Mixed Dimensional Modeling with Overlapping Continua on Cartesian Grids for Complex Applications

We outline a strategy for prototyping computational models for complex applications on domains with disparate volumes. Instead of mixed dimensional approaches, we exploit the idea of overlapping continua and Cartesian grids. This strategy allows to build prototypes and explore model sensitivities in a robust simulation framework. As specific examples we consider thermal conduction in human tissue and hypothermia, Richards-Darcy coupled system for soil-root flow, and mixed use traffic simulation on and off paved paths in urban environment.