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A Variational Multiscale method with immersed boundary conditions for incompressible flows
1Department of Civil and Environmental Engineering, University of Illinois at Urbana-Champaign, Urbana, IL 61801, USA.
Meccanica
|September 1, 2023
Summary
This study introduces a new stabilized Navier-Stokes method for fluid dynamics simulations. It accurately models boundary layers around immersed objects using a parameter-free approach derived from the Variational Multiscale method.
Area of Science:
- Computational Fluid Dynamics
- Numerical Analysis
- Fluid Mechanics
Background:
- Incompressible Navier-Stokes equations are fundamental in fluid dynamics.
- Accurate enforcement of Dirichlet boundary conditions at immersed boundaries is challenging.
- Existing methods often require user-defined parameters or struggle with complex geometries.
Purpose of the Study:
- To develop a novel stabilized formulation of the incompressible Navier-Stokes equations.
- To enable weak enforcement of Dirichlet boundary conditions at immersed boundaries.
- To create a parameter-free stabilization method for robust fluid simulations.
Main Methods:
- Derivation of boundary terms using the Variational Multiscale (VMS) method.
- Local solution of fine-scale variational problems near boundaries.
- Variational embedding of the fine-scale model into the coarse-scale formulation.
- Implementation with quadrilateral and hexahedral finite elements.
Main Results:
- A stabilized method free of user-defined parameters was developed.
- The method naturally incorporates area-averaging and stress-averaging properties.
- Numerical simulations using 2D and 3D benchmark problems demonstrated robustness and accuracy.
- Effective modeling of boundary layers around immersed objects was achieved.
Conclusions:
- The proposed method provides a mathematically robust and computationally stable approach.
- It accurately captures fluid behavior near immersed boundaries, even when misaligned with the mesh.
- This work advances numerical techniques for complex fluid flow problems.
Keywords:
Immersed boundaryIncompressible fluidsInterfacial stabilizationVariational Multiscale methodWeakly imposed essential boundary conditionsMore Related Videos
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