Lattice Boltzmann method for thermal flow simulation on standard lattices

TL;DR

This paper extends a lattice Boltzmann model with energy conservation to simulate thermal flows on standard lattices, validated through classical convection problems, enhancing the method's applicability.

Contribution

The paper introduces a thermal lattice Boltzmann model on standard square lattices with nine velocities, enabling accurate thermal flow simulations.

Findings

Successful simulation of thermal Couette flow

Accurate modeling of Rayleigh-Bénard convection

Validation against benchmark problems

Abstract

The recently introduced consistent lattice Boltzmann model with energy conservation [S. Ansumali, I.V. Karlin, Phys. Rev. Lett. 95, 260605 (2005)] is extended to the simulation of thermal flows on standard lattices. The two-dimensional thermal model on the standard square lattice with nine velocities is developed and validated in the thermal Couette and Rayleigh-B\'{e}nard natural convection problems.