Scientific Computation and Applied & Industrial Mathematics: David Moulton

Modeling and simulation are playing an increasingly critical role in understanding and predicting climate impacts and feedbacks in terrestrial systems. Managing the complexity of these process-rich integrated hydrologic and biogeochemical models requires flexible software designs that enable exploration of model features and model coupling. In addition, flexibility in meshing and robust discretization techniques are required to capture topographic features, such as hill slopes and rivers, and subsurface stratigraphy.

In this talk we highlight a flexible and extensible approach to multiphysics frameworks for these applications that specifies interfaces for coupled processes and automates weak and strong coupling strategies to manage this complexity. Process management is accomplished through a dual view of the model system: a high-level view ideal for model configuration represents the system of equations as a tree, where individual equations are associated with leaf nodes, and coupling strategies with internal nodes; and a low-level dynamically generated dependency graph that connects a variable to its dependencies, streamlining and automating model evaluation, easing model development, and ensuring models are modular and flexible. We use this multiphysics framework, dubbed Arcos, to support both model and algorithm development for environmental applications in the open-source code Amanzi. For example, we have developed infrastructure for general unstructured polyhedral meshing with a flexible operator-based implementation of the Mimetic Finite Difference method, and used it to simulate coupled surface/subsurface flow. Here we use a diffusive wave approximation for surface flow, and a Richards equation for subsurface flow. Coupling is accomplished by ensuring continuity of both pressure and fluxes from the surface to the subsurface, and the system can be solved using either sequential or implicit coupling. We show results for several benchmark problems, as well as physically relevant, large-scale simulation of rainfall on arctic tundra based upon LIDAR data from Barrow, Alaska. This demonstration shows the parallel performance of the code and its feasibility for use in watershed scale, high resolution simulations.