Table of Contents

ADVEC

Description

Advection-diffusion constitutive law for solid eulerian elements (element CONV2 and ADVE2)

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 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)
ILLaw 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
TETAconstant apparent velocity direction (angle in RAD)
CIM0initial immobile water concentration
ALALXfirst facultative imposed upwind in X direction
ALALYfirst facultative imposed upwind in Y direction
BEBEXsecond facultative imposed upwind in X direction
BEBEYsecond facultative imposed upwind in Y direction
Line 2 (7G10.0)
ATRANStransversal dispersivity of the porous medium
ALONGlongitudinal dispersivity of the porous medium
DIFFMmolecular diffusion of the porous medium
RDMretardation factor for mobile water
RDIMretardation factor for immobile water
AMdegradation constant for mobile water
AIMdegradation constant for immobile water
Line 3 (3G10.0)
ALMtransfer constant for mobile water
ALIMtransfer constant for immobile water
PEFFeffective surface porosity of the porous medium.

Remarks on parameters

  1. 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
  2. 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.