This paper presents a lattice Boltzmann method for simulating non-ideal fluids, focusing on phase separation and two-phase flow. The method introduces a non-ideal pressure tensor directly into the collision operator to ensure thermodynamic consistency. It also incorporates an external chemical potential to study the effect of wetting on phase separation and fluid flow in confined geometries. The approach reduces many unphysical discretization problems found in previous lattice Boltzmann methods. The method is based on the Van-der-Waals equation of state and uses a non-ideal pressure tensor to model phase transitions. The equilibrium conditions are satisfied by ensuring the pressure tensor defines surface tension in inhomogeneous regions. The lattice Boltzmann simulation is set up on a triangular lattice to reproduce Navier-Stokes equations. The distribution functions evolve according to a discrete Boltzmann equation, with the equilibrium distribution chosen to reproduce the correct dynamic equations for density and velocity. The method includes non-local terms in the equilibrium distribution to account for non-ideal thermodynamic properties. The coefficients of the equilibrium distribution are determined by macroscopic constraints. The continuum hydrodynamic equations are derived from a Chapman-Enskog expansion of the Boltzmann equation. The results show that the non-ideal pressure tensor correctly describes the dynamics of phase separation and interfacial behavior. The method is tested on a Van-der-Waals fluid, showing good agreement with continuum thermodynamic equations. The interface width can be varied, and the method reduces microscopic velocity fluctuations in the interfacial region. The surface tension is consistent with both mechanical and thermodynamic definitions. The method also allows for the introduction of an external chemical potential to study wetting effects, enabling the simulation of different boundary conditions. The method provides a physically motivated way to tune boundary conditions and reduces unphysical velocity oscillations at surfaces and interfaces. It is simple to implement and suitable for studying multi-phase hydrodynamical systems. The method can be extended to non-isothermal situations where heat transfer is important. The results demonstrate the effectiveness of the lattice Boltzmann method in modeling non-ideal fluids and phase separation.This paper presents a lattice Boltzmann method for simulating non-ideal fluids, focusing on phase separation and two-phase flow. The method introduces a non-ideal pressure tensor directly into the collision operator to ensure thermodynamic consistency. It also incorporates an external chemical potential to study the effect of wetting on phase separation and fluid flow in confined geometries. The approach reduces many unphysical discretization problems found in previous lattice Boltzmann methods. The method is based on the Van-der-Waals equation of state and uses a non-ideal pressure tensor to model phase transitions. The equilibrium conditions are satisfied by ensuring the pressure tensor defines surface tension in inhomogeneous regions. The lattice Boltzmann simulation is set up on a triangular lattice to reproduce Navier-Stokes equations. The distribution functions evolve according to a discrete Boltzmann equation, with the equilibrium distribution chosen to reproduce the correct dynamic equations for density and velocity. The method includes non-local terms in the equilibrium distribution to account for non-ideal thermodynamic properties. The coefficients of the equilibrium distribution are determined by macroscopic constraints. The continuum hydrodynamic equations are derived from a Chapman-Enskog expansion of the Boltzmann equation. The results show that the non-ideal pressure tensor correctly describes the dynamics of phase separation and interfacial behavior. The method is tested on a Van-der-Waals fluid, showing good agreement with continuum thermodynamic equations. The interface width can be varied, and the method reduces microscopic velocity fluctuations in the interfacial region. The surface tension is consistent with both mechanical and thermodynamic definitions. The method also allows for the introduction of an external chemical potential to study wetting effects, enabling the simulation of different boundary conditions. The method provides a physically motivated way to tune boundary conditions and reduces unphysical velocity oscillations at surfaces and interfaces. It is simple to implement and suitable for studying multi-phase hydrodynamical systems. The method can be extended to non-isothermal situations where heat transfer is important. The results demonstrate the effectiveness of the lattice Boltzmann method in modeling non-ideal fluids and phase separation.