Cascaded lattice Boltzmann method for incompressible thermal flows with heat sources and general thermal boundary conditions

TL;DR

This paper extends the cascaded lattice Boltzmann method (CLBM) to simulate incompressible thermal flows with heat sources and complex boundary conditions, demonstrating improved stability and accuracy over traditional methods.

Contribution

The authors develop a new CLBM framework incorporating a discrete source term and general boundary conditions for thermal flow simulations.

Findings

Numerical results agree well with analytical solutions.

The method effectively handles complex thermal boundary conditions.

The approach improves numerical stability and accuracy.

Abstract

Cascaded or central-moment-based lattice Boltzmann method (CLBM) is a relatively recent development in the LBM community, which has better numerical stability and naturally achieves better Galilean invariance for a specified lattice compared with the classical single-relation-time (SRT) LBM. Recently, CLBM has been extended to simulate thermal flows based on the double-distribution-function (DDF) approach [L. Fei \textit{et al.}, Int. J. Heat Mass Transfer 120, 624 (2018)]. In this work, CLBM is further extended to simulate thermal flows involving complex thermal boundary conditions and/or a heat source. Particularly, a discrete source term in the central-moment space is proposed to include a heat source, and a general bounce-back scheme is employed to implement thermal boundary conditions. The numerical results for several canonical problems are in good agreement with the analytical solutions and/or numerical results in the literature, which verifies the present CLBM implementation for thermal flows.