A lattice Boltzmann method for simulation of liquid–vapor phase-change heat transfer
A lattice Boltzmann model for the liquid–vapor phase change heat transfer is proposed in this paper. Two particle distribution functions, namely the density distribution function and the temperature distribution function, are used in this model. A new form of the source term in the energy equation is derived and the modified pseudo-potential model is used in the proposed model to improve its numerical stability. The commonly used Peng–Robinson equation of state is incorporated into the proposed model. The problem of bubble growth and departure from a horizontal surface is solved numerically based on the proposed model.
Lattice Boltzmann model for nonlinear convection-diffusion equations.
A lattice Boltzmann model for convection-diffusion equation with nonlinear convection and isotropic-diffusion terms is proposed through selecting equilibrium distribution function properly. The model can be applied to the common real and complex-valued nonlinear evolutionary equations, such as the nonlinear Schrödinger equation, complex Ginzburg-Landau equation, Burgers-Fisher equation, nonlinear heat conduction equation, and sine-Gordon equation, by using a real and complex-valued distribution function and relaxation time. Detailed simulations of these equations are performed, and it is found that the numerical results agree well with the analytical solutions and the numerical solutions reported in previous studies.
An improved lattice Boltzmann model for multicomponent reactive transport in porous media at the pore scale
[1] In this paper, we improve the lattice Boltzmann pore-scale model for multicomponent reactive transport in porous media developed in a previous study. Instead of applying a thermal boundary condition to solute transport, we rigorously derive the distribution function boundary condition for the total solute concentration. This is achieved first by correcting an expression of the particle distribution function in terms of the corresponding concentration and its gradient and then by deriving and using the relation that the nonequilibrium portion of the distribution function in opposite directions takes on opposite signs. We implement the new boundary condition in both the two-dimensional nine-speed (D2Q9) and four-speed (D2Q4) lattices. Simulations of reactive transport in various chemical and geometrical systems using different models are carried out, and results are compared to analytic expressions or two-dimensional FLOTRAN simulations. It is found that with this new boundary condition, the solute mass is strictly conserved by heterogeneous reactions, as was not the case using the thermal boundary condition. It is also found that compared with the D2Q9 model, the D2Q4 model has comparable accuracy and better computational efficiency.
Lattice Boltzmann model for free-surface flow and its application to filling process in casting
A generalized lattice Boltzmann model to simulate free-surface is constructed in both two and three dimensions. The proposed model satisfies the interfacial boundary conditions accurately. A distinctive feature of the model is that the collision processes is carried out only on the points occupied partially or fully by the fluid. To maintain a sharp interfacial front, the method includes an anti-diffusion algorithm. The unknown distribution functions at the interfacial region are constructed according to the first-order Chapman-Enskog analysis. The interfacial boundary conditions are satisfied exactly by the coefficients in the Chapman-Enskog expansion. The distribution functions are naturally expressed in the local interfacial coordinates. The macroscopic quantities al the interface are extracted from the least-square solutions of a locally linearized system obtained from the known distribution functions. The proposed method does not require any geometric front construction and is robust for any interfacial topology. Simulation results of realistic filling process are presented: rectangular cavity in two dimensions and Hammer box, Campbell box, Sheffield box, and Motorblock in three dimensions. To enhance the stability at high Reynolds numbers, various upwind-type schemes are developed. Free-slip and no-slip boundary conditions are also discussed.
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