A New Equation Solver for Modeling Turbulent Flow in Coupled Matrix-Conduit Flow Models

Area of Science:

• Hydrogeology
• Computational modeling
• Environmental science

Background:

• Karst aquifers exhibit dual flow systems: a conduit network and a porous rock matrix.
• Existing hybrid models are computationally intensive due to nonlinear turbulent conduit flow.

Purpose of the Study:

• To develop a faster iterative equation solver for karst conduit systems.
• To reduce computational time in hybrid karst aquifer models.

Main Methods:

• Developed a new iterative solver using an approximated Newton-Raphson expression.
• Implemented a Gauß-Seidel or successive over-relaxation scheme with a single iteration.
• Tested the solver in the CAVE code and discussed adaptability to MODFLOW-2005.

Main Results:

• Substantially reduced computational effort in steady-state and transient simulations.
• Demonstrated acceptable water balance errors across most test cases.
• Identified potential performance and accuracy degradation under rapid flow field changes.

Conclusions:

• The new solver offers a significant improvement in computational efficiency for karst aquifer modeling.
• The method provides a viable alternative for simulating complex karst hydrological processes.
• Further research may be needed to address limitations under dynamic flow conditions.