====== ADVE2 ======
Plane or axisymmetric advection-diffusion
===== Description =====
{{  :elements:plani.png?250|}}
For the axisymmetric element, the symmetry axis is Y. \\ \\
The element is defined by 4 nodes specified in NODES following the order indicated in the figure. \\ \\
The element must be used with law [[laws:advec|ADVEC]] \\ \\
The resolution method is the UPWIND FUPG method (with second order derivatives of the interpolation functions). The time discretization must therefore be small enough (Courant number less than unity) but the mesh can be more distorted than for the element [[elements:conv2|CONV2]] (that element is not in the Lagamine manual but it exists in the code). \\ \\
In case of a dissipation problem, oscillations can persist. \\ \\
Type: 171 \\
Implemented by: P. Biver, 1990

==== Files ====
Prepro: ADVE2A.F \\
Lagamine: ADVE2B.F

===== Input file =====
^Title (A5)^^
|TITLE|"ADVE2" in the first 5 columns|
^Control data (2I5)^^
|NELEM|Number of elements|
^Definition of the elements (2I5/4I5)^^
|NINTE|Number of integration points (4)|
|LMATE|Material law|
|NODES|List of nodes|
===== Results =====
SIGMA(8):
  * $f_{x,tot}$ the total pollutant flow in the x direction
  * $f_{y,tot}$ the total pollutant flow in the y direction
  * $f_{x,disp}$ the dispersive pollutant flow in the x direction
  * $f_{y,disp}$ the dispersive pollutant flow in the y direction
  * $f_{e,trans}$ the pollutant flow stored by temporal variation of concentration
  * $f_{e,conv}$ the pollutant flow stored by convection and unloaded by degradation
  * $f_{e,m-im}$ the pollutant flow transfered from mobile water to still water
  * $f_{e,degr}$ quantity of degraded pollutant

These flows are given with respect to the fluid volume except for total flows that are given with respect to the porous medium volume. \\
\\
Four state variable are also given: 
  * $v_x$ Darcy's flow rate in the x direction
  * $v_y$ Darcy's flow rate in the y direction
  * divv the divergence of Darcy's rate
  * $c_{im}$ pollutant concentration in the still water