An accelerated multi-relaxation-time lattice Boltzmann method for natural convection coupled with an improved U-net

An improved U-net accelerated coupling model, tailored for multi-relaxation-time lattice Boltzmann method (MRT-LBM), is proposed in the current paper. The coupling model is employed to analyze the natural convection process with a protruded triangular thermal conductivity boundary on high-temperature wall in a square cavity. The acceleration effect of the coupling model is analyzed and compared under different arrangements of the thermal conductivity triangle at several positions (Lc), varying hypotenuse lengths (Lb), and different Rayleigh number (Ra), leading to the following significant findings: The application of the coupling model with different Lc results in significant improvements in convergence iteration steps and computation time, achieving the maximum efficiencies improvement of 16.77% and 19.03%, respectively. Then, the coupling model demonstrates an enhanced efficiency of up to 19.31% and 27.33% in terms of convergence iteration steps and computation time, respectively, when considering Lb variations; When the coupling model is applied in different Ra conditions, the efficiency of converging number and computation time is improved by 25.9% and 25.44%, respectively. Additionally, the maximum relative error of the average Nu numbers under different Lc, Lb, and Ra conditions is 0.66%, 0.89%, and 0.77%, respectively (all less than 1%), which indicates that the model has high generalization performance and accuracy and provides an effective reference for the acceleration of MRT-LBM.