For tangential fired furnace, the false diffusion will occur when the flow is oblique to the grid lines. It is a major factor to cause serious errors to the prediction of tangential fired furnace. In order to decrease this false diffusion, this study has considered several alternative to the widely used upwind-differencing scheme with the aim of identifying which could be regarded as the most suitable in a general-purpose solving procedure for tangential furnace. The representations adopted are 'hybrid', 'quick' and '27-point' treatments. Here, '27-point' is a new discrete arithmetic scheme developed by the authors. All these schemes are used to simulate a constrained jet and a lab-scale tangential furnace and to compare solutions with the datum. Overall, the '27-point' approximation emerged as the most satisfactory for simulating tangential furnace.

A lattice Bhatnagar-Gross-Krook (LBGK) model for reaction-diffusion systems is presented. This model provides a mesoscopic approach to the dynamics of spatially-distributed reacting systems. Pure diffusion phenomena are computed and the results are agreement with the theoretical predictions. This method is also applied to formation of Turing patterns in chloride-iodide-malonic acid (CIMA) reactive model. We get hexagonal structures and stripes which are agreement with other numerical results and experimental results.

A second-order moment (SOM) model for gas-phase turbulence, combined with a Langevin-based probability density function (PDF) transport model for particle-phase turbulence, named SOM-PDF model for gas-particle turbulence, is proposed here. The SOM is solved by the well-known finite-volume method (FVM), while the PDF is solved by directly calculate the Langevin equation for both particle velocity and fluid velocities seen by particles, as proposed by Simonin (1996), using pseudo time-dependent Monte-Carlo method (MC). A time-averaged method is used to reduce the amount of stochastic-particle needed. The DSM-PDF model was applied to simulate a gas-particle turbulent flow in a pipe with expansion. The prediction results are compared with PDPA measured results and those predicted using the PDF derived ensemble-averaged stress model (ESM). The comparison shows that both models can well predict the averaged flow field of particle phase, while the DSM-PDF model got a better distribution of particle time-averaged velocity and fluctuation velocity at the area where shear is dominant. The difference may arise from several aspects: the merits of MC technology of no numerical diffusion, and most important, the capability of taken into account the effect of non-Gaussian distribution of particle velocities at shear dominant area, while Gaussian distribution is pre-assumed for ESM.

The standard Lattice BGK (LBGK) scheme often encounters numerical instability in simulation of fluid flow with small kinematic viscosity or as the nondimensional relaxation timey is close to 0.5. In this paper, based on a timesplitting scheme for the Boltzmann equation with discrete velocities, a new LBGK scheme with general propagation step is proposed to address this problem. In this model, two free parameters are introduced into the propagation step, which can be adjusted to obtain a small kinematic viscosity and improved numerical stability as well. Numerical simulations of the two-dimensional Taylor vortex and the unsteady Womersley flow are carried out to test the kinematic viscosity, numerical diffusion, and numerical stability of the proposed scheme.

Two type of structures-Turing patterns and spiral waves-are obtained in chloride-iodide-malonic acid (CIMA) reaction-diusion model by using lattice Bhatnagar-Gross-Krook (LBGK) method.