Application of superposition with nonlinear head-dependent fluxes

Area of Science:

• Hydrogeology
• Groundwater Modeling
• Applied Mathematics

Background:

• Superposition is a standard technique for linear groundwater flow problems.
• Certain nonlinear groundwater problems possess characteristics that allow for the application of superposition.
• Nonlinear head-dependent fluxes, common in hydrological systems, pose challenges for traditional modeling.

Purpose of the Study:

• To demonstrate the applicability of the superposition principle to specific nonlinear groundwater flow problems.
• To present a method for addressing nonlinear head-dependent fluxes using superposition.
• To extend the utility of superposition beyond linear systems in hydrogeology.

Main Methods:

• Separating nonlinear problems into steady-state and transient-state components.
• Simulating transient-state head changes independently of steady-state conditions.
• Referencing elevations to the local steady-state water table for analysis.
• Imposing the negative of the steady-state flux onto the transient-state problem.

Main Results:

• Superposition can effectively address nonlinear groundwater problems with head-dependent fluxes.
• The method allows for independent simulation of transient-state head changes.
• Applicable scenarios include phreatophyte discharges, stream-aquifer interactions, spring discharges, and drain discharges.
• The technique involves specific referencing and flux imposition strategies.

Conclusions:

• The superposition principle offers a viable approach for modeling certain nonlinear groundwater dynamics.
• This method simplifies the analysis of complex systems involving nonlinear head-dependent fluxes.
• The findings expand the practical applications of superposition in hydrogeological studies.