49 research outputs found
Double-distribution-function discrete Boltzmann model for combustion
A 2-dimensional discrete Boltzmann model for combustion is presented.
Mathematically, the model is composed of two coupled discrete Boltzmann
equations for two species and a phenomenological equation for chemical reaction
process. Physically, the model is equivalent to a reactive Navier-Stokes model
supplemented by a coarse-grained model for the thermodynamic nonequilibrium
behaviours. This model adopts 16 discrete velocities. It works for both
subsonic and supersonic combustion phenomena with flexible specific heat ratio.
To discuss the physical accuracy of the coarse-grained model for nonequilibrium
behaviours, three other discrete velocity models are used for comparisons.
Numerical results are compared with analytical solutions based on both the
first-order and second-order truncations of the distribution function. It is
confirmed that the physical accuracy increases with the increasing moment
relations needed by nonequlibrium manifestations. Furthermore, compared with
the single distribution function model, this model can simulate more details of
combustion.Comment: Accepted for publication in Combustion and Flam
Modeling incompressible thermal flows using a central-moment-based lattice Boltzmann method
In this paper, a central-moment-based lattice Boltzmann (CLB) method for
incompressible thermal flows is proposed. In the method, the incompressible
Navier-Stokes equations and the convection-diffusion equation for the
temperature field are sloved separately by two different CLB equations. Through
the Chapman-Enskog analysis, the macroscopic governing equations for
incompressible thermal flows can be reproduced. For the flow field, the tedious
implementation for CLB method is simplified by using the shift matrix with a
simplified central-moment set, and the consistent forcing scheme is adopted to
incorporate forcing effects. Compared with several D2Q5
multiple-relaxation-time (MRT) lattice Boltzmann methods for the temperature
equation, the proposed method is shown to be better Galilean invariant through
measuring the thermal diffusivities on a moving reference frame. Thus a higher
Mach number can be used for convection flows, which decreases the computational
load significantly. Numerical simulations for several typical problems confirm
the accuracy, efficiency, and stability of the present method. The grid
convergence tests indicate that the proposed CLB method for incompressible
thermal flows is of second-order accuracy in space
Kinetic modeling of economic markets with heterogeneous saving propensities
The lattice gas automaton (LGA) is proposed for a closed economic market of
agents with heterogeneous saving interests. There are two procedures in the
standard LGA, i.e., "propagation" + "transaction". If the propagation step is
removed and the transaction is conducted among all agents, the LGA reduces to a
more simplified kinetic model. In addition, two dealing rules are imposed on
the transaction phase. Under Rule I, the trading volume depends on the average
saving propensities of an arbitrary pair of agents in trade. Under Rule II, the
exchange is governed by a stochastic parameter between the saving propensities
of two traders. Besides, two sampling methods are introduced for the random
selection of two agents in the iterative process. Specifically, Sampling I is
the sampling with replacement and is easier to program. Sampling II is the
sampling without replacement and owns a higher computing efficiency. There are
slight differences between the stationary wealth distributions simulated by
using the two transaction rules and sampling approaches. In addition, the
accuracy, robustness and efficiency of the econophysics models are validated by
typical numerical tests. The reduced LGA without the propagation step owns a
higher computational efficiency than the standard LGA. Moreover, the impact of
saving propensities of agents in two groups on the wealth distributions is
studied, and the influence of proportions of agents is investigated as well. To
quantitatively measure the wealth inequality, the Gini coefficients, Kolkata
indices, and deviation degrees of all agents and two groups are simulated and
analyzed in detail. This work is helpful to further analyze and predict the
dynamic process of wealth distribution in the realistic economic market
Multiple-relaxation-time lattice Boltzmann kinetic model for combustion
To probe both the Hydrodynamic Non-Equilibrium (HNE) and Thermodynamic
Non-Equilibrium (TNE) in the combustion process, a two-dimensional
Multiple-Relaxation-Time (MRT) version of Lattice Boltzmann Kinetic Model(LBKM)
for combustion phenomena is presented. The chemical energy released in the
progress of combustion is dynamically coupled into the system by adding a
chemical term to the LB kinetic equation. Beside describing the evolutions of
the conserved quantities, the density, momentum and energy, which are what the
Navier-Stokes model describes, the MRT-LBKM presents also a coarse-grained
description on the evolutions of some non-conserved quantities. The current
model works for both subsonic and supersonic flows with or without chemical
reaction. In this model both the specific-heat ratio and the Prandtl number are
flexible, the TNE effects are naturally presented in each simulation step. The
model is verified and validated via well-known benchmark tests. As an initial
application, various non-equilibrium behaviours, including the complex
interplays between various HNEs, between various TNEs and between the HNE and
TNE, around the detonation wave in the unsteady and steady one-dimensional
detonation processes are preliminarily probed. It is found that the system
viscosity (or heat conductivity) decreases the local TNE, but increase the
global TNE around the detonation wave, that even locally, the system viscosity
(or heat conductivity) results in two kinds of competing trends, to increase
and to decrease the TNE effects. The physical reason is that the viscosity (or
heat conductivity) takes part in both the thermodynamic and hydrodynamic
responses.Comment: 32 pages, 11 figure