====== ADV3D ======
===== Description =====
Advection-diffusion constitutive law for 3D solid eulerian elements ([[elements:adve3|ADVE3]])
==== The model ====
This law is only  used for linear pollutant transport in isotropic solids by upwind methods.\\
This constitutive law takes into account the advection‑dispersion in the moving fluid but also degradation, adsorption on the solid matrix and immobile fluid effect as linear phenomena. This law is used for three‑dimensional flow. 

==== Files ====
Prepro: LADV3D.F \\
===== Availability =====
|Plane stress state| NO |
|Plane strain state| NO |
|Axisymmetric state| NO |
|3D state| YES |
|Generalized plane state| NO |
===== Input file =====
==== Parameters defining the type of constitutive law ====
^ Line 1 (2I5, 60A1)^^
|IL|Law number|
|ITYPE| 135 |
|COMMENT| Any comment (up to 60 characters) that will be reproduced on the output listing|
==== Integer parameters ====
^ Line 1 (2I5) ^^
|INDV|= 0 constant advection|
|:::|= 1 space time variation of advection|
|:::|= 2 only space variation of advection|
|INDM|= 0 same meshing for flow and pollution|
|:::|= 1 different meshing|

==== Real parameters ====
^ Line 1 (7G10.0) ^^
|UABS	|- constant apparent velocity modulus|
|TETA|constant apparent velocity theta angle (angle in RAD)|
|PHI|constant apparent velocity phi angle (angle in RAD)|
|CIM0|initial immobile water concentration|
|ATRANS|transversal dispersivity of the porous medium|
|ALONG|longitudinal dispersivity of the porous medium|
|DIFFM|molecular diffusion of the porous medium|
^Line 2 (7G10.0) ^^
|RDM|retardation factor for mobile water|
|RDIM|retardation factor for immobile water|
|AM|degradation constant for mobile water|
|AIM|degradation constant for immobile water|
|ALM|transfer constant for mobile water|
|ALIM|transfer constant for immobile water|
|PEFF|effective surface porosity of the porous medium.|

=== Remarks on parameters ===
  - Upwind parameters: 
    * Optimum formulation in FRENET axes
  - Physical parameters:
    * RDM=$1 + \theta_s \rho_s p K_d / \theta_m$
    * RDIM=$1 + \theta_s \rho_s (1-p) K_d / \theta_{im}$
    * AM =$k_s.(RDM -1).+ k_m  + ALM$
    * AIM=$k_s.(RDIM -1).+ k_{im} + ALIM$
    * ALM =$\alpha_\alpha/\theta_m$
    * ALIM=$\alpha_\alpha/\theta_{im}$ \\ With:
      * $\theta_s$=1-total porosity
      * $\theta_{m}$=effective porosity
      * $\theta_{im}$=non effective porosity
      * $k_{s,m,im}$=degradation coefficients in solid, moving and non-moving fluids
      * $K_{d}$=linear adsorption coefficient
      * $p$=part of solid surface in contact with the moving fluid
      * $\rho_s$=solid density
      * $\alpha_d$=exchange coefficient between mobile and immobile fluids

===== Stresses =====
==== Number of stresses ====
10
==== Meaning (numerical, not physical) ====
|SIG(1)|pollutant flow in the X direction $(=q_X)$|
|SIG(2)|pollutant flow in the Y direction $(=q_Y)$|
|SIG(3)|pollutant flow in the Z direction $(=q_Z)$|
|SIG(4)|pollutant dispersive flux in X direction|
|SIG(5)|pollutant dispersive flux in Y direction|
|SIG(6)|pollutant dispersive flux in Z direction|
|SIG(7)|pollutant storage due to time variation of concentration|
|SIG(8)|pollutant storage by convection and not restored by degradation|
|SIG(9)|pollutant flux from moving to non moving fluid|
|SIG(10)|pollutant degradation|

===== State variables =====
==== Number of state variables ====
5
==== List of state variables ====
|Q(1)| fluid Darcy velocity in the X direction |
|Q(2)| fluid Darcy velocity in the Y direction |
|Q(3)| fluid Darcy velocity in the Z direction |
|Q(4)| fluid storage |
|Q(5)| immobile water concentration. |