A Modified Regularized Lattice Boltzmann Method for Coupled Thermal-Solutal Problems of Non-Newtonian Fluids in Heterogeneously Porous Media (Advances in Applied Mathematics and Mechanics, 2025)
In this study, we present a modified regularized lattice Boltzmann method(RLBM) designed to simulate double-diffusive convection of non-Newtonian fluidswithin heterogeneously porous media. The modification involves the incorporation ofcorrection terms related to shear rate and heat (or concentration) flux into the evolutionequations of the RLBM for hydrodynamic equations and convection-diffusion equation, respectively. This allows shear-dependent viscosities and diffusion coefficients tobe controlled by additional parameters, enabling the relaxation coefficients in the collision process to remain fixed at optimal values. Through multi-scale Chapman-Enskoganalysis, the modified RLBM accurately recovers the governing equations for double-diffusive convection of non-Newtonian fluids within porous media at the representative elementary volume scale. The validity of the method is demonstrated by simulating double-diffusive natural convection in a two-dimensional porous cavity filledwith power-law and viscoplastic fluids, with the numerical results showing strongagreement with established data from prior studies. Additionally, the influences ofkey dimensionless parameters, such as porosity, Bingham number, and power-law index, are thoroughly examined across a range of values.