Numerical Aspects In Modeling Coupled Conduit-Matrix Flow In Karst Aquifers Under Variably Saturated Conditions

In discrete-continuum models the flow in a three-dimensional matrix representing the fissured limestone volumes can be coupled with the flow in one-dimensional conduits. Common assumptions used in these models are laminar conduit flow and saturated conditions. We have developed an innovative numerical tool for simulating turbulent conduit coupled with laminar matrix flow under variably saturated conditions.

To describe the flow in the matrix and the conduits we use respectively the Richard's equation and the diffusive wave equation. When discretised, these equations can be combined into a single matrix system. This strategy is also often used in coupled river-aquifer models.

For the diffusive wave equation there exists a special positivity preserving scheme. We show that this scheme does not only preserve positivity but also allows the simulation of steady state, free-surface flows without any restriction on the time step size. This scheme results in a better efficiency of the coupled model. Typically, the steep hydraulic gradients in the conduits disappear faster then those in the matrix. Consequently, a simulation may contain a relatively long time period during which an almost steady state conduit flow is coupled with a transient matrix flow.

It is shown that the common node approach and dual node approach as used in existing discrete-continuum models for karst aquifers are inappropriate. Instead a special dual node approach as commonly used in well-aquifer models should be used. Using this approach the exchange parameter depends on the wetted surface of the conduit, the conductivity of the matrix and the spatial discretisation of the matrix.

The positivity preserving scheme and the special dual node approach may also be useful for coupled river-aquifer models.