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Understanding and predicting the dynamics of complex fluid systems including liquid–liquid phase separation, relevant to both biological and engineered applications, typically uses a nonideal free energy. Introducing such a thermodynamic constraint into the Lattice-Boltzmann Method can be accomplished by altering either the equilibrium distribution function or the external force. The former requires a lengthy parameterization for a free energy of multiple independent variables which becomes cumbersome for more than three components. The latter has been done for a multicomponent compressible system, but a correction term for the force is required to recover the expected conservation equations. This work builds upon the incompressible single component forcing method from He et al. (Journal of Computational Physics, Vol. 152, No. 2, 1999) by deriving and implementing the required force needed to successfully recover the expected mass conservation from a nonideal free energy with an arbitrary number of components. This allows the simulation of more realistic phase separating fluid systems by including many interacting components, which is demonstrated here for up to five components and phases. 

Abstract We study the ionization and excitation structure of the interstellar medium in the late-stage gas-rich galaxy merger NGC 6240 using a suite of emission-line maps at ∼25 pc resolution from the Hubble Space Telescope, Keck/NIRC2 with Adaptive Optics, and the Atacama Large Millimeter/submillimeter Array (ALMA). NGC 6240 hosts a superwind driven by intense star formation and/or one or both of two active nuclei; the outflows produce bubbles and filaments seen in shock tracers from warm molecular gas (H₂2.12μm) to optical ionized gas ([Oiii], [Nii], [Sii], and [Oi]) and hot plasma (FeXXV). In the most distinct bubble, we see a clear shock front traced by high [Oiii]/Hβand [Oiii]/[Oi]. Cool molecular gas (CO(2−1)) is only present near the base of the bubble, toward the nuclei launching the outflow. We interpret the lack of molecular gas outside the bubble to mean that the shock front is not responsible for dissociating molecular gas, and conclude that the molecular clouds are partly shielded and either entrained briefly in the outflow, or left undisturbed while the hot wind flows around them. Elsewhere in the galaxy, shock-excited H₂extends at least ∼4 kpc from the nuclei, tracing molecular gas even warmer than that between the nuclei, where the two galaxies’ interstellar media are colliding. A ridgeline of high [Oiii]/Hβemission along the eastern arm aligns with the southern nucleus’ stellar disk minor axis; optical integral field spectroscopy from WiFeS suggests this highly ionized gas is centered at systemic velocity and likely photoionized by direct line of sight to the southern active galactic nucleus.