Mesoscopic simulation of non-ideal fluids with self-tuning of the equation of state

A dynamic optimization strategy is presented to generate customized equations of state (EOS) for the numerical simulation of non-ideal fluids at high density ratio. While stable branches of the analytical EOS are preserved, the spinodal region is self-tuned during the simulation, in order to compensate for numerical errors caused by discretization in phase space. The employed EOS permits the readily setting of the sound speeds for the gas and liquid phases, thus allowing stable simulation with high density (1:10 to 1:1000) and compressibility ratios (250:1-25000:1). The present technique is demonstrated for lattice Boltzmann simulation of (free-space) multiphase systems with flat and circular interfaces.