A partitioned model for fluid–structure interaction problems using hexahedral finite elements with one‐point quadrature

Abstract

A partitioned numerical model for fluid-structure interaction analysis of incompressible flows and structures with geometrically non-linear behavior is presented in this work. The flow analysis is performed considering the well-known Navier-Stokes equations for Newtonian fluids and the continuity equation, obtained from the pseudo-compressibility hypothesis. An explicit two-step Taylor-Galerkin scheme is employed in the time discretization procedure of the system of governing equations, which is expressed in terms of an arbitrary Lagrangean-Eulerian description. The structural subsystem is analyzed using a geometrically non-linear elastic model and the respective equation of motion is discretized in the time domain employing the Generalized-scheme. Fluid-structure coupling is taken into account regarding a new energy-conserving partitioned scheme with non-linear effects, which is accomplished by enforcing equilibrium and kinematical compatibility conditions at the solid-fluid interface. Non-matching meshes and subcycling are also considered in the present model. The finite element method is employed for spatial discretizations using eight-node hexahedral elements with one-point integration in both fields. Some numerical examples are simulated in order to demonstrate the applicability of the proposed formulation.A. L. BRAUN AND A. M. AWRUCH associated physical problem adequately. Consequently, an increasing demand for accurate numerical models to simulate fluid-structure interaction (FSI) phenomena has been observed in recent years. These models may present different levels of accuracy, depending on the different approaches assumed for the fluid field (Navier-Stokes equations for viscous incompressible flows or Euler equations for inviscid compressible flows), for the structural field (rigid-body motion analysis, geometrically linear/non-linear elastodynamic analysis) and for the coupling scheme (monolithic or partitioned methods). Moreover, owing to the huge computational efforts inherent to FSI analyses, numerical facilities are also very helpful to obtain efficient algorithms, which include nonmatching meshes for fluid and structure at the interface, an unique finite element formulation (for instance, eight-node hexahedral elements with one-point integration) for spatial approximation in both subsystems and subcycling techniques to enable independent time approximation for each physical field.Many realistic flows (for instance, wind action over bluff bodies) may be well represented using the viscous incompressible flow theory, which is fully described by the Navier-Stokes equations. However, incompressible flow analyses are very hard to perform by numerical simulation owing to restrictions imposed by the continuity equation, which is reduced to the divergencefree condition on the velocity field. The incompressibility constraint usually leads to implicit treatment of the pressure field, which requires additional storage capacity of the computational memory. Moreover, implicit algorithms are not suitable to analy...

Aerodynamic and aeroelastic analyses on the CAARC standard tall building model using numerical simulation

“…(8) demands two filtering processes on the flow governing equations: the first filtering is associated to the classical LES formulation, which is related to the grid filter D and the large scale variables. The second filtering process is referred to another filter called test filter hDi, which must be larger than the first grid filter D. Further information about the turbulence model adopted in this work may be found in Braun and Awruch [48].…”

“…An algorithm for FSI analysis is presented in Table 3 and a complete description of the coupling model as well as the matching and data transfer schemes utilized in this work may be found in Braun and Awruch [48].…”

“…In the present work a coupling formulation presented by Braun and Awruch [48] to analyze highly nonlinear structures is adopted, which may be described by the following expressions (see also Fig. 1):…”

“…[48]) should be implemented in order to perform the load transfer from nodes of the fluid domain to nodes of element faces of the structural domain and to transfer the kinematical conditions from the structural domain to the fluid domain at the interface. After the relation between nodes belonging to the fluid domain and the corresponding local coordinates on element faces belonging to the structure is established in the preprocessing stage, the data transfer procedure across the interface is performed in the same manner throughout the numerical simulation.…”

Combined interface boundary condition method for fluid–structure interaction: Some improvements and extensions

“…Farhat and Lesoinne (2000) proposed a conserving partitioned coupling algorithm via offsetting half a time step to satisfy geometric conservation law (GCL) without violating the continuity condition on the interface. This notion was later extended by Braun and Awruch (2009) to the generalized-α time marching method. A transpiration condition was derived from the truncated Taylor expansion of the fluid velocity in the reference interface's neighborhood (Fanion et al, 2000;Deparis et al, 2003).…”