For the transport equation (for transport of a solute in the fluid the mass transport equation and the energy transport equation for temperature-dependent problems), the discretization of the asymmetrical operator leads to an unbalanced system of equations.

This cannot be solved with the iterative PCG solver. Therefore, in steady-state transport the system of equations for the transport part is solved always using an LU-reduction (direct solver). In large models with many nodes this can result in an extreme computing time.

For transient transport processes, the time discretization is performed using the by König ['Numerical calculation of three-dimensional solute transport in groundwater', TWM 91-13, RUB 1991] developed operator split method.

Using this method in each time step two systems of equations with symmetric positive definite matrices have to be solved for the transport part. Here, the iterative solver can be used. Should steady-state transport processes be calculated for large models, it is recommended to calculate the steady state by a transient calculation (to reach the steady state) to reduce the computation time.

 

Stability criterion of the time discretization