A Fully Implicit Computational Strategy for Strongly Coupled Fluid–Solid Interaction

Abstract

This article summarises the authors' research work in the area of computational modelling of interaction of fluid flow with solid structures. Our approach relies on a fully implicit iterative solution strategy which resolves the strong coupling and allows for optimal rate of convergence of the residuals. Therefore, the methodology is a viable competitor for the solution of the highly nonlinear interaction of fluid flow with solid structures that experience large displacements and deformations.The key ingredients of our strategy include the following: Stabilised low order velocity-pressure finite elements are used for the modelling of the fluid flow combined with an arbitrary Lagrangian-Eulerian (ALE) strategy. For the temporal discretisation of both fluid and solid bodies, the discrete implicit generalised-α method is employed. An important aspect of the present work is the introduction of the independent interface discretisation, which allows an efficient, modular and expandable implementation of the solution strategy. A simple data transfer strategy based on a finite element type interpolation of the interface degrees of freedom guarantees kinematic consistency and equilibrium of the stresses along the interface. The resulting strongly coupled set of nonlinear equations is solved by means of a partitioned solution procedure, which is based on the Newton-Raphson methodology and incorporates the full linearisation of the overall incremental problem. Thus, asymptotically quadratic convergence of the residuals is achieved.Numerical examples are presented to demonstrate the robustness and efficiency of the methodology. Finally, we present the results obtained by combining the presented methodology with a remeshing procedure.

Partitioned solution to fluid–structure interaction problem in application to free-surface flows

“…For coupled fluid-structure interaction problems, the monolithic [38,65,20] and partitioned strategy [24,53,59,11,27,58,18,31,26,77] can be used. The monolithic approach is abandoned in favor of the partitioned approach.…”

On the temporal stability and accuracy of coupled problems with reference to fluid–structure interaction

“…After substitution of Equations (8), (10), (14) and (15) into Equation (18), and combining this with Equations (11), (12), (16), (19) and (20), the total set of equations to describe …”

“…At the interface, Equation (18) requires that the force exerted by m s on m f is equal to the force exerted by m f on m s . However, if two different time integration schemes are used, the forces are not evaluated at exactly the same time instant within a time step.…”

“…In order to demonstrate the relevance of the above findings for fluid-structure interaction problems, the flow-induced oscillation of a flexible beam, as first simulated in [5] and since then commonly used as a benchmark problem (see e. g. [17,18]), is considered. A flexible beam attached to a square rigid body is placed in a uniform flow field.…”

“…The publications [5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20] and references therein describe different computational strategies for fluid-structure interaction and involve either one or more time integration schemes. It is noted that the information provided on the integration of time and the temporal matching of kinematic quantities at the interface is often missing or simply not given in an explicit way.…”