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Including fluid shear viscosity in a structural acoustic finite element model using a scalar fluid representation
Lei Cheng1, Yizeng Li, Karl Grosh
1Department of Mechanical Engineering University of Michigan, Ann Arbor, MI 48109, USA.
Journal of Computational Physics
|June 5, 2013
Summary
This study introduces an approximate boundary condition to model fluid shear viscosity in fluid-structure interaction. The new method offers computational advantages and accurate results comparable to Navier-Stokes models.
Area of Science:
- Computational fluid dynamics
- Fluid-structure interaction modeling
- Viscous flow approximations
Background:
- Modeling fluid shear viscosity at boundaries is crucial for accurate fluid-structure interaction (FSI) simulations.
- Existing methods often require computationally expensive solutions of the full Navier-Stokes equations.
Purpose of the Study:
- To develop an approximate boundary condition for modeling fluid shear viscosity in FSI.
- To create a computationally efficient viscous finite element method (FEM) model based on this approximation.
- To evaluate the accuracy and applicability of the developed approximations.
Main Methods:
- Developed an approximate boundary condition using a correction term to inviscid conditions, incorporating second-order in-plane pressure derivatives.
- Formulated both thin and thick viscous boundary layer approximations.
- Integrated these approximations into a variational formulation for a viscous FEM model, requiring minimal changes to inviscid FEM models.
- Compared simulation results with a full, linearized Navier-Stokes model.
Main Results:
- The viscous FEM formulation with the approximate boundary condition offers significant computational advantages due to a single degree of freedom for pressure.
- The thick viscous boundary layer approximation demonstrated good agreement with Navier-Stokes model predictions.
- The thin viscous boundary layer approximation provided accurate results with greater computational simplicity than the thick approximation.
Conclusions:
- The developed approximate boundary conditions provide an accurate and computationally efficient alternative for modeling fluid shear viscosity in FSI problems.
- Guidelines are provided for the parameter ranges where thin and thick boundary layer approximations can be reliably applied.
- The FEM formulation based on these approximations presents a valuable tool for FSI analysis.
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