Continuum-particle hybrid coupling for mass, momentum, and energy transfers in unsteady fluid flow

Abstract

The aim of hybrid methods in simulations is to communicate regions with disparate time and length scales. Here, a fluid described at the atomistic level within an inner region P is coupled to an outer region C described by continuum fluid dynamics. The matching of both descriptions of matter is made across an overlapping region and, in general, consists of a two-way coupling scheme (C-->P and P-->C) that conveys mass, momentum, and energy fluxes. The contribution of the hybrid scheme hereby presented is twofold. First, it treats unsteady flows and, more importantly, it handles energy exchange between both C and P regions. The implementation of the C-->P coupling is tested here using steady and unsteady flows with different rates of mass, momentum and energy exchange. In particular, relaxing flows described by linear hydrodynamics (transversal and longitudinal waves) are most enlightening as they comprise the whole set of hydrodynamic modes. Applying the hybrid coupling scheme after the onset of an initial perturbation, the cell-averaged Fourier components of the flow variables in the P region (velocity, density, internal energy, temperature, and pressure) evolve in excellent agreement with the hydrodynamic trends. It is also shown that the scheme preserves the correct rate of entropy production. We discuss some general requirements on the coarse-grained length and time scales arising from both the characteristic microscopic and hydrodynamic scales.

Algorithm refinement for the stochastic Burgers’ equation

“…In contrast to other AR approaches (see, e.g., [13]), the AMAR approach maintains a solution of the macroscopic model over the entire domain (see Fig. 1).…”

“…A related issue is the establishment of "refinement criteria" that specify when a microscopic representation is needed and when a macroscopic representation is sufficient. Examples of Algorithm Refinement applied to fluid dynamics may be found in [13,15,27,32,33,36]; AR hybrids for interfacial propagation are discussed in [25,26,28].…”

Algorithm Refinement for Fluctuating Hydrodynamics

“…In contrast to other algorithm refinement (AR) approaches (see, e.g. [16]), in AMAR (as in AMR) the solution of the macroscopic model is maintained over the entire domain. A refinement criterion is used to estimate where the improved representation of the particle method is required.…”

Adaptive molecular resolution via a continuous change of the phase space dimensionality

“…The transition region is well defined by the here introduced generalization of the equipartition theorem for fractional dimension of phase space. While it directly applies to a scheme recently tested by the authors [19,20] it in the same way should also provide the general theoretical framework to extend other commonly used schemes, such as [12,16,17] towards a truly adaptive multiscale simulation scheme.…”

“…Their efficiency and scope increases significantly if two or more such different approaches are combined into hybrid multiscale schemes. This is the case for the quantum based QM/MM ap-proach [4] and that of dual scale resolution techniques [5,6,7,8,9,10,11,12,13,14,15,16,17,18] aiming at bridging the atomistic and mesoscale length scale. However, the common feature and limitation of all these methods is the fact that the regions or parts of the system treated at different level of resolution are fixed and do not allow for free exchange.…”