格子Boltzmann流体模型与有限差分Navier-Stokes方程的空间耦合
Spatial Coupling of a Lattice Boltzmann fluid model with a Finite Difference Navier-Stokes solver
摘要：
在多尺度、多物理场应用中，越来越需要耦合数值求解器，每个求解器都应用于问题的不同部分。在这里，我们考虑的情况下，耦合的格子玻尔兹曼流体模型和有限差分Navier-Stokes求解器。耦合的实施，使整个计算域可以分为两个区域，与FD求解器上运行的其中一个和LB上的另一个。我们展示了两种方法的各种物理量应如何相关，以确保在区域之间的界面处的平滑过渡。我们证明了该方法的可行性Poietille流，其中LB和FD计划使用相邻的子域。同样的想法也可以发展到耦合LB模型与有限元或有限元计算。开发这种类型的耦合的动机是，根据流动的几何形状，一种技术可以更有效，更少的内存消耗，或在某些区域（例如，边界附近）比另一种技术更合适，而对于同一系统的其他部分则相反。我们还可以想象，一个给定的系统解决，说FD，可以在一些空间区域中增加一个新的物理过程，更好地处理LB模型。我们的方法允许我们只修改相关区域，而不改变其余的计算。
英文摘要：
In multiscale, multi-physics applications, there is an increasing need for coupling numerical solvers that are each applied to a different part of the problem. Here we consider the case of coupling a Lattice Boltzmann fluid model and a Finite Difference Navier-Stokes solver. The coupling is implemented so that the entire computational domain can be divided in two regions, with the FD solver running on one of them and the LB one on the other. We show how the various physical quantities of the two approaches should be related to ensure a smooth transition at the interface between the regions. We demonstrate the feasibility of the method on the Poiseuille flow, where the LB and FD schemes are used on adjacent sub-domains. The same idea can be also developed to couple LB models with Finite Volumes, or Finite Elements calculations. The motivation for developing such a type of coupling is that, depending on the geometry of the flow, one technique can be more efficient, less memory consuming, or physically more appropriate than the other in some regions (e.g. near the boundaries), whereas the converse is true for other parts of the same system. We can also imagine that a given system solved, say by FD, can be augmented in some spatial regions with a new physical process that is better treated by a LB model. Our approach allows us to only modify the concerned region without altering the rest of the computation.
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