Flow characteristics in porous media based on fractional order and multiple relaxation time lattice Boltzmann method and improver Ghost Fluid Method boundary processing mode

In this paper, the multiple relaxation time (MRT) lattice Boltzmann method (LBM) is combined with fractional differentiation to efficiently and accurately model fluid transport in porous media. According to the method of improving fluid-solid boundary processing by the Ghost Fluid (GF) method of Lagrange surface interpolation, the accuracy is at least second order, and two classic cases that the flow around the cylinder and the natural convection of the cylinder in the square cavity are used to verify. In addition, a mathematical model of nanofluid in porous media based on meso-macro-level MRT-GF-LBM and fractional-order theory has been established. It provides a new paradigm for the analysis of multiphase flow characteristics by fractional calculus. Fractional-order theory has the advantage of time memory for the motion analysis of viscoelastic fluids in porous media, while the LBM study is from an interface perspective, which in turn allows the material parameters needed to simulate flow in a macroscopic fractional fluid model to replace experiments. The research results reveal the correlation between the fractional-order parameters α and β and the mass and heat transfer model: as α increases, the velocity increases, while β weakens heat transfer.