Recent advances in numerical methods for micro and macro models in fluid dynamics

April 5, 2017 to April 7, 2017


  • Maurizio Falcone (Università di Roma "La Sapienza", Italy)
  • Giovanni Ciccotti (University of Rome La Sapienza, Italy)
  • Simona Perotto (Politecnico di Milano, Italy)
  • Gianluigi Rozza (SISSA, Trieste, Italy)




Linked to the incredible increase of computer speed calculation, scientific computation may be decisive enough to define the border between complex problems that can be treated and those which, on the contrary, cannot. The aim of scientific computation is the development of versatile and reliable models, detailed in closed form, and tested on a wide range of test cases, either analogical or experimental, which there are helpful reference solutions for. 
A mathematical model must simulate universal concepts, such as, for instance, the conservation of mass or the momentum of a fluid, or the moment of inertia of a structure; moreover, in order to obtain a successful numerical simulation, it is necessary to define which level of detail must be introduced in the different parts of a model, and which simplifications must be carried out to facilitate its integration into different models.
Models able to simulate very complex problems should take into account uncertainty due to the lack (or uncertainty) of data (or data affected by noise)  which feed the model itself. The risk analysis, which arises from uncertainty and exposition to “defeat” (i.e. profit reduction, environmental damage, health damage, and so on) is another feature that a good model should have.
These kind of models are used to foresee natural, biological and environmental processes, in order to better understand how complex phenomena work, and also to contribute to the design of innovative products and technologies.
 An important aspect of scientific computation is represented by computational fluid dynamics (CFD), a discipline which aims to solve by computers problems governed by fluids.
In aerospace, for example, CFD can be applied in many ways. Numerical models based on potential flow equations or on the more sophisticated Euler or Navier-Stokes equations can be used, for example, in the aerodynamic analysis of wing tips or for the whole fuselage for performance optimization. 
Simulation implies validation and optimization, with the aim of designing aircrafts able to meet certain requirements: better structural reliability, better aerodynamic performance, lower environmental impact thanks to the reduction in noise emissions (in the case of commercial airplanes), speed optimization, and improvement of manoeuvrability (in the case of military aircrafts).
The solution to these problems requires multi-objective optimization algorithms: deterministic, stochastic or genetic. Moreover, models of electromagnetic diffusion are used to simulate external electromagnetic fields in order to refrain them from interfering with those generated by the several electronic circuits that are contained in the instrumentation on board. Models are used to simulate the stresses and the deformation of some parts of the aircraft (for the simulation of the analysis of materials strain), through algorithms for the interaction between fluid and structure with the aim of improving structural and dynamic stability.
Similar analyses are studied in the car industry, where numerical simulation is used virtually in every aspect of design and car production. Models are used to simulate internal engine combustion in order to save fuel, improve the quality of emissions, and reduce noise. Moreover, to improve performance, security and comfort, several kind of equations must be solved, such as those modeling external and internal fluid dynamics, aero-elasticity, aero-acoustic vibration dynamics, but also those governing thermal exchange, combustion processes, shock waves (occurring during the opening phase of an air bag), structural dynamics under large stresses and large deformations to simulate the consequences of car crashes.
The chemical industry uses mathematical models to simulate polymerization processes, pressing or extrusion for complex rheologic materials, where the typical macro analysis of continuum mechanics must be connected to the micro one, the latter being more adequate to describe the complex rheology of materials with nanostructure. This requires the development of multiscale analysis techniques and algorithms, which are able to describe the exchange of mechanical, thermal and chemical processes in heterogeneous spatial scales.
As a result of the appreciation of the importance of nanoscale phenomena for current and future technologies, there has been a growing interest in using molecular simulation methods as a primary tool to describe them. In our view, these methods comprise anything between electronic structure calculations of the properties of nanostructures and particle-based mesoscale simulations of complex fluids. Their use has expanded considerably over the last twenty years, from a relatively small community of chemists and physicists, to molecular biology, and more recently to many engineering disciplines -- chemical, materials, biomedical, mechanical, civil and electronic engineering. In some of these areas, its importance is now comparable to continuum mechanics simulations of liquids and solids. Indeed, one of the current challenges in the field is that of interfacing and bridging the scales of molecular and continuum mechanics simulations, and many researchers with an engineering background are at the forefront in this pursuit. This workshop will stimulate  a greater involvement of applied mathematicians and engineering scientists in the development and application of molecular simulation methods to the solution of large-scale, real-world problems.

The aim of this workshop is to build a bridge between the micro and the macro scientific communities. The International conference FEF 2017 conference hosted in Rome at Università La Sapienza has a long tradition and focuses on several  topics related with advanced numerical methods for flows problems, not limited to finite element, but including spectral methods, finite volume, as well as techniques for granular flows, porous media. All the minisymposia and special sessions organised at FEF are related with fluids problems solved with a macroscopic approach and several applications of computational fluid dynamics and related problems such as fluid-structure interactions, naval or aeronautical applications, as well as turbo machinery, just to cite few topics have special sessions at FEF 2017.
Micro approaches are less spread in FEF community with respect to the macro ones, they more related with classical computational mechanics. So the goal of this workshop is to present recent advances in both areas, offering an up-dated picture of advantages and disadvantages of the two approaches. We hope that the workshop and the discussion will stimulate contacts and research in collaboration between the researchers of the two communities.


1. C. Hirsch, Numerical Computation of Internal and External Flows, The Fundamentals of Computational Fluid Dynamics, Butterworth-Heinemann, 2007
2. D. Calvetti, E. Somersalo, Computational Mathematical Modeling, SIAM, 2013
3. R.J. Leveque, Finite-volume methods for hyperbolic problems, Cambridge University Press, 2002
4. M.P. Allen, D.J. Tildesley, Computer simulation of Liquids, Oxford Science Publications, 1989
5. D. Frenkel and B. Smit, Understanding molecular simulation (2nd edition), Academic Press, 2002
6. E. Toro, Riemann solvers and numerical methods for fluid dynamics, Springer, 1997