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

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.

Prepro: LADVEC.F

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

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