Documentation du code de simulation numérique SUNFLUIDH

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===== Hyperbolic tangent function "two side" =====

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__ Description:__

Function with an extremum. \\
Cell size is refined at left and right tips of the segment.\\

__Namelist :__

   &MESH_FUNCTION_DATA  Function_Name="TANH_TWO_SIDES"  ,
                        Number_of_Cells= 32 ,
                        Length= 1.0  ,
                        Left_Cell_Size= 2.0d-02 ,
                        Right_Cell_Size= 3.0d-02 ,
                        Reverse_Ordering= .false. /

__Cell size distribution h(l) :__

$L$ is the Length.\\
$N$ is the Number_of_Cells}.\\
$\alpha(l)$ is function of Left_Cell_Size and Right_Cell_Size.\\
$x(l)$ is the coordinate.\\
$h(l)$ is the cell size.\\
$l$ is the cell index.\\

\begin{align*} 
x(1)&= 0 \\
F(l)&=\frac{1}{2}(1 + \tanh( \alpha(l)(\frac{l-1}{N})-\frac{1}{2})/\tanh(\frac{1}{2}) \alpha(l)), 2 \leq l \leq N+1\\
x(l)&= L \cdot (\frac{F(l)}{\alpha(l) + (1- \alpha(l)) F(l)})\\
x(N+1)&= L \\
h(l)&= x(l+1)-x(l)\\
\end{align*}



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