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Projection-based model reduction for the immersed boundary method.

Yushuang Luo1, Xiantao Li1, Wenrui Hao1

  • 1Department of Mathematics, The Pennsylvania State University, University Park, Pennsylvania, USA.

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|December 5, 2021
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Summary
This summary is machine-generated.

This study introduces a computationally efficient reduced-order model (ROM) for simulating fluid-structure interactions in biofluid systems. The method ensures stability and accuracy, significantly reducing computational costs for complex biomolecular simulations.

Keywords:
fluid-structure interactionimmersed boundary methodmodel reduction

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Area of Science:

  • Computational fluid dynamics
  • Biomolecular modeling
  • Scientific computing

Background:

  • Fluid-structure interactions are crucial in biomolecular processes but computationally expensive to model.
  • The immersed boundary method (IBM) is a common approach for biofluid systems.
  • Existing methods face challenges in computational cost and efficiency.

Purpose of the Study:

  • To develop a computationally efficient reduced-order model (ROM) for biofluid systems using the immersed boundary method (IBM).
  • To reduce the computational burden associated with large numbers of fluid variables.
  • To ensure the stability and accuracy of the reduced model.

Main Methods:

  • Application of reduced-order techniques to eliminate fluid degrees of freedom.
  • Derivation of reduced models using Petrov-Galerkin projection.
  • Utilizing subspaces that preserve the incompressibility condition.
  • Employing an interpolation technique for computing coefficient matrices in the ROM.

Main Results:

  • The proposed reduced-order model (ROM) is derived and shown to preserve Lyapunov stability.
  • The method effectively reduces computational cost while maintaining accuracy.
  • Interpolation techniques provide a practical way to compute ROM coefficient matrices.
  • The formulation demonstrates efficiency and robustness across various applications.

Conclusions:

  • The developed ROM offers a significant advancement in simulating fluid-structure interactions in biofluid systems.
  • This approach alleviates computational challenges, making complex biomolecular simulations more feasible.
  • The method is robust and efficient, validated by diverse test cases.