CFD is the combined use of partial differential equations, numerical methods and computing sciences. It allows for solving complex systems in three or two spatial dimensions and time with the highest accuracy.
The computing cost of a CFD simulation is usually high, so it cannot be directly used for real-time monitoring purposes.
ODEs capture the temporal changes of a system, assuming its spatial homogeneity. It allows for understanding the dynamic evolution of several compounds or species that take part in a (bio)chemical process.
The computing cost of an ODE system is not high, so it can be directly used for real-time monitoring purposes.
This approach involves techniques searching for correlations within a data set, without considering the underlying fundamental principles that govern the specific process.
It allows a large amount of data from different categories of systems that are otherwise difficult to model to be processed.
Hybrid modeling comprehensively combines CFD, EDO and Machine Learning techniques. In this approach, mechanistic models (CFD/EDO) generate volumes of high-quality data to calibrate and validate Machine Learning models, ensuring their robustness and reliability. Additionally, we develop simplified ODE-based models optimized for real-time execution.
These are fed by detailed CFD simulations, which, due to their high computational demand, are processed asynchronously. This architecture allows us to offer precise and agile solutions for the supervision and control of industrial processes.
At Modela, our modeling workflows are built on field-tested mathematical and numerical tools, with a strong preference for open-source frameworks like OpenFOAM. Leveraging open-source software allows us to deliver high-performance, fully customized simulations while redirecting financial resources toward top-tier computing infrastructure—dramatically reducing simulation times and overall project costs. However, we remain software-agnostic in principle; while our experience proves that open-source tools can successfully handle complex geometry, meshing, and solver demands, we seamlessly adapt to and integrate commercial software whenever specific project requirements or client workflows dictate it.
