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Zhenhua Chai1,2, Baochang Shi1,2, Chengjie Zhan1

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A novel multiple-distribution-function lattice Boltzmann method (MDF-LBM) accurately solves incompressible Navier-Stokes equations. This method enables direct computation of velocity and pressure, achieving second-order spatial accuracy in simulations.

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Area of Science:

  • Computational Fluid Dynamics
  • Numerical Analysis
  • Fluid Mechanics

Background:

  • Incompressible Navier-Stokes equations govern fluid flow.
  • Lattice Boltzmann Methods (LBM) offer a powerful approach for fluid dynamics simulations.
  • Accurate computation of velocity and pressure is crucial for fluid flow analysis.

Purpose of the Study:

  • To propose a multiple-distribution-function lattice Boltzmann method (MDF-LBM) for incompressible Navier-Stokes equations.
  • To demonstrate the recovery of Navier-Stokes equations from the MDF-LBM.
  • To develop a locally computational scheme for velocity gradients and related quantities.

Main Methods:

  • Multiple-distribution-function lattice Boltzmann method (MDF-LBM) with a multiple-relaxation-time model.
  • Taylor expansion analysis to recover Navier-Stokes equations.
  • Computation of velocity and pressure via moments of the distribution function.
  • Local scheme for velocity gradient using non-equilibrium distribution moments.

Main Results:

  • The MDF-LBM correctly recovers the incompressible Navier-Stokes equations.
  • Velocity and pressure are directly computable from distribution function moments.
  • A local computational scheme for velocity gradient, divergence, strain rate, shear stress, and vorticity is developed.
  • Numerical simulations show agreement with analytical/numerical solutions.
  • The method achieves a second-order convergence rate in space.

Conclusions:

  • The proposed MDF-LBM is a valid and accurate method for solving incompressible Navier-Stokes equations.
  • The developed local scheme efficiently computes important flow quantities.
  • The MDF-LBM demonstrates robust performance and high accuracy for fluid dynamics problems.