Documentation du code de simulation numérique SUNFLUIDH

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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) :

$L=\text{Length}$
$N=\text{Number_of_Cells}$
$\alpha(l)$ is function of $\text{Left_Cell_Size}$ and $\text{Right_Cell_Size}$.
$x(l)$ 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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