随机受迫一维Burgers方程的计算粗粒化
Computational coarse graining of a randomly forced 1-D Burgers equation
摘要：
我们探讨了一种计算方法粗粒化的随机强迫Burgers方程在一个空间维度的大规模功能的演变。溶液能谱的长期演化在时间上表现出自相似性。我们展示了粗投影积分和粗动态重正化的工具，加速提取的宏观信息（整合时间，自相似的形状，和非平凡的动态指数）从适当初始化的直接模拟的短脉冲。这些程序解决了数值有效的演化方程的能量谱，而无需导出这个方程的封闭形式。
英文摘要：
We explore a computational approach to coarse graining the evolution of the large-scale features of a randomly forced Burgers equation in one spatial dimension. The long term evolution of the solution energy spectrum appears self-similar in time. We demonstrate coarse projective integration and coarse dynamic renormalization as tools that accelerate the extraction of macroscopic information (integration in time, self-similar shapes, and nontrivial dynamic exponents) from short bursts of appropriately initialized direct simulation. These procedures solve numerically an effective evolution equation for the energy spectrum without ever deriving this equation in closed form.
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