. This allows to circumvent the dilemma of the fluid's incompressibility. At the same time the use of a Lagrangian multiplier to introduce the volume constraint allows to obtain the pressure level of the fluid domain. However, the customary applied relaxation of the interface displacements has to be abandoned in favor of the relaxation of coupling forces. These modifications applied to a particular strong coupled Dirichlet-Neumann partitioning scheme result in an efficient and robust approach that exhibits only little additional numerical effort. Numerical examples with largely changing volumes of the enclosed fluid show the capabilities of the proposed scheme

The artificial added mass effect in sequential staggered fluid-structure interaction algorithms

The artificial added mass effect inherent in sequentially staggered coupling schemes is investigated by means of a fluid-structure interaction problem. A discrete representation of a simplified added mass operator in terms of the participating coefficient matrices is given and instability conditions are evaluated for different temporal discretisation schemes. With respect to the time discretisation two different cases are distinguished. Discretisation schemes with stationary characteristics might allow for stable computations when good natured problems are considered. Such schemes yield a constant instability limit. Temporal discretisation schemes which exhibit recursive characteristics however yield an instability condition which is increasingly restrictive with every further step. Such schemes will therefore definitively fail in long time simulations irrespective of the problem parameters. It is also shown that for any sequentially staggered scheme and given spatial discretisation of a problem, a mass ratio between fluid and structural mass density exists at which the coupled system becomes unstable. Numerical observations confirm the theoretical results

Multiscale Methods in Computational Fluid and Solid Mechanics

The basic idea of multiscale methods, namely the decomposition of a problem into a coarse scale and a fine scale, has in an intuitive manner been used in engineering for many decades, if not for centuries. Also in computational science, large-scale problems have been solved, and local data, for instance displacements, forces or velocities, have been used as boundary conditions for the resolution of more detail in a part of the problem. Recent years have witnessed the development of multiscale methods in computational science, which strive at coupling fine scales and coarse scales in a more systematic manner. Having made a rigorous decomposition of the problem into fine scales and coarse scales, various approaches exist, which essentially only differ in how to couple the fine scales to the coarse scale. The Variational Multiscale Method is a most promising member of this family, but for instance, multigrid methods can also be classified as multiscale methods. The same conjecture can be substantiated for hp-adaptive methods. In this lecture we will give a succinct taxonomy of various multiscale methods. Next, we will briefly review the Variational Multiscale Method and we will propose a space-time VMS formulation for the compressible Navier-Stokes equations. The spatial discretization corresponds to a high-order continuous Galerkin method, which due to its hierarchical nature provides a natural framework for `a priori' scale separation. The latter property is crucial. The method is formulated to support both continuous and discontinuous discretizations in time. Results will be presented from the application of the method to the computation of turbulent channel flow. Finally, multigrid methods will be applied to fluid-structure interaction problems. The basic iterative method for fluid-structure interaction problems employs defect correction. The latter provides a suitable smoother for a multigrid process, although in itself the associated subiteration process converges slowly. Indeed, the smoothed error can be represented accurately on a coarse mesh, which results in an effective coarse-grid correction. It is noted that an efficient solution strategy is made possible by virtue of the relative compactness of the displacement-to-pressure operator in the fluid-structure interaction problem. This relative compactness manifests the difference in length and time scales in the fluid and the structure and, in this sense, the multigrid method exploits the inherent multiscale character of fluid-structure-interaction problems.Aerospace Engineerin