Thermal cascaded lattice Boltzmann method

TL;DR

This paper introduces a thermal cascaded lattice Boltzmann method (TCLBM) that effectively simulates low-Mach number compressible flows with heat transfer, incorporating viscous heat dissipation, external forces, and adjustable parameters, validated through various flow problems.

Contribution

The paper develops a novel TCLBM combining cascaded and BGK schemes for flow and temperature fields, with improved force handling and broader applicability to compressible flows.

Findings

Accurate simulation of thermal flows with viscous heat dissipation.

Validation against analytical solutions and previous research.

Effective modeling of low-Mach number compressible flows.

Abstract

In this paper, a thermal cascaded lattice Boltzmann method (TCLBM) is developed in combination with the double-distribution-function (DDF) approach. A density distribution function relaxed by the cascaded scheme is employed to solve the flow field, and a total energy distribution function relaxed by the BGK scheme is used to solve temperature field, where two distribution functions are coupled naturally. The forcing terms are incorporated by means of central moments, which is consistent with the previous force scheme [Premnath \emph{et al.}, Phys. Rev. E \textbf{80}, 036702 (2009)] but the derivation is more intelligible and the evolution process is simpler. In the method, the viscous heat dissipation and compression work are taken into account, the Prandtl number and specific-heat ratio are adjustable, the external force is considered directly without the Boussinesq assumption, and the low-Mach number compressible flows can also be simulated. The forcing scheme is tested by simulating a steady Taylor-Green flow, and the new TCLBM is then tested by numerical experiments of the thermal Couette flow, low-Mach number shock tube problem, and Rayleigh-B\'{e}nard convection. The simulation results agree well with the analytical solutions and/or results given by previous researchers.