====== ADVE3 ======
===== Description =====

The element is defined by 8 nodes specified in NODES(8) following the order given in the figure. \\ \\
{{  :elements:jet3t.png?300|}}
This element uses law [[laws:adv3d|ADV3D]]. \\ \\
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 distorted. \\ \\
In case of a problem where convection is significant, oscillations can persist. \\ \\
Type: 191 \\
Implemented by: J-P. Radu, 1990 
==== Files ====
Prepro: ADVE3A.F \\
Lagamine: ADVE3B.F

===== Input file =====
^Title (A5)^^
|TITLE|"ADVE3" in the first 5 columns|
^Control data (I5)^^
|NELEM|Number of elements|
^Definition of the elements (5I5/8I5)^^
|NNODE|Number of nodes (= 8)|
|NP1|Number of integration points in the first direction|
|NP2|Number of integration points in the first direction|
|NP3|Number of integration points in the first direction|
|LMATE|Material law|
|NODES(8)|List of nodes|

===== Results =====
SIGMA(10):
  * $f_{x,tot}$ the total pollutant flow in the x direction
  * $f_{y,tot}$ the total pollutant flow in the y direction
  * $f_{z,tot}$ the total pollutant flow in the z direction
  * $f_{x,disp}$ the dispersive pollutant flow in the x direction
  * $f_{y,disp}$ the dispersive pollutant flow in the y direction
  * $f_{z,disp}$ the dispersive pollutant flow in the z 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. \\
\\
Six 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
  * $v_z$ Darcy's flow rate in the z direction
  * divv the divergence of Darcy's rate
  * $c_{im}$ pollutant concentration in the still water
  * $\theta_m$ effective porosity