Fluctuating hydrodynamic descriptions provide a promising mesoscale approach for modelling and simulation of many-body molecular systems such as lipid bilayer membranes. For implicit-solvent coarse-grained (IS-CG) models, we show how kinetic contributions from the solvent can be incorporated using fluctuating hydrodynamics to develop dynamically accurate momentum conserving thermostats. We discuss theoretical foundations in statistical mechanics and the development of robust computational methods for simulations in several different physical regimes. We then present results from continuum theory and large-scale molecular simulations of lipid bilayer vesicles investigating the hydrodynamics and diffusion of lipids and molecules within leaflets of the bilayer. We also discuss our software package SELM for fluctuating hydrodynamic simulations available within the molecular dynamics software LAMMPS.
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