The lattice Boltzmann method for the fractional Navier-Stokes equation
For the numerical solution problem of fractional Navier-Stokes equation,the equation is first discretized.Then the D1 Q3 lattice Boltzmann model is constructed.The macroscopic equation is recovered by Taylor expansion and Chapman-Enskog multi-scale expansion techniques.At the same time,the expression of the equilibrium state distribution function of the model is derived.Finally,according to two numerical examples of one-dimensional,the equation is numerically simulated and its error is analyzed.The obtained numerical solution is compared with the exact solution.Thus,the accuracy and effectiveness of the lattice Boltzmann method are verified.
Caputo fractional-order derivativelattice Boltzmann methodfractional Navier-Stokes equationequilibrium state distribution function
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