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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]

• A new LBM that remedies four inadequacies of conventional LBM is formulated. • It requires only a relaxation time scale of the flow and fluid properties as inputs. • It is solved with finite difference splitting on minimal D2Q9 and D3Q13 lattices. • It simulates a wide ranges of flow problems with different fluid media correctly. • Its solutions agree excellently with existing experimental and numerical results. A new modeled Boltzmann equation (MBE) with four improvements made to conventional MBE is formulated. The first improvement is to include the particle internal rotational degree of freedom in the derivation of a continuous equilibrium velocity distribution function f eq ; thus, rendering the MBE applicable to diatomic gas. The second improvement is made in the expansion assumed for f α eq in the lattice Boltzmann equation (LBE). This expansion is expressed in terms of the particle velocity vector ( ξ ) alone; hence, the LBE is no longer limited by a very low Mach number (M) assumption, and it also allows the LBE to correctly satisfy the zero divergence of the velocity field for incompressible flow. The third improvement is made to eliminate the bounce-back rule used to model no-slip wall boundary condition for f α because the rule leads to leakage at solid walls and mass conservation is compromised. The fourth improvement is carried out to render the modeled LBE truly valid for hydrodynamic flow simulation. Thus improved, the new lattice Boltzmann method (LBM) is no longer subject to the M << 1 condition and can be confidently extended to hydrodynamic simulations where the flow is truly incompressible. The f α eq expansion coefficients are found to be functions of the primitive variables, their derivatives and their products. In this LBE, fluid properties are inputs, and boundary values of f α are deduced from the primitive variables at the boundaries. Only a D2Q9 and a D3Q15 lattice model are required for 2-D and 3-D flow simulation, respectively. A finite difference splitting method is used to solve the new LBM; the scheme is labeled FDLBM, and it has been used to simulate widely different laminar flow of gas and liquid; incompressible with/without heat transfer, compressible with/without shocks, aeroacoustics with/without scattering, thermo-aeroacoustics, buoyant and double diffusive flow, and non-Newtonian flow, as well as blood flow in arteries with/without blockage. Accurate results are obtained, and they agree with other finite-difference numerical simulations of the same problems, and experimental and theoretical results whenever available. Furthermore, the aeroacoustics results are in agreement with those obtained from direct aeroacoustics simulations of the same problems. [ABSTRACT FROM AUTHOR]