On Solving Groundwater Flow and Transport Models with Algebraic Multigrid Preconditioning.

Area of Science:

• Geosciences
• Computational Hydrogeology
• Numerical Methods

Background:

• Large sparse linear systems are common in subsurface flow and transport modeling.
• Efficient solvers are crucial for handling complex geological models and reducing simulation time.
• Existing methods like MODFLOW's GMG solver have limitations in heterogeneous and anisotropic conditions.

Purpose of the Study:

• To implement and evaluate algebraic multigrid (AMG) preconditioning within the dual delineation approach for groundwater flow and transport.
• To compare the performance of AMG-based solvers against other iterative and direct solvers.
• To assess the scalability and efficiency of AMG for large-scale, complex geological models.

Main Methods:

• Implementation of AMG preconditioning for iterative solvers in the dual delineation framework.
• Comparison of AMG solvers with MODFLOW's GMG solver and direct sparse solvers.
• Testing on 2D and 3D benchmark problems with varying geological properties (homogeneous, heterogeneous, anisotropic).

Main Results:

• AMG preconditioning accelerated groundwater flow solutions by one to two orders of magnitude.
• AMG efficiency was maintained for 3D heterogeneous and anisotropic problems, outperforming MODFLOW's GMG.
• Direct sparse solvers were most efficient for pure advective transport simulations.
• The dual delineation approach with optimal solvers can process millions of grid blocks in seconds.

Conclusions:

• AMG preconditioning is a highly effective technique for accelerating groundwater flow simulations in large, complex geological models.
• The choice of solver (AMG vs. direct) depends on the specific transport processes (e.g., advection-dominated vs. advection-dispersion).
• This approach enables routine application to large geological models, significantly reducing computational time.