Nearly exact solution for coupled continuum/MD fluid simulation

A general statistical approach is described to couple the continuum with molecular dynamics in fluid simulation. Arbitrary thermodynamic field boundary conditions can be imposed on an MD system while minimally disturbing the particle dynamics of the system. And by acting away from the region of interest through a feedback control mechanism, across a buffer zone where the disturbed dynamics are allowed to relax, we can eliminate that disturbance entirely. The field estimator, based on maximum likelihood inference, serves as the detector of the control loop, which infers smooth instantaneous fields from the particle data. The optimal particle controller, defined by an implicit relation, can be proved mathematically to give the correct distribution with least disturbance to the dynamics. A control algorithm compares the estimated current fields with the desired fields at the boundary and modifies the action of the particle controller far way, until they eventually agree. This method, combined with a continuum code in a Schwarz iterative domain-decomposition formalism, provides a mutually consistent solution for steady-state problems, as particles in the MD region of interest have no way to tell any difference from reality. Finally, we explain the importance of using a higher order single-particle distribution function, in light of the Chapman–Enskog development for shear flow.