تابع توزیع دوگانه

In this paper, the thermo-hydrodynamic analysis of incompressible fluid flow in conjunction with cell-centered finite volume-lattice Boltzmann method is developed. To demonstrate the temperature field, the double distribution function model was used. Since, instability is the most severe problem of the thermal lattice Boltzmann methods to handle flows; a stable and accurate cell-centered scheme is presented. For this purpose, the pressure and temperature based upwind biasing factors are used as flux correctors. Also, additional lattices at the edge of each boundary cell are introduced, which allow a much better description of the actual geometrical shape. The unknown energy distribution at the boundary cells were decomposed into its equilibrium and non-equilibrium parts. This treatment enlarges the domain stability and leads to faster convergence. In addition of calculating numerical viscosity, The method is applied to two dimensional incompressible thermal plane duct flow. The results show a very good accuracy and agreement with the exact solution and previous numerical results.

In this paper، the thermo-hydrodynamical analysis of incompressible flow in conjunction with cell-centered finite volume-lattice Boltzmann method (FV-LBM) was developed. To demonstrate the temperature field، the double distributions function (DDF) was used. A novel approach was applied in cell flux calculation by definition of biasing factors based on pressure and temperature. This treatment enlarges the domain stability and leads to faster convergence. A consistent open and solid boundary treatment of flow was also addressed. The unknown energy distribution at the boundary cells were decomposed into its equilibrium and non-equilibrium parts. Then، the non-equilibrium part was approximated with extrapolation of the non-equilibrium part of the populations at the neighboring nodes. Two test cases namely، thermo-hydrodynamic in a backward-facing step and around a circular cylinder inserted within the backward-facing step were carried out. The results were compared with the available solutions in the technical literature showing reasonable agreements.