In chemical, metallurgical, aerospace, and nuclear industries, we may find very complex processes that need understanding, are short of detailed observations and need sufficiently accurate prediction tools. In most cases, we must deal with a hierarchy of levels. Here we may find complex interactions between levels and scales in time and space. This type of challenge is called multi-scale or multi-level, and where there is a need for models which give fast enough responses to be useful in operation, operator training, troubleshooting, and sometimes design of new or improved processes. Useful simulation tools should support process control and act as a digital twin. The range of methods and sub-scale tools range from quantum mechanics to computational fluids and solid mechanics and techniques for model optimization based on available measurement data (e.g. extended Kalman filter).

For this Research Topic, we are looking for updates on recent advances, but also contributions that demonstrate the capability of multi-scale or multi-level physics-based models that are assembled to replicate a process or a part of a process. The final approaches should be capable of fast predictions, based on fast models or look-up tables where that is feasible. It is interesting to learn about the strategy to develop such a model and the underlying concepts, and how the presented approach can represent actual data. We want to see included demonstrations of the use of fundamental physics-based methods, and how these, together with empirical data, are merged into working models. Reduced order methods and singular value decomposition are examples of possible toolbox elements.

Specific papers on derivation and /or validation of multiphase modelling techniques (volume averaging, ensemble phase averaging, ensemble averaging) are welcome. Putting this in the larger context presented above is preferred. It is of interest to see discussions on the limits of physics-based approaches and how the exploitation of data can be used to develop better models.

We welcome the submission of Original Research, Review, Mini Review, and Perspective articles on themes including, but not limited to:

• Application to processes involving reactive single-phase or multiphase systems

• Pragmatism-based approaches to arrive at fast models that can be used in control applications

• Multi-level and multi-scale modelling approaches

• Novel methods to produce efficient high-level models of complex multi-level and multi-scale systems

• Use of pre-simulated data to support higher-level models

• Exploitation of empirical data in physics-based models

In all these cases the work must be related to a process industry challenge, and it must be explained how the work supports a faster, more accurate, or more robust and reliable model. New approaches that allow modelling of processes that previously could not be modelled are of special interest.

Other challenges to arrive at sufficiently accurate high-level models should be addressed.

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Frontiers in Chemical Engineering

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