Overleg:Shallow water equations

Ik probeer de vergelijkingen er ook nog even netje bij te maken, maar dat is nog best lastig. Willem 22 Dec 2008 17:10 (CET)

$\begin{aligned} \frac{\partial W_{X, Y}}{\partial t} \cdot D X \cdot D Y_{X} = & u_{x, Y} \cdot W_{x, Y} * D Y_{x} - u_{x + 1, Y} \cdot W_{x + 1, Y} \cdot D Y_{x + 1} + \\ v_{X, y} * W_{X, y} * D X - v_{X, y + 1} * W_{X, y + 1} * D X \end{aligned}$

$\frac{\partial u_{x, Y}}{\partial t} \cdot D X \cdot D Y_{x} \cdot W_{x Y} = i m p u l s_{n o r m a a l} + i m p u l s_{t a n g e n t i e e l} + z w a a r t e k r a c h t + k r o m m i n g + c o r i o l i s + g e t i j k r a c h t + f r i c t i e$

$i m p u l s_{n o r m a a l} = \frac{W_{x - 1, Y} \cdot u_{x - 1, y}^{2} \cdot D Y_{x - 1} - W_{x + 1, Y} \cdot u_{x + 1, y}^{2} \cdot D Y_{x + 1}}{2}$

$i m p u l s_{t a n g e n t i e e l} = W_{x, y} \cdot v_{x, y}^{2} \cdot D X - W_{x + 1, y} \cdot u_{x + 1, y}^{2} \cdot D X$

$d w d t [x] [y] = u [x] [y] * u W [x] [y] * d y o [x] - u [x + 1] [y] * u W [x + 1] [y] * d y o [x + 1] + (v [x] [y] * v W [x] [y] - v [x] [y + 1] * v W [x] [y + 1]) * D X; W [x] [y] + = d w d t [x] [y] * D T / D X / d y m [x]; d u d t [x] [y] = (u W [x - 1] [y] * u [x - 1] [y] * u [x - 1] [y] * d y o [x - 1] - u W [x + 1] [y] * u [x + 1] [y] * u [x + 1] [y] * d y o [x + 1]) / 2.0 + / / i m p u l s t r a n s p o r t . 5 * g * (H [x - 1] [y] - H [x] [y]) * d y o [x] * u W [x] [y] + / / p o t e n t i e l e e n e r g i e (L O W [x] [y] * (v [x] [y] + v [x - 1] [y]) * (u [x] [y] + u [x] [y - 1]) - R O W [x] [y] * (v [x] [y + 1] + v [x - 1] [y + 1]) * (u [x] [y + 1] + u [x] [y])) / 4.0 * D X + / / t a n g e n t i e e l i m p u l s t r a n s p o r t - u [x] [y] / R * d y o [x] * D X * v o p u [x] [y] * s i n o [x] + / / c u r v a t u r e - 2 * o m e g a * v o p u [x] [y] * s i n o [x] * u W [x] [y] * D X * d y o [x] + / / c o r i o l i s k r a c h t u G M [x] [y] * u W [x] [y] * D X * d y o [x] + / / m a a n g e t i j k r a c h t - u [x] [y] * 0.01 * D X * d y o [x]; / / f r i c t i e d v d t [x] [y] = (v W [x] [y - 1] * v [x] [y - 1] * v [x] [y - 1] - v W [x] [y + 1] * v [x] [y + 1] * v [x] [y + 1]) / 2.0 * D X + . 5 * g * (H [x] [y - 1] - H [x] [y]) * v W [x] [y] * D X + (L O W [x] [y] * (u [x] [y] + u [x] [y - 1]) * (v [x] [y] + v [x - 1] [y]) * d y o [x] - L B W [x] [y] * (u [x + 1] [y] + u [x + 1] [y - 1]) * (v [x + 1] [y] + v [x] [y]) * d y o [x + 1]) / 4.0 + u o p v [x] [y] / R * d y m [x] * D X * u o p v [x] [y] * s i n m [x] + 2 * o m e g a * u o p v [x] [y] * s i n m [x] * v W [x] [y] * D X * d y m [x] + v G M [x] [y] * v W [x] [y] * D X * d y m [x] + - v [x] [y] * 0.01 * D X * d y m [x]; d u d t [x] [y] / = u W [x] [y] * D X * d y o [x]; d v d t [x] [y] / = v W [x] [y] * D X * d y m [x];$

Overleg:Shallow water equations

Navigatiemenu

Zoeken