Energy conservation equation for one-component pseudopotential lattice Boltzmann method

The pseudopotential lattice Boltzmann method has become an alternative tool to simulating multiphase systems. As is typically done, the lattice Boltzmann equation LBE is only used to solve the mass and momentum conservation equations. To solve non-isothermal problems an appropriate energy conservation equation ECE is solved using finite differences. When the LBE is coupled with an ECE, simulations often become more unstable and can be difficult to reach high values of the density ratio. Also, most ECE are written as a discrete equation for temperature, not exactly conserving total energy in a periodic domain. This talk focuses on studying the application of an ECE coupled to the pseudopotential method for multiphase simulation. The goals are: evaluate the presence of discretization errors, violation in the conservation of total energy and analyze current methods stability. A smooth oscillation problem is employed to evaluate the ECE. The comparison between numerical and analytical results revealing that the second order of the numerical scheme is not sufficient to properly model the non-isothermal oscillation problem.