Multi-X modeling is essential for predicting flow, material-, and system-inherent effects in our Visionary Examples of Engineered Geosystems, the Digital Human Model, and Next-Generation Virtual Materials Design. It encompasses modeling spatial and temporal scales of several orders (multiscale), a wide variety of coupled physical phenomena, fluids, and materials (multiphysics), and different modeling approaches (multimodel). In addition, we have to cope with heterogeneous data fidelity (multidata), and we are challenged by widely different demands on, e.g., output dimensionality and response (multicontext). To advance environmental engineering will require coupling processes from the molecular scale to field scale. Predictive multi-X models require bridging of length and time scales that are characteristic, for example, of cellular processes and biomechanical systems. Especially challenging will be
- controlling interactions not only on mesoscopic ranges but also of physics-based mechanisms on the microscopic scale;
- adaptively integrating different scales, physical processes, and data; and,
- linking particle models and experimental data to the continuum scale.
Coming to grips with these challenges will require new discretization and solution techniques, validation, benchmarking, a posteriori error estimation as well as novel modeling and homogenization approaches.