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Influence of boundary condition types on unstable density-dependent flow
Behzad Ataie-Ashtiani1, Craig T Simmons, Adrian D Werner
1National Centre for Groundwater Research & Training and School of the Environment, Flinders University, G.P.O. Box 2100, Adelaide, SA 5001, Australia; craig.simmons@flinders.edu.au.
Ground Water
|May 11, 2013
Summary
Boundary conditions significantly impact numerical simulations of unstable density-dependent flow. Choosing solute mass flux over concentration at the source eliminates spatial discretization effects on plume configuration.
Area of Science:
- Geosciences
- Environmental Engineering
- Computational Hydrogeology
Background:
- Mathematical models for unstable density-dependent flow require precise boundary conditions.
- Numerical simulations are critical for understanding flow and transport phenomena.
Purpose of the Study:
- To investigate the influence of various boundary conditions on unstable density-dependent flow systems using numerical simulations.
- To analyze the impact of different boundary condition implementations on simulation results, particularly concerning spatial discretization effects.
Main Methods:
- Numerical simulations were performed using the FEFLOW model, adapting the Elder problem setup.
- The study compared solute mass flux boundary conditions with specified concentration boundary conditions at the solute source.
- Various boundary condition types for non-source boundaries were evaluated, alongside different solute transport equation forms and time integration schemes.
Main Results:
- Employing a solute mass flux boundary condition at the source mitigates spatial discretization's influence on convective solution modes.
- Non-source boundary conditions, transport equation forms (divergent vs. convective), and discretization significantly affect plume configuration in coarser meshes.
- The Adams-Bashford/Backward Trapezoidal time integration method exhibited higher sensitivity and lower numerical solution stability compared to Euler-Backward/Euler-Forward.
Conclusions:
- Boundary condition selection is a critical factor in the accurate numerical modeling of unstable density-dependent flow.
- Understanding the interplay between boundary conditions, discretization, and equation forms is essential for reliable simulation outcomes.
- The choice of time integration scheme also plays a role in the stability and sensitivity of numerical solutions for these systems.
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