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An Immersed Boundary method with divergence-free velocity interpolation and force spreading
Yuanxun Bao1, Aleksandar Donev1, Boyce E Griffith2
1Courant Institute of Mathematical Sciences, New York University, 251 Mercer Street, New York, NY, USA.
Journal of Computational Physics
|October 10, 2019
Summary
This study introduces a new Immersed Boundary (IB) method to improve volume conservation in fluid-structure interaction simulations. The enhanced method significantly reduces volume errors for elastic structures in viscous fluids.
Area of Science:
- Computational fluid dynamics
- Fluid-structure interaction
Background:
- The Immersed Boundary (IB) method models fluid-structure interaction using Eulerian and Lagrangian frames.
- Conventional IB methods often exhibit poor volume conservation due to non-divergence-free interpolated velocity fields, especially with thin structures and pressure differences.
Purpose of the Study:
- To significantly reduce volume errors in the Immersed Boundary method.
- To develop novel velocity-interpolation and force-spreading schemes for improved accuracy and conservation.
Main Methods:
- Introduced new velocity-interpolation and force-spreading schemes.
- Ensured the interpolated velocity field is divergence-free and the force-spreading operator is the adjoint of the interpolation operator.
- Conducted numerical experiments in 2D and 3D periodic domains.
Main Results:
- Achieved substantial improvement in volume conservation compared to existing IB methods.
- Demonstrated smoother Lagrangian forces (tractions).
- Observed a modest increase in computational cost.
Conclusions:
- The new IB method effectively enhances volume conservation for fluid-structure interaction simulations.
- The method offers improved accuracy and smoother force calculations.
- Future work includes generalizing the method to non-periodic domains.
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