Skip Links

USGS - science for a changing world

Techniques and Methods 6—A45

Groundwater Resources Program
Prepared in collaboration with AMEC

MODFLOW–USG Version 1: An Unstructured Grid Version of MODFLOW for Simulating Groundwater Flow and Tightly Coupled Processes Using a Control Volume Finite-Difference Formulation

By Sorab Panday, Christian D. Langevin, Richard G. Niswonger, Motomu Ibaraki, and Joseph D. Hughes

Thumbnail of report PDF (8.41 MB)


A new version of MODFLOW, called MODFLOW–USG (for UnStructured Grid), was developed to support a wide variety of structured and unstructured grid types, including nested grids and grids based on prismatic triangles, rectangles, hexagons, and other cell shapes. Flexibility in grid design can be used to focus resolution along rivers and around wells, for example, or to subdiscretize individual layers to better represent hydrostratigraphic units. MODFLOW–USG is based on an underlying control volume finite difference (CVFD) formulation in which a cell can be connected to an arbitrary number of adjacent cells. To improve accuracy of the CVFD formulation for irregular grid-cell geometries or nested grids, a generalized Ghost Node Correction (GNC) Package was developed, which uses interpolated heads in the flow calculation between adjacent connected cells. MODFLOW–USG includes a Groundwater Flow (GWF) Process, based on the GWF Process in MODFLOW–2005, as well as a new Connected Linear Network (CLN) Process to simulate the effects of multi-node wells, karst conduits, and tile drains, for example. The CLN Process is tightly coupled with the GWF Process in that the equations from both processes are formulated into one matrix equation and solved simultaneously. This robustness results from using an unstructured grid with unstructured matrix storage and solution schemes. MODFLOW–USG also contains an optional Newton-Raphson formulation, based on the formulation in MODFLOW–NWT, for improving solution convergence and avoiding problems with the drying and rewetting of cells. Because the existing MODFLOW solvers were developed for structured and symmetric matrices, they were replaced with a new Sparse Matrix Solver (SMS) Package developed specifically for MODFLOW–USG. The SMS Package provides several methods for resolving nonlinearities and multiple symmetric and asymmetric linear solution schemes to solve the matrix arising from the flow equations and the Newton-Raphson formulation, respectively.

First posted May 2, 2013

For additional information contact:
Office of Groundwater
U.S. Geological Survey
Mail Stop 411
12201 Sunrise Valley Drive
Reston, VA 20192
(703) 648–5001

Part or all of this report is presented in Portable Document Format (PDF); the latest version of Adobe Reader or similar software is required to view it. Download the latest version of Adobe Reader, free of charge.

Suggested citation:

Panday, Sorab, Langevin, C.D., Niswonger, R.G., Ibaraki, Motomu, and Hughes, J.D., 2013, MODFLOW–USG version 1: An unstructured grid version of MODFLOW for simulating groundwater flow and tightly coupled processes using a control volume finite-difference formulation: U.S. Geological Survey Techniques and Methods, book 6, chap. A45, 66 p.,





Mathematical and Numerical Formulation

Implementation and Program Design

Guidance for Applying MODFLOW–USG

Example Problems


References Cited

Appendix A. Notation Used in this Report

Accessibility FOIA Privacy Policies and Notices logo U.S. Department of the Interior | U.S. Geological Survey
Page Contact Information: Contact USGS
Page Last Modified: Friday, December 02, 2016, 03:51:21 PM