Draft:Anaqsim

• Comment: Sources are not properly wikilinked with a reflist. Given this and the prose structure, I have reason to beleive that this was written at least partially from a software such as ChatGPT. TheBritinator (talk) 12:02, 23 February 2024 (UTC)

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AnAqSim

AnAqSim (Analytic Aquifer Simulator) is a groundwater modelling application based on the analytical element method (AEM).  The application is computationally efficient for solving complex hydrogeological and fluid transport problems by representing the behavior of specific elements or features within a system using analytical solutions to governing equations. This makes AnAqSim a quick and flexible method for simulating 3-dimensional, transient, heterogeneous, and anisotropic groundwater systems.  AnAqSim was originally developed by Dr. Charles Fitts and first released in 2011. It has been continuously updated since its release.

Applications

Due to their simplicity and capacity to handle realistic properties and geometries, AnAqSim and other AEM-based models find common use in rapid hydrologic analyses and screening models^[1]. The method offers practical advantages, such as flexible boundary conditions and the absence of a grid, ensuring accurate representation of hydrologic features' geometry across the entire domain^[2]. The flexibility of analytic element models allows for easy adjustments in model construction, enabling expansion or refinement without altering boundary conditions or redesigning the computational grid. This adaptability is crucial for stepwise modeling approaches, where simpler models guide initial project phases and gradually evolve into more complex representations as more data and insights become available^{[3] [4]}.  The absence of grids in AEM also makes this method ideal for examining the impact of grids on simulations of various hydrologic factors, including simulation of groundwater heads, water budgets, pathlines ^{[5] [6]}, residence times in watersheds ^{[7] [8]}, and aquifer remediation ^[9].  The grid-free nature of AnAqSim and other AEM programs also means that they are particularly well-suited to working directly and quickly with vector-based Geographic Information System data sets ^[10].  Application examples of AnAqSim can be found in peer-reviewed journals^{[11] [12] [13] [14]}.

Development History

AnAqSim’s solution method, AEM, is a mathematical technique used in many fields of science and engineering, including studies of flow and conduction, periodic waves, and deformation by force ^[15]. The principal concept of the AEM is “superposition”, which involves summing the effects of many mathematical functions, or “elements”, used to define the system of interest.  The superposition of mathematical functions is an old concept; however, the idea to apply superposition of a large number of functions with the aid of a computer to problems in hydrogeology was founded by Otto Strack in the late 1970’s ^[16].  Strack’s original application of AEM to hydrogeology involved modelling the environmental impact of the Tennessee-Tombigbee Waterway for the U.S. Army Corps of Engineers^{[17] [18]}. Since Strack’s original application, the method has been continuously developed and improved through the contributions of many researchers^{[19] [20] [21] [22] [23] [24] [25] [26] [27] [28] [29] [30]}.

The advances to AEM leading to AnAqSim

Early applications of AEM were limited to 2D steady state flow.  However, Charles Fitts identified a significant conceptual breakthrough when the concept of spatially variable area sinks (SVAS) was published ^[31] in 1999. These SVAS are 2D functions with a sink term whose strength (rate) varies with position in the plane using radial basis functions. SVAS functions create a smooth, irregular surface of sink strength that passes through any number of basis points where the strength is set. The radial basis functions used in SVAS were first employed in 1971 by others to interpolate smooth topographic surfaces from point elevation data ^[32].

After it was demonstrated that the SVAS functions in a model simulating leakage from a single-layer aquifer to an overlying surface water using relatively few basis points, Fitts recognized that these SVAS functions could be used in a different way with larger numbers of basis points to significantly improve multi-layer and transient modeling with the AEM. The distributions of vertical leakage between layers in multi-layer models and the storage fluxes in transient models may be combined and viewed as spatially variable distributed sinks. The SVAS functions could be used to approximate the required sink distribution.

Fitts also developed capabilities for modeling anisotropy in the plane of the domain, using some classic coordinate transformations^[33] and newer coordinate transformations^[34]. Concurrently, he also worked on a subdomain approach in AEM where the model layer could be divided into separate finite subdomains instead of one infinite domain^{[35] [36]}. Using this approach, each subdomain has its own mathematical model and can have its own direction and ratio of anisotropy, making for very robust anisotropy capabilities. A subdomain approach has been used with boundary element methods, which are like AEM but use numerical integrations along boundary elements instead of analytic solutions^{[37] [38]}.  

The subdomain approach has other benefits, including: 1) it makes the equations for potential or discharge shorter, 2) model layering can vary from one region of a model to another, and 3) heterogeneity boundaries can be a mix of different boundary types such as specified head, specified normal flux, and interdomain.  Fitts later added storage terms and transience using the same SVAS functions as are used for vertical leakage between layers. For the transient term, Fitts used finite difference time steps. Such approximations are also employed by MODFLOW and other numerical modeling programs.  These advances give Anaqsim the accuracy, minimal inputs and other benefits of AEM, but with comprehensive capabilities for anisotropy, multi-layer systems, and transient flow.

References

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Hunt, R. 2006. Ground Water Modeling Applications Using the Analytic Element Method. Ground Water 44(1):5-14

Fredrick, K, M. Becker, D. Flewelling, W. Silavisesrith. 2004. Enhancement of aquifer vulnerability indexing using the analytic-element method. Environmental Earth Sciences 45(8):1054-1061

Haitjema, H.M. 1992. Modeling regional ground-water flow in Fulton County, Indiana: Using the analytic element method. Ground Water 30, no. 5: 660–666.

^[4] Haitjema, H.M. 1995. Analytic Element Modeling of Groundwater Flow. San Diego, California: Academic Press Inc

^[5] Hunt, R.J., and J.T. Krohelski. 1996. The application of an analytic element model to investigate groundwater-lake interactions at Pretty Lake, Wisconsin. Journal of Lakes and Reservoir Management 12, no. 4:487–495.

^[6] Hunt, R.J., V.A. Kelson, and M.P. Anderson. 1998b. Linking an analytic element flow code to MODFLOW—Implementation and benefits. In MODFLOW’98: Proceedings of the 3rd International Conference of the International Ground Water Modeling Center, ed. E.P. Poeter, C. Zheng and M.C. Hill, 497–504. Golden, Colorado: Colorado School of Mines.

^[7] Haitjema, H.M. 1995. On the residence time distribution in idealized groundwatersheds. Journal of Hydrology 172, no. 1–4: 127–146.

^[8] Luther, K.H., and H.M. Haitjema. 2000. Approximate analytic solutions to 3D unconfined groundwater flow within regional 2D models. Journal of Hydrology 229, no. 3–4: 101–117.

^[9] Tolika, M. and E.K. Paleologos. 2004. Groundwater modeling of a complex hydrologic system in South Carolina through the use of analytic elements. Water, Air, & Soil Pollution 4, no. 4–5: 215–226

^[10] Steward, D.R., and E.A. Bernard. 2006. The synergistic powers of AEM and GIS geodatabase models in water resources studies. Ground Water 44, no. 1: 56–61.

^[11] Padam, O., S. Gaur, S. Dwivedi, and P. Dikshit.  2019. Groundwater modelling using an analytic element method and finite difference method: An insight into Lower Ganga River basin. Journal of Earth System Science. 128: 195

^[12] Yihdego, Y., and A. Paffard. 2017. Predicting Open Pit Mine Inflow and Recovery Depth in the Durvuljin soum, Zavkhan Province, Mongolia. Mine Water Environment 36:114–123

^[13] Dechinlkhundev, D., M. Zorigt, and I. Dorjsuren. 2021. The Sustainable use of groundwater resources concerning further climate change scenarios in Uiaanbaatar City Area, Mongolia. Journal of Water and Climate Change. 12.5

^[14] Kraemer, S. 2023. Analytic Element Domain Boundary Conditions for Site-Scale Groundwater Flow Modeling Los Angeles Basin. Groundwater 61(5)

^[15] Steward, David, R. 2020. Analytic Element Method: Complex Interactions of Boundaries and Interfaces. Oxford University Press, UK.

^[16] Fitts, Charles, R. 2023.  Groundwater Science.  Academic Press, MA USA. 3^rd Ed.

^[17] Haitjema, H.M. 1995. Analytic Element Modeling of Groundwater Flow.  Academic Press. London, UK.

^[18] Strack, Otto, D.L. 1989. Groundwater Mechanics.  Prentice-Hall. NJ, USA.

^[19] Bakker, M., and O.D.L. Strack. 2003. Analytic elements for multi-aquifer flow. Journal of Hydrology 271, no. 1–4: 119–129.

^[20] Craig, J.R., I. Jankovic, and R.J. Barnes. 2006. The nested superblock approach for regional scale analytic element models. Ground Water 44, no. 1: 76–80.

^[21] Fitts, C.R. 1997. Analytic modeling of impermeable and resistant barriers. Ground Water 35, no. 2: 312–317.

^[22] Fitts, C.R. 1989. Simple analytic functions for modeling three-dimensional flow in layered aquifers. Water Resources Research 25, no. 5: 943–948.

^[23] Furman, A., and S.P. Neuman. 2003. Laplace-transform analytic element solution of transient flow in porous media. Advances in Water Resources 26, no. 12: 1229–1237

^[24] Haitjema, H.M. 2006. A fast direct solution method for non-linear equations in an analytic element model. Ground Water 44, no. 1: 102–105.

^[25] Fitts, C.R., 2010. Modeling Aquifer Systems with Analytic Elements and Subdomains, Water Resources Research, 46, W07521, doi:10.1029/2009WR008331.

^[26] Fitts. C.R. 2018. Modeling Dewatered Domains in Multilayer Analytic Element Models. Groundwater. Vol. 56, No. 4 (557–561)

^[27] Bakker, M. and V.A. Kelson. 2009. Writing Analytic Element Programs in Python. Ground Water. Vol. 47, No. 6  (828–834)

^[28] Mohammadi, A, M. Ghaeini‑Hessaroeyeh, E. Fadaei‑Kermani. 2020. Contamination transport model by coupling analytic element and point collocation methods. Applied Water Science. 10(13)

^[29] Strack, O, and E. Toller. 2021. An analytic element model for highly fractured elastic media. Numerical and Analytical Methods in Geomechanics. 46(2): 297-314

^[30] Fitts, C., J. Godwin, K. Feiner, C. McLane, S. Mullendore.  2015. Analytic Element Modeling of Steady Interface Flow in Multilayer Aquifers Using AnAqSim. Groundwater 53(3)

^[31] Strack, O., and I. Jankovic. 1999. A multi-quadric area-sink for analytic element modeling of groundwater flow. Journal of Hydrology. Vol 226, No. 3-4.

^[32] Hardy, R. 1971.  Multiquadric equations of topography and other irregular surfaces. Journal of Geophysical Research.  Vol. 6, No. 8 (1905 -1915).

^[33] Muskat, M. 1937. The Flow of Fluids Through Porous Media. Journal of Applied Physics. 8, 274–282.

^[34] Fitts, C.R. 2006. Exact Solution for Two-Dimensional Flow to a Well in an Anisotropic Domain. Groundwater, 44(1), 99-101.

^[35] Fitts, C.R. 2004. Discrete Analytic Domains: A New Technique for Groundwater Flow Modeling in Layered, Anisotropic, and Heterogeneous Aquifer Systems, American Geophysical Union Fall Meeting, San Francisco, CA.

^[36] Fitts, C.R. 2010. Modeling Aquifer Systems with Analytic Elements and Subdomains. Water Resources Research, 46, W07521.

^[37] Liggett, J. A., and P. L‐F. Liu. 1983.  The Boundary Integral Equation Method for Porous Media Flow, Allen and Unwin, London.

^[38] Bruch, E., and A. Lejeune. 1989.  An effective solution of the numerical problems at multi‐domain points for anisotropic Laplace problems, in Advances in Boundary Elements, vol. 2, Field and Flow Solutions, edited by C. A. Brebbia and J. J. Connor, pp. 3–14, Comput. Mech., Boston.