Philosophical Transactions of the Royal Society A Mathematical Physical and Engineering Sciences · 2014 · 102 citations · 30 references
ComputingComputer ScienceComputational Fluid DynamicsMultiscale ModelingScientific ComputingMultiscale Fluid DynamicsMultiscale MechanicsError PropagationMulti-scale ModelingMultiscale Error EstimationNumerical Uncertainty PropagationOpen Questions
Multiscale modelling and simulation has achieved notable successes yet remains riddled with unresolved questions, partly because the field has largely developed within disciplinary silos. The paper calls for multidisciplinary research to reach consensus on the definition of multiscale modelling, develop a generic theory, address validation and verification, and study numerical error propagation. The authors propose a targeted multidisciplinary research agenda that includes defining multiscale modelling, developing a generic theory, validating and verifying models, and analyzing numerical error propagation. They argue that such research would establish more efficient, well‑defined multiscale computing environments and has substantial potential impact across scientific disciplines.
We argue that, despite the fact that the field of multiscale modelling and simulation has enjoyed significant success within the past decade, it still holds many open questions that are deemed important but so far have barely been explored. We believe that this is at least in part due to the fact that the field has been mainly developed within disciplinary silos. The principal topics that in our view would benefit from a targeted multidisciplinary research effort are related to reaching consensus as to what exactly one means by ‘multiscale modelling’, formulating a generic theory or calculus of multiscale modelling, applying such concepts to the urgent question of validation and verification of multiscale models, and the issue of numerical error propagation in multiscale models. Moreover, we believe that this would, in principle, also lay the foundation for more efficient, well-defined and usable multiscale computing environments. We believe that multidisciplinary research to fill in the gaps is timely, highly relevant, and with substantial potential impact on many scientific disciplines.
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