Interdisciplinary Applied Mathematics

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In summary, some of the key ingredients for effective MD-continuum coupling are:


   Use of a constraint to minimize density variations at the interface.


• Modification of the potential at the interface to eliminate local artificial structure.


   Use of a relaxation procedure to accelerate convergence of the coupled algorithm.


   Incorporation of constrained dynamics.


Mass and momentum flux exchange to maintain conservativity.


In the following section we present another approach to multiscale modeling in the context of electroosmotic flow in a nanochannel.

16.3 Embedding Multiscale Methods


In Chapter 12 (Sections 12.2 and 12.3), we observed that near the channel wall various atomistic characteristics (e.g., finite size of the ions, layering of water molecules) that were neglected in the classical continuum theory for the electroosmotic flow become important. In order to predict the electroosmotic flow in the entire channel accurately, one has to capture these atomistic details in the near-wall region. Multiscale simulation can be very helpful in such a scenario. In this section, we discuss a multiscale simulation method that is based on the embedding technique. Figure 16.6 shows a schematic of the embedding technique. The central ideas in the embedding technique are:


1. To simulate a wider (or coarser) length scale problem (see Figure 16.6(a)), we    first    set    up    an    auxiliary smaller    (or    finer)    length    scale


problem (see Figure 16.6(b)) using similar input conditions (e.g., wall surface charge density) such that the near-wall noncontinuum behavior is captured.


2. An MD simulation is performed on the finer length scale problem.


3. The MD results from the finer scale channel are embedded into the continuum simulation of the coarser length scale problem.

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