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Lid-driven cavity case with Fluent2D and KratosStructure2D

This case is an FSI-adaptation of the famous lid-driven cavity case, calculated using Fluent and KratosMultiphysics StructuralMechanicsApplication. Here, the bottom wall is deformable and an oscillatory velocity is applied at the top.

geometry

The oscillatory x-component of the velocity is applied not only at the top, but also in a region at the upper left side wall. As shown in the figure above, the velocity increases linearly with the height. The y-component of the velocity is zero. The oscillating velocity \bar{v} is given by $$ \bar{v}=1-\cos\left(\frac{2\pi t}{5}\right), $$ with t the time. On the corresponding region on the right side, zero pressure is applied. The deformable bottom is fixed at the corners.

The fluid parameters are:

  • density: 1 kg/mÂł
  • dynamic viscosity: 0.01 Pa\cdots

The deformable bottom is fixed at its left and right side and consists of a linear elastic material with the follwing properties:

  • density: 500 kg/mÂł
  • modulus of elasticity: 250 Pa
  • poisson's ratio: 0.0

The total simulated time is 70 s in time steps of 0.1 s.

Reference solutions are available from Mok [1] and Valdes [2]. The figure belows shows a comparison with the solution of the examples with Fluent and OpenFOAM.

comparison

The following figures show contour plots of the pressure and velocity for this example (with Fluent).

velocity pressure

A script evaluate_benchmark.py is provided to compare the results with the benchmark results in [1] and lid_driven_cavity_. Furthermore, the script animate_lid_driven_cavity.py can be used to visualize the interface data throughout the calculation.

Coupling algorithm

The coupling technique used is the interface quasi-Newton algorithm with an approximation for the inverse of the Jacobian from a least-squares model (IQN-ILS). No reuse is employed, so the reuse parameter q is set to 0.

Predictor

The initial guess in every time step is done using the linear predictor.

Convergence criterion

Two convergence criteria have been specified:

  • The number of iterations in every time step is larger than 15.
  • The residual norm of the displacement is smaller than 10^{-9}.

When either criterion is satisfied the simulation stops.

Solvers

Fluent is used as flow solver. A quadrilateral mesh is used with 32 cells on each side of the cavity. A script to regenerate it using Gambit is included. This script allows to change the resolution and geometrical parameters. Dynamic mesh motion is achieved using a spring method.

The structural solver is KratosMultiphysics StructuralMechanicsApplication (abbreviated KratosStructure). The deformable bottom is meshed with 2 layers of 32 TotalLagrangianElement2D4N elements. The movement of the left and right side is constrained.

To exchange information between the solvers on the fluid-structure interface, the use of mappers is required. In the structural solver wrapper, a linear interpolation mapper is used to interpolate in the x-direction from and to the coupled solver.

References

[1] Mok D. P., “Partitionierte LösungsansĂ€tze in der Strukturdynamik und der Fluid−Struktur−Interaktion”, PhD thesis: Institut fĂŒr Baustatik, UniversitĂ€t Stuttgart, 2001.

[2] ValdĂ©s G. and Gerardo J., “Nonlinear Analysis of Orthotropic Membrane and Shell Structures Including Fluid-Structure Interaction”, PhD thesis: Universitat PolitĂšcnica de Catalunya, 2007.