Link to USGS home page.
Techniques and Methods 6-A12


By Steffen W. Mehl and Mary C. Hill

This report is also available as a pdf.


        This report documents the addition of shared node Local Grid Refinement (LGR) to MODFLOW-2005, the U.S. Geological Survey modular, transient, three-dimensional, finite-difference ground-water flow model. LGR provides the capability to simulate ground-water flow using one block-shaped higher-resolution local grid (a child model) within a coarser-grid parent model.  LGR accomplishes this by iteratively coupling two separate MODFLOW-2005 models such that heads and fluxes are balanced across the shared interfacing boundary.  LGR can be used in two-and three-dimensional, steady-state and transient simulations and for simulations of confined and unconfined ground-water systems.

    Traditional one-way coupled telescopic mesh refinement (TMR) methods can have large, often undetected, inconsistencies in heads and fluxes across the interface between two model grids. The iteratively coupled shared-node method of LGR provides a more rigorous coupling in which the solution accuracy is controlled by convergence criteria defined by the user.  In realistic problems, this can result in substantially more accurate solutions and require an increase in computer processing time.  The rigorous coupling enables sensitivity analysis, parameter estimation, and uncertainty analysis that reflects conditions in both model grids. 

    This report describes the method used by LGR, evaluates LGR accuracy and performance for two- and three-dimensional test cases, provides input instructions, and lists selected input and output files for an example problem.  It also presents the Boundary Flow and Head (BFH) Package, which allows the child and parent models to be simulated independently using the boundary conditions obtained through the iterative process of LGR.





    Purpose and Scope 


Highlights and Compatibility

    Highlights for New Users and Quick Reference 

    Compatibility with Other MODFLOW Packages and Processes

Description of Local Grid Refinement (LGR)

    The Grid Structure of the LGR Shared-Node Method - Parent Grid, Child Grid, and the Interface

    The Iterative Coupling 

    Closure Criteria 

    Transient Simulations

Evaluation of LGR Convergence and Numerical Accuracy Using a Two-Dimensional Test Case with Varying Levels of Heterogeneity

    Parent Grid error

    Child Grid Error

    Effects of the Refinement Ratio

    Convergence Properties

    Practical Lessons Learned


    Example 1: Two-Dimensional Steady State Test Case with Heterogeneity and Pumping - Forward, Sensitivity, and Inverse Simulations

    Example 2: Two-Dimensional Transient Test Case with Homogeneity and Pumping - Forward Simulations

    Example 3: Three-Dimensional Steady State Test Case with Homogeneity and Stream-Aquifer Interactions - Forward Simulations

Literature Cited

Appendix 1 - LGR Input Instruction and Selected Input and Output Files from Examples 1 and 3    

Appendix 2 - Independent Simulations Using the Boundary Flow and Head (BFH) Package

 Appendix 3 -Error Propagation in LGR

Appendix 4 - Using MODTMR and MF96TO2K to Create Child-Model Input Files

Appendix 5 - Brief Program Description


This report is available online in Portable Document Format (PDF). If you do not have the Adobe Acrobat PDF Reader, it is available for free download from Adobe Systems Incorporated.

Download the report (PDF, 1MB)

Document Accessibility: Adobe Systems Incorporated has information about PDFs and the visually impaired. This information provides tools to help make PDF files accessible. These tools convert Adobe PDF documents into HTML or ASCII text, which then can be read by a number of common screen-reading programs that synthesize text as audible speech. In addition, an accessible version of Acrobat Reader 5.0 for Windows (English only), which contains support for screen readers, is available. These tools and the accessible reader may be obtained free from Adobe at Adobe Access.

For product and ordering information:

World Wide Web:

Telephone: 1-888-ASK-USGS

For more information on the USGS—the Federal source for science about the Earth, its natural and living resources, natural hazards, and the environment:

World Wide Web:

Telephone: 1-888-ASK-USGS


FirstGov button  Take Pride in America button