Multiblock approach for the passive scalar thermal lattice Boltzmann method

Area of Science:

• Computational Fluid Dynamics
• Thermal Physics
• Numerical Methods

Background:

• The thermal lattice Boltzmann method (TLBM) is a powerful tool for simulating heat transfer phenomena.
• Existing TLBM implementations face challenges with computational efficiency and accurate heat flux calculation.

Purpose of the Study:

• To develop a multiblock approach for TLBM with a multiple-relaxation-time collision scheme.
• To introduce a local scheme for computing heat flux, avoiding explicit temperature gradient calculations.
• To validate the proposed methods through simulations of thermal Couette flow and natural convection.

Main Methods:

• Chapman-Enskog analysis to derive the multiblock approach.
• Direct interaction in moment space for block coupling.
• A local pseudoparticle-based scheme for heat flux computation.
• Simulation of thermal Couette flow and natural convection in a square cavity.

Main Results:

• Theoretical analysis confirms the rescaling of nonconserved moments and direct calculation of conserved moments.
• The multiblock approach does not degrade the convergence rate of TLBM.
• The local heat flux scheme achieves a second-order convergence rate.
• Successful simulation of natural convection up to a Rayleigh number of 10^9.

Conclusions:

• The proposed multiblock TLBM approach is computationally efficient and accurate.
• The local heat flux scheme provides a robust and accurate alternative to finite-difference methods.
• The developed methods are suitable for simulating complex thermal flows, including high Rayleigh number natural convection.