Special issue on the lattice Boltzmann method

A new low-Mach algorithm based on thermal Lattice Boltzmann method (LBM) is proposed aiming at reducing the computational cost of thermal flow simulations in low Mach number limit.Considering the time-step restriction of fully compressible solvers, the Low Mach Number Approximation (LMNA) allows to accelerate significantly the simulations by re-scaling the acoustic speed to the same order of the velocity of the fluid motion when calculating the time-step.The proposed method is inspired by the similarity between the artificial compressibility method and isothermal LBM, and is further extended to thermal counterpart.It must be emphasized that this kind of low-Mach acceleration strategy is a general form and can be easily applied to other thermal LB methods.The present method overcomes the drawback of classical PGS (Pressure Gradient Scaling) method due to the pressure gradient changing. The new algorithm is validated by benchmarking the code on various well-documented academic test cases in laminar (1D gravity column, 2D rising thermal bubble, 2D differentially heated square cavity) and turbulent (Taylor Green Vortex and 3D heated cylinder) regimes.All the results show excellent agreement with reference data of the literature and demonstrate high computational efficiency.

https://hal.science/hal-03796386/document

A new hybrid Lattice-Boltzmann method for thermal flow simulations in low-Mach number approximation

This paper addresses simulation of heat dominated compressible flows in a closed cavity using a pressure-based lattice Boltzmann (LB) method, in which thermal effects are modeled by applying a pressure-featured zero-order moment of distribution functions. A focus is made on the conservation of mass at boundary nodes, which is a challenging issue that significantly complicated by the density-decoupled zero-order moment here. The mass leakage at boundary nodes is mathematically quantified, which enables an efficient local mass correction scheme. The performance of this solver is assessed by simulating buoyancy-driven flows in a closed deferentially heated cavity with large temperature differences (non-Boussinesq) at Rayleigh numbers ranging from 103 to 107. Simulations show that mass leakage at solid walls in such configurations is a critical issue to obtain reliable solutions, and it eventually leads to simulations overflow when the cavity is inclined. The proposed mass correction scheme is, however, shown to be effective to control the mass leakage and get accurate solutions. Thus, associated with the proposed mass conservation scheme, the pressure-based LB method becomes reliable to study natural convection dominated flows at large temperature differences in closed geometries with mesh aligned boundaries or not.

Guanxiong Wang

Papers

Large temperature difference heat dominated flow simulations using a pressure-based lattice Boltzmann method with mass correction