Interdisciplinary Applied Mathematics

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molecular description.

This method employs a particle reservoir to satisfy the mass flux across the hybrid interface; this reservoir is taken as the outer ring of the MD domain. The particles do not drift away, because of the periodic boundary conditions imposed on the MD domain. The particle velocity in a bin of

the overlap region is drawn from a Maxwellian distribution at each time step, adopting the so-called Maxwell demon procedure. In this approach the particle nonequilibrium distributions are not included. In addition, there are sudden changes    of    the    particle    velocities    from    one    step    to    another.

In general, this type of iterative coupling may depend on the relative size of the domains and could lead to possible divergence of solutions for large disparity in domain sizes, which is typical in microfluidic and nanofluidic applications. The relaxation procedure for в = 0 has been shown to weaken the strong dependence on the domain size (Henderson and Karniadakis, 1991). This is typical of algorithms based on the classical Schwarz algorithm, and for coupling of elliptic problems with heterogeneous discretization, convergence of the в-relaxation iterative procedure is independent of the domain sizes. In addition to the iterative coupling and the dynamic constraint in the overlap region, convergence of the coupled solution is accomplished only if there is compatibility between transport coefficients on the two sides and the scatter of quantities on the microscopic side is minimized using spatial averages, for example, by exploiting homogeneity in planar slices about 2a thick.

The flux-exchange method developed by (Flekkoy et al., 2000) is conservative, since it relies in the matching of fluxes of mass and momentum between the MD and Navier-Stokes domains. In particular, the mass flux continuity is enforced by the equation

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