The simulation of multiphase flows is one of the most challenging problems in engineering and industry. In this research the Gong and Cheng and the Kupershtokh exact difference method (EDM) are applied for the pseudo-potential Shan-Chen model. A study of various equations of state (EOS) is conducted to discover the Gong and Cheng model applicability. The proper beta parameter for each EOS is obtained by simulation and then various EOS are compared. In addition, a function is proposed to predict the best ? parameter for the Shan-Chen and cubic EOS which is noticeably accurate in comparison with the obtained parameters by simulation. It is found out that by means of the predicted equation for noncubic EOS the proper ? parameters in different temperature ranges can be calculated. Furthermore, this method and the Carnahan-Starling equation of state are coupled in the Shan-Chen multiphase lattice Boltzmann model and some major test cases such as the Laplace test, the bubbles coalescence, the squared bubble, and the segregation are simulated in high density ratios (800 and 8400). In addition, the process of a droplet impact on a solid surface is modeled by the Kupershtokh method at various Reynolds and Weber numbers. The effect of a variety of parameters such as the spread factor, the pressure, the density ratio, the droplet thickness and the contact angel are studied. The results illustrate a very good performance for the Shan-Chen model for large density ratios. It is found out that the Shan-Chen model is able to simulate large density ratio flows quite well for most simulations such as the Laplace test. However, it has some disadvantages such as the interface oscillation. Meanwhile, as the density ratio increases the interface oscillation and the convergence time increase dramatically. Although this model enjoys the ability to simulate high density ratio phenomena in static cases accurately, its performance deteriorates for more sophisticated problems because of large changes in the interface boundary and the instability of vapor density prediction. In spite of some drawbacks, this model is a powerful tool for the simulation of high density ratio flows and the results show that it can simulate multiphase flows with larger density ratios in comparison with other multiphase lattice Boltzmann models. Keywords: Lattice Boltzmann method, Shan-Chen model, Multiphase flows, Equation of
