在高效的无方程多尺度模拟中自适应地检测和准确地解决宏观冲击
Adaptively detect and accurately resolve macro-scale shocks in an efficient Equation-Free multiscale simulation
摘要：
有效的多尺度数值计算的无方程方法将可信的微观模拟与数值宏观尺度缩减的框架--补丁动力学方案结合起来。最近的一种新的补丁计划授权的方程自由的方法来模拟系统的宏观尺度上的冲击。然而，该方案没有准确地预测冲击的形成，它不能模拟移动的冲击。本文解决了这两个问题，作为第一步，在一个空间维度，通过嵌入方程自由，冲击解决补丁计划在一个经典的框架自适应移动网格。我们的典型的微尺度问题表现出异质非线性平流和异质扩散。我们证明了许多显着的好处，从移动补丁计划，包括高效和准确的宏观尺度预测，尽管未知的宏观尺度关闭。无方程方法在这里扩展到模拟移动，形成和合并的冲击，没有先验知识的存在或关闭的冲击。而自适应移动网格方程通常是刚性的，通常需要在宏观尺度上的小时间步长，移动的宏观尺度网格的补丁通常不是刚性给定的上下文的子补丁动态所需的微尺度时间步长。
英文摘要：
The Equation-Free approach to efficient multiscale numerical computation marries trusted micro-scale simulations to a framework for numerical macro-scale reduction -- the patch dynamics scheme. A recent novel patch scheme empowered the Equation-Free approach to simulate systems containing shocks on the macro-scale. However, the scheme did not predict the formation of shocks accurately, and it could not simulate moving shocks. This article resolves both issues, as a first step in one spatial dimension, by embedding the Equation-Free, shock-resolving patch scheme within a classic framework for adaptive moving meshes. Our canonical micro-scale problems exhibit heterogeneous nonlinear advection and heterogeneous diffusion. We demonstrate many remarkable benefits from the moving patch scheme, including efficient and accurate macro-scale prediction despite the unknown macro-scale closure. Equation-free methods are here extended to simulate moving, forming and merging shocks without a priori knowledge of the existence or closure of the shocks. Whereas adaptive moving mesh equations are typically stiff, typically requiring small time-steps on the macro-scale, the moving macro-scale mesh of patches is typically not stiff given the context of the micro-scale time-steps required for the sub-patch dynamics.
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