For the transport equation (for the transport of a solute in a fluid, the mass transport equation or the energy transport equation for temperature-dependent problems), the discretisation of the asymmetric operator leads to an asymmetric system of equations. This cannot be solved with the iterative PCG equation solver. Therefore, in the case of steady-state transport, the equation system for the transport part is always solved using an LU decomposition (direct equation solver). This can lead to extreme computing time requirements for large models with many nodes.

For transient transport processes, the time discretisation is carried out using the operator split method developed by König ['Numerische Be- rechnung des dreidimensionalen Stofftransports im Grundwasser', TWM 91-13, RUB 1991]. When using this method, two systems of equations with symmetrical, positive definite matrices must be solved in each time step for the transport part. The iterative equation solver can then be used againin this case. If steady-state transport processes are to be calculated for large models, it is recommended to calculate the steady-state using a transient calculation (until the steady- state is reached) in order to reduce the calculation time

Stability criterion of the time discretization