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CFD中文网

CFD中文网

  1. CFD中文网
  2. Algorithm
  3. 波方程

波方程

Scheduled Pinned Locked Moved Algorithm
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  • 李东岳李 Online
    李东岳李 Online
    李东岳 管理员
    wrote on last edited by 李东岳
    #1

    \begin{equation}
    \zeta =x-ct,\eta=x+ct
    \end{equation}
    \begin{equation}
    \frac{\p\eta}{\p x}=1,\frac{\p\zeta}{\p x}=1
    \end{equation}
    \begin{equation}
    \frac{\p\eta}{\p t}=c,\frac{\p\zeta}{\p t}=-c
    \end{equation}
    对任意变量关于$\zeta,\eta$的函数
    \begin{equation}
    \frac{\p}{\p x}=\frac{\p}{\p\eta}\frac{\p\eta}{\p x}+\frac{\p}{\p\zeta}\frac{\p\zeta}{\p x}=\frac{\p}{\p\eta}+\frac{\p}{\p\zeta}
    \end{equation}
    \begin{equation}
    \frac{\p}{\p t}=\frac{\p}{\p\eta}\frac{\p\eta}{\p t}+\frac{\p}{\p\zeta}\frac{\p\zeta}{\p t}=c\frac{\p}{\p\eta}-c\frac{\p}{\p\zeta}
    \end{equation}
    \begin{equation}
    \frac{\p^2}{\p x^2}=\left(\frac{\p}{\p\eta}+\frac{\p}{\p\zeta}\right)\left(\frac{\p}{\p\eta}+\frac{\p}{\p\zeta}\right)=\frac{\p^2}{\p\eta^2}+\frac{\p^2}{\p\zeta^2}+2\frac{\p^2}{\p\eta\p\zeta}
    \end{equation}
    \begin{equation}
    \frac{\p^2}{\p t^2}=\left(c\frac{\p}{\p\eta}-c\frac{\p}{\p\zeta}\right)\left(c\frac{\p}{\p\eta}-c\frac{\p}{\p\zeta}\right)=c^2\frac{\p^2}{\p\eta^2}+c^2\frac{\p^2}{\p\zeta^2}-2c^2\frac{\p^2}{\p\eta\p\zeta}
    \end{equation}

    9月CFD算法编程课: http://dyfluid.com/class.html

    需要帮助debug算例的看这个 https://cfd-china.com/topic/8018

    1 Reply Last reply

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