2025-11-27 课程笔记

数值模式对波的解析

如果网格分辨率是$\Delta x$，区域的长度是$L$

• 能够解析的最小的波长是$2\Delta x$

• 能够解析的最长的波长是$2L$

• 能够解析的最大的波数是$\rho = \frac{2\pi}{W_L} = \frac{2\pi}{2\Delta x} = \frac{\pi}{\Delta x}$

一些要点

• Donor-Cell Approximation
• Upstream forward scheme
• $k\frac{\partial^2u}{\partial x^2}$：湍流项

Quantitative Estimate of Phase and Amplitude Errors

• Neumann Method
• First-order upwind scheme
• Leapfrog Fourth-order Centered-in-Space Scheme
• Leapfrog scheme for advection
• 二阶和三阶荣格库塔方案