In this paper phase transition of van der Waals gas is simulated by the Boltzmann Lattice method.Thermodynamics and Maxwellian area rule have been taken into account.With the primary Lattic Boltzmann(LB) method one can study the behavior of the ideal gas,i.e.,the equation of state is given by p=ρε[1,2,3,],By adding a potential termmore sophisticated cases can be studied.If the potential introduced leads to van de Waals equation of state,simulations show the separation of the fluid into domains with different mass densities,as reproted by Qian,Y.H.and Orszag[4].Unfortunately without further modification of their model the two densities coming out in the simulation strongly depend on the average density given initially.Table 1 shows several simulations done by us according to the model of qian and Orszag with grid D2Q9.Fixing the parameter T,we start from density spatial homogeneous equilibrium vlocity distribution with several different initial densities<ρ>.We find that below the critical temperature Tc the homogeneous state is usnstable,domains with two different densities ρ1 and ρ2 appear,but their values for different global average<ρ> are not identical .Further studies show that in each case the pressures p of the two phases are equal but the chemical potentials not,and therefore the Maxwellian Area rule does not hold.This result is understandable,co-existence of two phases in equilibrium is a thermodynamic effect,while temperature in the simulation described above is taken as a parameter given to each site prerequisitely.What is more,as the noise is effaced form the LB method.the system could stay in the super-cooled or super-heated metastable state forever,Modifications of the model are needed for better results.
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