New Cascaded Thermal Lattice Boltzmann Method for simulations of advection-diffusion and convective heat transfer

Abstract

A Cascaded Thermal Lattice Boltzmann Method (CTLBM) is presented for efficient simulations of fluid flow and heat transfer problems. Contrary to the Bhatnagar-Gross-Krook Single Relaxation Time (BGK-SRT or just BGK) and Multiple Relaxation Times (MRT) methods of the LBM used for thermal problems, the proposed CTLBM improves Galilean invariancy of the method. The cascaded collision scheme was proved to increase the stability of the LBM in the case of fluid flow. Here we prove the enhanced stability and accuracy of the CTLBM scheme for thermal problems by comparing our results to traditional thermal BGK and MRT lattice Boltzmann methods. The proposed numerical scheme employs cascaded D2Q9 model for fluid flow and cascaded D2Q5 model for the temperature to study advection diffusion of sine wave and forced convection phenomena in forced cooling of a cylinder with heated core. To validate the proposed scheme, we compare our numerical results to the exact solutions of the sine wave advection-diffusion in 1D system for Peclet numbers between 102 and 106. We also present comparisons of our CTLBM with BGK and two widely used MRT lattice Boltzmann methods for several lattice resolutions. For 2D case, we present numerical validation of forced cooling of a cylinder with heated core. To show the stability of the proposed CTLBM even for moderate lattice resolutions, we also present numerical simulations of forced convection across the row of hot tubes and double shear layer flow. The numerical simulations are faster and numerical results are in strong agreements with those available in the literature. The enhanced stability and accuracy of the cascaded scheme are clearly evident in the numerical results. Therefore, we show that the proposed CTLBM possesses higher stability and good accuracy with faster computation speed when compared to the other thermal BGK and MRT LBMs.