What's on the Menu? Finite Difference, Finite Element, or Finite Volume?

There have been significant advances in hardware and modeling software since numerical codes were introduced more than 20 years ago. However, for many modellers the approach to modeling remains the same: select the numerical method, build a grid/mesh, populate with parameters, run the simulation, and analyze results. If the results are invalid, adjust the inputs and repeat. With this approach, a modeller can quickly find themselves in a predicament: a numerical model that is unnecessarily complex or a model that reaches the limitations of the selected numerical method.

This approach to modeling has a fundamental flaw at the very beginning: which numerical method to use? This decision is typically based on available GUIs (licenses), the modeller’s expertise/comfort level with a specific code, or client/regulatory requirements. However, often the most appropriate simulator is not known until later stages of model development when limitations are reached. By this time, the effort involved in building a new model using a different simulator code can be significant.

One way to improve the acceptance of a model is to build and evaluate multiple numerical models: compare finite difference to finite element representations, compare various grid resolutions, compare variably-spaced grids to locally-refined grids. However, due to the time/effort required in building numerical models and constraints on budgets for modeling projects, this is not practical.

This paper presents a conceptual approach to modeling that facilitates building multiple numerical models for different simulators. With conceptual modeling, inputs are designed as 2D/3D objects independent of the simulator. The decision of what numerical method to use is delayed until later in the modeling workflow, allowing the modeller to generate several finite difference, finite element and finite volume models. With this approach, the modeller can identify vulnerabilities in each numerical method and reduce uncertainty of the assumptions/predictions as a whole.