Numerical Simulation of Power-Law Fluid Flow in a Trapezoidal Cavity Using the Incompressible Finite-Difference Lattice Boltzmann Method (Communications in Computational Physics, 2025)
In this paper, a numerical investigation of power-law fluid flow in the trapezoidal cavity has been conducted by incompressible finite-difference lattice Boltzmannmethod (IFDLBM). By designing the equilibrium distribution function, the Navier-Stokes equations (NSEs) can be recovered exactly. Through the coordinate transformation method, the body-fitted grid in physical region is transformed into a uniform gridin computational region. The effect of Reynolds $(Re)$ number, the power-law index $n$ and the vertical angle $θ$ on the trapezoidal cavity are investigated. According to thenumerical results, we come to some conclusions. For low $Re$ number $Re =100,$ it canbe found that the behavior of power-law fluid flow becomes more complicated withthe increase of $n.$ And as vertical angle $θ$ decreases, the flow becomes smooth and thenumber of vortices decreases. For high $Re$ numbers, the flow development becomesmore complex, the number and strength of vortices increase. If the Reynolds numberincreases further, the power-law fluid will changes from steady flow to periodic flowand then to turbulent flow. For the steady flow, the lager the $θ,$ the more complicatedthe vortices. And the critical $Re$ number from steady to periodic state decreases withthe decrease of power-law index $n.$
Keywords: Finite difference lattice Boltzmann method; coordinate transformation; power-law fluid; trapezoidal cavity