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Evolution of Staircase Structures in Diffusive Convection
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Multiple-time-scaling lattice Boltzmann method for the convection diffusion equation.

Like Li1

  • 1Department of Mechanical Engineering, Mississippi State University, Mississippi State, Mississippi 39762, USA.

Physical Review. E
|July 24, 2019
PubMed
Summary

A novel multiple-time-scaling (MTS) strategy for the lattice Boltzmann method (LBM) allows flexible time steps in simulations. This approach enhances modeling of complex fluid dynamics and transport phenomena.

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Area of Science:

  • Computational fluid dynamics
  • Numerical methods
  • Partial differential equations

Background:

  • The lattice Boltzmann method (LBM) is a powerful tool for simulating fluid flow and transport phenomena.
  • Accurate and efficient time discretization is crucial for LBM simulations, especially for complex problems.
  • Existing LBM methods often face limitations in handling varying temporal scales.

Purpose of the Study:

  • To develop a multiple-time-scaling (MTS) strategy for the LBM.
  • To enable flexible time-step control (coarsening, refinement, stretching) in LBM simulations.
  • To improve the efficiency and applicability of LBM for complex flow and transport problems.

Main Methods:

  • Developed a multiple-time-scaling (MTS) strategy that decouples time discretization across different domains.
  • Implemented interface schemes for distribution functions to satisfy physical conditions without nested iterations.
  • Applied the MTS strategy to the convection-diffusion equation within the LBM framework.

Main Results:

  • Demonstrated the applicability and second-order accuracy of the MTS-LBM approach through two numerical tests.
  • The MTS strategy allows for flexible time-step adjustments without compromising accuracy.
  • Successfully modeled convection-diffusion phenomena with improved efficiency.

Conclusions:

  • The developed MTS-LBM strategy offers a flexible and accurate approach for time discretization.
  • This method significantly expands the scope of LBM for complex multiphase and multicomponent flows.
  • The MTS-LBM approach accelerates progress in simulating challenging transport phenomena with large property ratios.