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Abstract: This study reports on further development of a finite difference method formulated on the basis of a linearized-Boltzmann-type-equation for thermal incompressible flows with external body force effect. In classical lattice Boltzmann methods, a pressure-density relation, and/or a finite Mach number, no matter how small, are required in the solution of the linearized Boltzmann-type equation, thus generating inherent compressibility error unavoidably. In the present approach, the pressure field is determined by a pressure-correction method to ensure incompressibility, thus the approach is valid for both liquid and incompressible gas flows. A variety of thermal laminar incompressible flows, such as Couette flow, falling thin liquid film flow, fluid flow through porous plates, and two- and three-dimensional natural convection flow are simulated. The results compared extremely well with analytical solutions and other known numerical simulations of the thermal incompressible flows investigated. [Copyright &y& Elsevier]

This paper reports on a one-step simulation study of the generation and propagation of thermoacoustic waves in a two-dimensional enclosure using a finite-difference lattice-Boltzmann-type method (FDLBM) with a single relaxation time and one equilibrium particle distribution function (EPDF), and a direct aeroacoustic simulation (DAS) technique that solves the primitive Navier–Stokes (N–S) equations. Conventional expansion of the EPDF is not adopted; instead, it is expanded in terms of the particle velocity alone, and the expansion coefficients are determined by requiring the FDLBM to fully recover the N–S equations. The expansion coefficients are found to depend on the flow and thermal properties and their nonlinear interactions. Thus formulated, physical boundary conditions can be specified for the FDLBM. This EPDF has been validated against simple aeroacoustic problems and good agreement with DAS results is obtained. In this paper, the EPDF is further validated against three thermoacoustic cases: 1) a sudden increase of temperature on the left vertical wall of the enclosure; 2) a sudden increase of temperature on the left vertical wall coupled by a sudden decrease of temperature on the right vertical wall in the enclosure; 3) a gradually heated up left vertical wall of the enclosure. Comparisons with DAS simulations show that FDLBM and DAS give essentially identical results; hence, the validity and extent of the EPDF is ascertained for the calculation of these thermoacoustic waves. The FDLBM results are also compared with known theoretical and numerical results. These known solutions are found to be less accurate compared to the FDLBM results. The discrepancy could be attributed to the partially linearized equations solved in the theoretical analysis, and the inadequacy of the numerical scheme to replicate the nonlinear effects accurately in the generation and propagation of thermoacoustic waves. [ABSTRACT FROM AUTHOR]