====== ADVEC ======
===== Description =====
Advection-diffusion constitutive law for solid eulerian elements (element CONV2 and [[elements:adve2|ADVE2]])
==== The model ====
This law is only  used for linear pollutant transport in isotropic solids by upwind methods.\\
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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. \\
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This law is used for two‑dimensional flow. 

==== Files ====
Prepro: LADVEC.F \\
===== Availability =====
|Plane stress state| YES |
|Plane strain state| YES |
|Axisymmetric state| YES |
|3D state| NO |
|Generalized plane state| NO |
===== Input file =====
==== Parameters defining the type of constitutive law ====
^ Line 1 (2I5, 60A1)^^
|IL|Law number|
|ITYPE| 130 |
|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|
|:::|= 3 semi coupled analysis with flow|
|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 direction (angle in RAD)|
|CIM0|initial immobile water concentration|
|ALALX|first facultative imposed upwind in X direction|
|ALALY|first facultative imposed upwind in Y direction|
|BEBEX|second facultative imposed upwind in X direction|
|BEBEY|second facultative imposed upwind in Y direction|
^ Line 2 (7G10.0) ^^
|ATRANS|transversal dispersivity of the porous medium|
|ALONG|longitudinal dispersivity of the porous medium|
|DIFFM|molecular diffusion of the porous medium|
|RDM|retardation factor for mobile water|
|RDIM|retardation factor for immobile water|
|AM|degradation constant for mobile water|
|AIM|degradation constant for immobile water|
^ Line 3 (3G10.0) ^^
|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:
    * If ALALX and ALALY $\in \left[0,1\right] \rightarrow$ HUGHES formulation for the first upwind \\ BEBEY and BEBEY $\in \left[0,1\right] \rightarrow$ HUGHES formulation for the first upwind
    * If ALALX $\in \left[0,1\right] \rightarrow$ formulation in FRENET axes for the first upwind
    * If BEBEX $\in \left[0,1\right] \rightarrow$ formulation in FRENET axes for the second upwind
    * Otherwise 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 ====
8
==== 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 dispersive flux in X direction|
|SIG(4)|pollutant dispersive flux in Y direction|
|SIG(5)|pollutant storage due to time variation of concentration|
|SIG(6)|pollutant storage by convection and not restored by degradation|
|SIG(7)|pollutant flux from moving to non moving fluid|
|SIG(8)|pollutant degradation|

===== State variables =====
==== Number of state variables ====
4
==== 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 storage |
|Q(4)|immobile water concentration. |