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Mass-conserved volumetric lattice Boltzmann method for complex flows with willfully moving boundaries.

Huidan Yu1, Xi Chen1, Zhiqiang Wang2

  • 1Department of Mechanical Engineering, Indiana University-Purdue University Indianapolis, Indianapolis, Indiana 46202, USA.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|July 15, 2014
PubMed
Summary

A new mass-conserved volumetric lattice Boltzmann method (MCVLBM) accurately simulates fluid dynamics with moving boundaries. This computational fluid dynamics approach is validated for complex scenarios like blood flow in arteries.

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Area of Science:

  • Computational fluid dynamics
  • Numerical methods
  • Fluid mechanics

Background:

  • Simulating fluid dynamics with moving boundaries is challenging.
  • Existing methods often struggle with mass conservation and complex geometries.
  • Accurate modeling is crucial for applications in engineering and biomedical fields.

Purpose of the Study:

  • To develop a novel mass-conserved volumetric lattice Boltzmann method (MCVLBM).
  • To enable accurate numerical simulation of fluid dynamics involving willfully moving arbitrary boundaries.
  • To validate the method's reliability and simplicity for complex flow problems.

Main Methods:

  • Introduced a volumetric parameter P to classify lattice cells (solid, fluid, boundary).
  • Developed volumetric lattice Boltzmann equations with collision, streaming, and boundary-induced migration.
  • Implemented a volumetric bounce-back procedure for boundary cells.

Main Results:

  • MCVLBM strictly satisfies mass conservation for moving boundaries.
  • Validated against analytical solutions for 2D peristaltic and 3D pipe flows.
  • Successfully simulated complex 2D/3D blood flow in human aortic arteries, showing good agreement with Navier-Stokes solvers.

Conclusions:

  • MCVLBM is a reliable and relatively simple computational scheme.
  • The method effectively handles static or moving irregular boundaries.
  • Demonstrated accuracy and applicability for complex fluid dynamics simulations.