Shape Funcions checked

eddyshape.jpg
Eddies shape functions in the velocity field
eddyvorshape.jpg
Eddies shape function in the vorticity field

Reynolds stresses



   \begin{equation*} q_\sigma(y) =  \begin{cases} \frac{1}{\sqrt{4 \pi}} \sqrt{\frac{8}{3}} (sin(y))^2 y, & if~|y| < 1 \\ 0, & otherwise  \end{cases}  \end{equation*}  (1)

<uu> , <vv> , <ww> , MAX and min respectively all over the grid

<uv> , <uw> , <vw> , MAX and min respectively all over the grid



   \begin{equation*} q_\sigma(y) =  \begin{cases} \frac{1}{\sqrt{4 \pi}} \sqrt{\frac{35}{87}} \frac{27}{2} (-27x^5+5x^3), &amp; if ~ |y| &amp;lt; \frac{1}{3} \\ \frac{1}{\sqrt{4 \pi}} \sqrt{\frac{35}{87}} \frac{27}{2} (\frac{1}{2}x^3-x^2+\frac{1}{2}x), &amp; if~|y| &amp;lt; 1 ~ and ~ |y| \ge \frac{1}{3}\\ 0, &amp; otherwise  \end{cases}  \end{equation*}  (2)

<uu> , <vv> , <ww> , MAX and min respectively all over the grid

<uv> , <uw> , <vw> , MAX and min respectively all over the grid



   \begin{equation*} q_{\sigma}(r)=\frac{r^{3}(r^{2}+5/2)}{(r^{2}+1)^{5/2}}  \end{equation*}  (3)

<uu> , <vv> , <ww> , MAX and min respectively all over the grid

<uv> , <uw> , <vw> , MAX and min respectively all over the grid



   \begin{equation*} q_{\sigma}(r)=erf(\frac{r}{2^{0.5}})-r(\frac{2}{\pi})^{0.5}e^{-\frac{r^{2}}{2}}  \end{equation*}  (4)

<uu> , <vv> , <ww> , MAX and min respectively all over the grid

<uv> , <uw> , <vw> , MAX and min respectively all over the grid


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Topic revision: r5 - 2010-05-24 - 16:31:48 - RuggeroPoletto
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