porousScalarTransportFoam solver

Description

Solves the transport equation for a passive scalar in porous media with dispersion and retard coefficient model.

Multiple time-dependent injection source points can be specificied using the keyword sourceEventFileTracer in constant/transportProperties (see sourceEventFile class).

The transport is implicitly solved using a pre-computed flux phi or velocity U and optional water content theta or saturation S

Time step is managed using an estimation of the time truncation error of the scalar variation.

Configuration files

constant/transportProperties :

Example for one specie transport (or multi-species with similar properties):

eps eps [0 0 0 0 0 0 0] 0.25; // porosity (can be volScalarField in constant/)

Dm Dm [0 2 -1 0 0 0 0] 1e-9; // molecular diffusion

porousTransport // specific dictionary for transport
{
  phaseName theta; // to specify the flux field (phitheta here) or velocity field (Utheta). U and phi is not precised.
  Kd Kd [-1 3 0 0 0 0 0] 1e-3;
  rs rs [1 -3 0 0 0 0 0] 1000;
  epsTotal epsTotal [0 0 0 0 0 0 0] 0.30;
  lambda lambda [0 0 -1 0 0 0 0 ] 1e-9;// decay of the C scalar
}

dispersionModel alphaDispersion; // dispersion model

alphaDispersionCoeffs
{
  tau tau [0 0 0 0 0 0 0] 2; // tortuosity
  alphaL alphaL [0 1 0 0 0 0 0] 0.01; // longitudinal dispersivity
  alphaT alphaT [0 1 0 0 0 0 0] 0.002; // transverse dispersivity
}

sourceEventFileTracer injection.dat; // to specify event file for time-dependent source term

Example for multi-species transport (C1/C2 species) :

eps eps [0 0 0 0 0 0 0]     0.25;

porousTransport
{
    phaseName oil;
}

species
(
    C1
    C2
);


C1
{
  Dm Dm [0 2 -1 0 0 0 0] 1e-9;
  porousTransport
  {
      Kd Kd [-1 3 0 0 0 0 0] 1e-3;
      rs rs [1 -3 0 0 0 0 0] 0;
      epsTotal epsTotal [0 0 0 0 0 0 0] 0.30;
      lambda lambda [0 0 -1 0 0 0 0 ] 1.1574e-6;
  }

  dispersionModel alphaDispersion;
  alphaDispersionCoeffs
  {
      tau tau [0 0 0 0 0 0 0] 2;
      alphaL alphaL [0 1 0 0 0 0 0] 0.01;
      alphaT alphaT [0 1 0 0 0 0 0] 0.002;
  }
}

C2
{
  Dm Dm [0 2 -1 0 0 0 0] 1e-9;
  porousTransport
  {
      Kd Kd [-1 3 0 0 0 0 0] 1e-3;
      rs rs [1 -3 0 0 0 0 0] 0;
      epsTotal epsTotal [0 0 0 0 0 0 0] 0.30;
      lambda lambda [0 0 -1 0 0 0 0 ] 1.1574e-6;
  }

  dispersionModel alphaDispersion;
  alphaDispersionCoeffs
  {
      tau tau [0 0 0 0 0 0 0] 2;
      alphaL alphaL [0 1 0 0 0 0 0] 0.01;
      alphaT alphaT [0 1 0 0 0 0 0] 0.002;
  }
}

system/controlDict :

adjustTimeStep yes;

truncationError 0.001; // Allowed time-scheme truncation error used to manage time-step

CSVoutput       true; // active the CmassBalance.csv output

eventTimeTracking true; // to force the solver to compute solutions at each event time (patch/source/output)

Required fields

• 0/C : The concentration field (or 0/C1 0/C2 in the multi-specie example above)

• 0/UphaseName : (phaseName is read from transportProperties) Used to compute dispersion coefficient. Can be used to compute 0/phiphaseName if not present (Warning: velocity field U in FV formulation has been reconstructed from flux field phi and is not conservative, prefer the use of real phi field

Optional fields

• 0/phiphaseName : The pre-computed flux field where phaseName can be changed in porousTransport dictionary (0/phioil in multi-specie example)

• 0/SphaseName : Saturation field (S=1 if not present)

• 0/theta : Water content (overwrites Saturation if both are present)

• Other spatially defined parameters : alphaL , alphaT , eps.

Timestep managing

The computation of timestep for next iteration is directly computed using truncation error related to the time scheme defined (Euler, backward, CrankNicolson). The time step formula for backward time-scheme is for example :

deltaT = Foam::pow(3 x truncationError x Cmax[speciesi]/dC3dT3max[speciesi],1./3.)

where dC3dT3maxmaximal is the maximal value of the thid time derivative and Cmax the value of C in this cell.