In the past decades computing power has made possible simulations of unprecedented sophistication and detail, and allowed the resolution of coupled phenomena that occur on many different spatial and temporal scales. Paradoxically, as computational power increases, we become aware of finer scale effects and the consequent limits of our physical models. Moreover, we are more sensitive to the propagation of errors and uncertainties. Therefore, in spite of vastly expanded limits on computational power, we will continue into the foreseeable future to be thwarted in our efforts to understand the most complex coupled Multiphysics and multiscale phenomena. To this end, mathematical and computational modeling will remain a key enabling technology that must be developed and exploited.
A primary challenge in the modeling of complex systems is to determine the scale, accuracy, and model complexity that are necessary to achieve acceptable predictive capabilities, and to reflect these requirements in a stable, efficient computational framework. In this workshop we will discuss these problems on several interrelated topics:
- Physics-preserving discretizations leading to numerical models that preserve basic physical principles, such as conservation, on and across appropriate scales.
- Multiscale modeling techniques for handling multiscale systems in both time and space and provide high-fidelity and fine-scale detail by either describing the system by a macromodel based on theoretical or numerical upscaling from a physically correct, but overly detailed model; or by incorporating into the numerical model a reduced physics, coarse-grain approximation.
- Multiphysics couplings of phenomena occurring on multiple temporal and spatial scales. Some algorithms that combine existing codes through software often fail to adequately address the coupling physics as one code may violate basic physical principles assumed to hold by the other code, and other algorithms suffer from issues related to disparate temporal and/or spatial scales between coupled physical processes
- Approximation of continuum and discrete models. Continuum systems may contain discrete components, such as a well or fault in a porous geological formation; and on fine scales, some systems are naturally discrete, such as interacting molecules or biological cells. These systems require special techniques such as microstructure models and network and other techniques for their simulation.
- Additional topics will include estimational and control of errors and mesh generation.
This workshop will include a poster session; a request for posters will be sent to registered participants in advance of the workshop.