A hybrid molecular-continuum simulation method for incompressible flows in micro/nanofluidic networks
A hybrid molecular-continuum simulation method for incompressible flows in micro/nanofluidic networks
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DOI：
10.1007/s10404-013-1168-y
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发表时间：
2013-03
影响因子：
2.8
通讯作者：
M. Borg;D. Lockerby;J. Reese
中科院分区：
文献类型：
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作者：
M. Borg;D. Lockerby;J. Reese
我们提出了一种混合分子连续模拟方法，用于模拟网络型系统中的纳米和微米流。在这些类型的问题，一个完整的分子动力学（MD）的宏观流动行为的描述将是计算上棘手的，或至少太昂贵的工程设计的目的是实用的。表现出多尺度特征的系统，例如，可以使用混合方法来解决，该方法将问题区分为宏观和微观动力学，由各自的求解器建模。这项研究中提出的技术是一个扩展和除了混合方法开发的博格等人。（J Comput Phys 233：400-413，2013），称为内流多尺度方法（IMM）。通过用小得多但具有代表性的MD模拟来替换网络中高度尺度分离的长通道，可以节省计算量，而不会大幅降低精度。另一方面，结组件不表现出这种长度尺度分离，因此必须使用MD对其进行整体模拟。目前的技术结合了所有的网络元素（路口和通道）在一个耦合的模拟使用连续守恒定律。对于稳定的，等温的，不可压缩的，低速流动的情况下，我们使用的质量守恒和动量通量方程推导出一组分子连续约束。这里提出了一种算法，在每次迭代计算的压力差的新的约束施加在各个MD微元件（通道和路口），连续移动更接近宏观质量和动量守恒。我们表明，混合模拟的一些例子网络的情况下收敛速度很快，在只有几次迭代，并比较非常好的相应的完整的MD结果，这是作为最准确的解决方案。主要的计算节省可以提供IMM型近似的通道组件，但对于稳态的解决方案，甚至更大的节省是可能的。这是因为微元件耦合到稳态连续守恒表达式，与完整MD模拟相比，这大大加快了单个微元件到稳定条件的松弛。也可以模拟具有高时间尺度分离的非稳态问题，但是一般的瞬态问题超出了当前技术的能力。
We present a hybrid molecular-continuum simulation method for modelling nano- and micro-flows in network-type systems. In these types of problem, a full molecular dynamics (MD) description of the macroscopic flow behaviour would be computationally intractable, or at least too expensive to be practical for engineering design purposes. Systems that exhibit multiscale traits, such as this, can instead be solved using a hybrid approach that distinguishes the problem into macroscopic and microscopic dynamics, modelled by their respective solvers. The technique presented in this study is an extension and addition to a hybrid method developed by Borg et al. (J Comput Phys 233:400–413, 2013) for high-aspect-ratio channel geometries, known as the internal-flow multiscale method (IMM). Computational savings are obtained by replacing long channels in the network, which are highly scale-separated, by much smaller, but representative, MD simulations, without a substantial loss of accuracy. On the other hand, junction components do not exhibit this length-scale separation, and so must be simulated in their entirety using MD. The current technique combines all network elements (junctions and channels) together in a coupled simulation using continuum conservation laws. For the case of steady, isothermal, incompressible, low-speed flows, we use the conservation of mass and momentum flux equations to derive a set of molecular-continuum constraints. An algorithm is presented here that computes at each iteration the new constraints on the pressure differences to be applied over individual MD micro-elements (channels and junctions), successively moving closer to macroscopic mass and momentum conservation. We show that hybrid simulations of some example network cases converge quickly, in only a few iterations, and compare very well to the corresponding full MD results, which are taken as the most accurate solutions. Major computational savings can be afforded by the IMM-type approximation in the channel components, but for steady-state solutions, even greater savings are possible. This is because the micro-elements are coupled to a steady-state continuum conservation expression, which greatly speeds up the relaxation of individual micro-components to steady conditions as compared to that of a full MD simulation. Unsteady problems with high temporal scale separation can also be simulated, but general transient problems are beyond the capabilities of the current technique.