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Grid cell distortion and MODFLOW's integrated finite-difference numerical solution.

Dave M Romero¹, Steven E Silver

¹Balleau Groundwater, Inc. 901 Rio Grande Blvd. NW, Suite F-242, Albuquerque, NM 87104, USA. romerod@balleau.com

|November 8, 2006

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This study introduces MODFLOW IFD, a groundwater flow model using integrated finite-difference (IFD) schemes for curvilinear grids. Results show head solutions are insensitive to grid distortion, but velocity accuracy requires cell angles below 12.5 degrees.

Area of Science:

Hydrogeology
Numerical Modeling
Computational Science

Background:

Groundwater flow modeling relies on numerical schemes like finite-difference methods.
Traditional models use regular grids, limiting spatial discretization flexibility.
MODFLOW's integrated finite-difference (IFD) scheme enables non-orthogonal grids.

Purpose of the Study:

Introduce a modified MODFLOW-88 (MODFLOW IFD) capable of handling curvilinear grids.
Assess the sensitivity of numerical head and velocity solutions to grid cell distortion.
Establish criteria for designing distorted grid cells in flow models.

Main Methods:

Adapted MODFLOW-88 code to handle two-dimensional arrays for equivalent conductance calculations.
Developed a converging radial flow test problem with distorted trapezoidal grid cells.

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Performed sensitivity analysis on head and velocity solutions against varying grid distortion levels.

Main Results:

MODFLOW IFD successfully derives head solutions and intercell flow with distorted grids.
Numerical head solutions showed no significant sensitivity to grid cell distortion.
Velocity solution accuracy degraded with increased cell distortion, with <1% error for angles <12.5 degrees.

Conclusions:

The integrated finite-difference scheme in MODFLOW is robust for curvilinear grids.
Grid cell distortion impacts velocity accuracy, providing design guidelines.
MODFLOW 2000 and later versions can potentially utilize curvilinear grids with modifications.