A pseudo-spectral multiscale method: Interfacial conditions and coarse grid equations
A pseudo-spectral multiscale method: Interfacial conditions and coarse grid equations
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DOI：
10.1016/j.jcp.2005.08.001
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发表时间：
2006-03
期刊：
影响因子：
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通讯作者：
Shaoqiang Tang;T. Hou;Wing Kam Liu
中科院分区：
文献类型：
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作者：
Shaoqiang Tang;T. Hou;Wing Kam Liu
在本文中，我们提出了一个伪谱多尺度方法模拟复杂系统的多个空间尺度。使用谱分解，我们分裂成其平均和波动部分的位移。在局域非线性涨落的假设下，我们将该区域分为分子动力学（MD）子域和宏观（MC）子域。一个界面条件，提出了跨越两个尺度，在时间历程处理。在线性系统的特殊情况下，这是多尺度计算的第一个精确界面条件。同时，我们使用匹配微分算子方法设计粗网格方程。粗网格离散具有谱精度。在这种方法中，我们不使用握手区域。相反，我们定义了一个粗网格在整个域和重新分配的MD子域中的粗网格位移与MD解决方案的平均值。为了降低计算成本，我们计算粗网格位移的动力学，并将其与平均位移相关联。因此，我们的方法被称为伪谱多尺度方法。它允许通过平衡粗网格处的精度与界面处的精度来达到高分辨率。在一个和两个空间维度的数值实验，以证明该方法的准确性和鲁棒性。
In this paper, we propose a pseudo-spectral multiscale method for simulating complex systems with more than one spatial scale. Using a spectral decomposition, we split the displacement into its mean and fluctuation parts. Under the assumption of localized nonlinear fluctuations, we separate the domain into an MD (Molecular Dynamics) subdomain and an MC (MacrosCopic) subdomain. An interfacial condition is proposed across the two scales, in terms of a time history treatment. In the special case of a linear system, this is the first exact interfacial condition for multiscale computations. Meanwhile, we design coarse grid equations using a matching differential operator approach. The coarse grid discretization is of spectral accuracy. We do not use a handshaking region in this method. Instead, we define a coarse grid over the whole domain and reassign the coarse grid displacement in the MD subdomain with an average of the MD solution. To reduce the computational cost, we compute the dynamics of the coarse grid displacement and relate it to the mean displacement. Our method is therefore called a pseudo-spectral multiscale method. It allows one to reach high resolution by balancing the accuracy at the coarse grid with that at the interface. Numerical experiments in one- and two-space dimensions are presented to demonstrate the accuracy and the robustness of the method.