In 2013 Visual MODFLOW Flex demonstrated the power of MODFLOW-USG through the use of Voronoi polygon unstructured grids. By focusing the grid resolution “where it counts”, you can achieve higher accuracy and more efficient run times over structured MODFLOW grids. Building on the new capabilities of MODFLOW-USG and leveraging the flexibility that comes with a grid-independent conceptual model, we are pleased to demonstrate layer-dependent discretization using Quad-Based UnStructured grids in Visual MODFLOW Flex.
What is Layer-Dependent Discretization?
One of the key features of UnStructured grids is their ability to allow for a different level of discretization (cell sizing/refinement) in each model layer. This is a significant advancement over structured MODFLOW and finite element models which require that all model layers have the same grid/mesh discretization.
Advantages of Layer-Dependent Discretization
By following a layer-dependent approach for discretization, modelers are able to increase the grid resolution horizontally and vertically around desirable features without being forced to add unnecessary cells in other layers and areas outside of the region of interest. The benefit of this is two-fold: higher accuracy and shorter run times. This approach is useful in a variety of scenarios:
- Surface water / ground water interactions: upper layers can be refined around rivers/streams, with coarser grid resolution in lower layers
- Dewatering: focus resolution around the layers containing well screens, with coarser resolution in layers above and below.
- Modeling complex geological structures (such as faults)
- Minimizing Numerical Dispersion in a Localized Contaminant Transport model: focus vertical resolution around the migrating plume front, with coarser grids in lower layers
- Adaptive discretization in the gradients around steep surfaces in order to overcome “disconnected” cells
- Adaptive discretization around properties zones in order to ensure numerical accuracy and stability
A simple example is illustrated below for a three layer model. The grid was refined around river boundary conditions in layer 1 (Figure 1), smoothed downwards to layer 2 (Figure 2), until eventually there is no refinement as shown in layer 3 (Figure 3).
Figure 1: Layer 1 of a watershed model
Figure 2: Layer 2 of a watershed model
Figure 3: Layer 3 of a watershed model
A layer-dependent approach is also ideal for accommodating complex stratigraphy (cases where there is non-pancake geology). By eliminating the unnecessary “minimum layer thickness” cells, this will improve model stability and efficiency.
Figure 4: Gridlines for layer 2 and 3 showing discontinous layers correlating to the conceptual model.
What are Quad-Based Grids?
The premise behind Quad-Based Grids is that any rectangular-shaped cell can be divided into four equally-sized cells. Quad-Based grid refinement is a simple way to focus resolution in areas of interest in order to better represent hydraulic gradients or to more accurately represent known variations in hydraulic properties or boundary conditions.1 Examples of Quad-Based grids include Nested grids, Quadtree grids, and Octree grids (the case when a Quadtree grid is refined in three dimensions).
In order to reduce numerical errors and improve accuracy of the simulation it is generally recommended that Quad-Based grids are smoothed so that every cell is connected to no more than two cells in any direction. Doing so can simplify the calculation of the Ghost Node locations (for the Ghost Node Correction (GNC) package)1. Also, keeping with a limit of two connections per cell face may yield minimal errors in the calculated heads/fluxes such that the GNC package may not be needed. (See a discussion of results for the Biscayne Aquifer example in the MODFLOW-USG Manual, page 50).
Advantages of Quad-Based Grids
Since Quad-Based grids use rectangular geometry (similar to structured finite difference grids) they provide a natural means for MODFLOW modelers to transition into MODFLOW-USG1, thus reducing the learning curve. Similarly, Quad-Based grids offer a logical gridding approach for updating and improving existing MODFLOW-2000/2005/NWT models. For example, you could replace a variably-spaced grid with a high-resolution nested grid (with smoothing). This can improve model accuracy and stability and also reduce runtimes which is crucial when running PEST. Even though Quad-based grids are not as good as Voronoi grids from a numerical standpoint (see previous blog post on this topic), they are easy to deal with and are useful in a number of practical modeling scenarios.
Figure 5: Example of a nested grid with smoothing.
The flexibility that comes with MODFLOW-USG allows you to focus grid resolution “where it counts”, both horizontally and vertically. By providing a variety of unstructured grid geometries and refinement capabilities, Visual MODFLOW Flex gives you the ability to design and select the most suitable grid for your project needs, thus resulting in more accurate and reliable numerical models. Quad-Based grids are currently being developed in Visual MODFLOW Flex.
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. USGS Techniques and Methods 6–A45 http://water.usgs.gov/ogw/mfusg/