Analytic element method

Anaqsim is an analytic element software for simulating groundwater flow. It uses subdomains as described in Fitts (2010), which gives it strong capabilities with respect to heterogeneity and anisotropy. It also employs high-order line elements, spatially-variable area sinks, and finite-difference time steps to allow multi-level aquifer systems and wide-ranging transient flow simulations.

Anaqsim employs the analytic element method (AEM), which superposes analytic solutions to yield a composite solution consisting of equations for head and discharge as functions of location and time. The AEM is described in detail in books by Strack (1989) and Haitjema (1995). Shorter summaries of the method may be found in Fitts (2023) and Strack (2003).

How AEM differs from numerical methods

The AEM is fundamentally different than numerical methods like finite elements and finite differences, where the domain is broken into small blocks or elements and simple head distributions (e.g. linear) are assumed within these blocks or elements. In the AEM, boundaries of the domain are discretized, but the domain itself is not.

Anaqsim's subdomain approach

Anaqsim uses a variation of the AEM that divides the modeled region into subdomains, each with its own definition of aquifer parameters and its own separate AEM model (Fitts, 2010). The model for a given subdomain (called a domain in Anaqsim) includes contributions from elements inside and on the external boundary of the subdomain; elements beyond the subdomain do not contribute. Each subdomain model is written in terms of two-dimensional functions, but three-dimensional flow may be simulated using multiple levels in a model. In multi-level models, the resistance to vertical flow is accounted for in the vertical leakage between levels.

This subdomain approach allows for a high degree of flexibility with respect to a model's heterogeneity, anisotropy, and layering. For example, it is possible for a subdomain that is anisotropic to be adjacent to another subdomain that is isotropic or anisotropic with a different direction and ratio. The subdomain approach allows mixed layering schemes. For example, an area with multiple levels (subdomains stacked vertically and leaking vertically to each other) can abut an area with subdomains in just a single level. This allows the model to focus layering and computational effort in the area of interest, with a simpler single-level model for distant areas.

Transient simulation

Another key aspect of Anaqsim is that it allows complete transient simulation capabilities by using finite difference time steps as suggested by Haitjema and Strack (1985). The transient term in the flow equations is handled in essentially the same manner as it is in finite difference programs like MODFLOW.