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Algorithm to implement unsteady jump boundary conditions within the lattice Boltzmann method.

Badr Kaoui1

  • 1Biomechanics and Bioengineering Laboratory, Université de Technologie de Compiègne, CNRS, 60200, Compiègne, France. badr.kaoui@utc.fr.

The European Physical Journal. E, Soft Matter
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A new algorithm simplifies implementing unsteady jump boundary conditions in lattice Boltzmann methods (LBM) for mass transfer problems. This method accurately models concentration discontinuities across membranes and handles complex moving boundaries.

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Area of Science:

  • Computational fluid dynamics
  • Biophysics
  • Chemical engineering

Background:

  • Mass transfer across membranes is crucial in biological and industrial processes.
  • Modeling concentration discontinuities and resistance at membrane interfaces presents computational challenges.
  • Existing lattice Boltzmann methods (LBM) require robust algorithms for unsteady jump boundary conditions.

Purpose of the Study:

  • To develop and validate a novel algorithm for implementing unsteady jump boundary conditions within the LBM framework.
  • To enable accurate simulation of solute transport across membranes with discontinuous concentration profiles.
  • To extend LBM capabilities for handling complex geometries and moving boundaries in mass transfer problems.

Main Methods:

  • An algorithm was developed to incorporate unsteady jump boundary conditions into the LBM.
  • The algorithm was integrated into an existing LBM code for solute diffusion and advection.
  • The immersed boundary method was combined with the LBM algorithm to handle deformable and moving boundaries.

Main Results:

  • The proposed algorithm successfully implements unsteady jump boundary conditions in LBM.
  • Simulations recovered analytical solutions in the limiting case of planar membranes.
  • The method demonstrated the ability to simulate controlled solute release from stationary and moving particles with arbitrary geometries.

Conclusions:

  • The developed algorithm provides a simple and effective method for simulating mass transfer with discontinuous concentrations using LBM.
  • The approach is versatile, capable of handling complex, dynamic boundary conditions.
  • This work offers a valuable tool for studying solute transport in various scientific and engineering applications.