In the close proximity of the liquid-vapour saturation curve and critical point, well-known thermodynamic phenomena including large compressibility and critical point effects results in very unusual fluid dynamics features, including non-ideal or rarefaction shock waves, mixed and split waves. This unconventional behaviour, which cannot occur in the ideal flow of dilute gases, is referred to as Non-Ideal Compressible-Fluid Dynamics or NICFD. The focus of this short lecture is to review the theoretical background of NICFD and to discuss the impact of highly non-ideal conditions on the design and properties of numerical schemes for compressible flows. Exemplary flow fields will be presented and compared to available experimental data from the Test-Rig for Organic VApours (TROVA) of Politecnico di Milano, a unique facility in which supersonic flows in non-ideal conditions can be measured and observed. The present results are obtained within the framework of the ERC Consolidator Grant NSHOCK, of which the presenter is the PI.
contact:nicola.parolini@polimi.it
Prof. Alberto Guardone's research interests include the theoretical, numerical and experimental investigation of non-ideal compressible-fluid dynamics (NICFD). In particular, he is interested in the observation of so-called non-classical gas dynamics wave-fields in the vapour phase of complex organic compounds and in the near-critical region of pure, common substances. He is the coordinator of the Laboratory of Compressible-fluid dynamics for Renewable Energy Applications (CREA, crealab.polimi.it). He is the recipient of a ERC Consolidator Grant 2013, aimed at performing unique measurements of NCIFD flows in the Test-Rig for Organic Vapours (TROVA) facility in Milano. He is contributing as co-PI to two Marie Sk?odowska-Curie networks, the Joint European Doctorate NITROS (nitros-edj.eu) and the Training Network UTOPIAE (utopia.eu), in the field of in-flight icing prediction.
In un fluido, in assenza di un appoggio solido, la propulsione si ottiene accelerando del fluido in direzione opposta. Questo è quanto fanno le eliche, sia navali sia aeronautiche, che accelerano il fluido nel quale sono immerse. Anche i motori a reazione eiettano soprattutto aria dell'atmosfera. Per i viaggi spaziali, il movimento nel vuoto non subisce resistenze, ma richiede l'utilizzo dei razzi, che devono avere a bordo tutto il fluido che eietteranno. Questo pone dei requisiti molto stringenti alla realizzabilità dei voli, requisiti che vengono analizzati in qualche dettaglio, e che fanno sì che per l'accesso ai pianeti esterni venga utilizzato anche un altro meccanismo, la cosiddetta 'fionda gravitazionale'.
Prof. Alberto Guardone's research interests include the theoretical, numerical and experimental investigation of non-ideal compressible-fluid dynamics (NICFD). In particular, he is interested in the observation of so-called non-classical gas dynamics wave-fields in the vapour phase of complex organic compounds and in the near-critical region of pure, common substances. He is the coordinator of the Laboratory of Compressible-fluid dynamics for Renewable Energy Applications (CREA, crealab.polimi.it). He is the recipient of a ERC Consolidator Grant 2013, aimed at performing unique measurements of NCIFD flows in the Test-Rig for Organic Vapours (TROVA) facility in Milano. He is contributing as co-PI to two Marie Sk?odowska-Curie networks, the Joint European Doctorate NITROS (nitros-edj.eu) and the Training Network UTOPIAE (utopia.eu), in the field of in-flight icing prediction.
In un fluido, in assenza di un appoggio solido, la propulsione si ottiene accelerando del fluido in direzione opposta. Questo è quanto fanno le eliche, sia navali sia aeronautiche, che accelerano il fluido nel quale sono immerse. Anche i motori a reazione eiettano soprattutto aria dell'atmosfera. Per i viaggi spaziali, il movimento nel vuoto non subisce resistenze, ma richiede l'utilizzo dei razzi, che devono avere a bordo tutto il fluido che eietteranno. Questo pone dei requisiti molto stringenti alla realizzabilità dei voli, requisiti che vengono analizzati in qualche dettaglio, e che fanno sì che per l'accesso ai pianeti esterni venga utilizzato anche un altro meccanismo, la cosiddetta 'fionda gravitazionale'.
Prof. Alberto Guardone's research interests include the theoretical, numerical and experimental investigation of non-ideal compressible-fluid dynamics (NICFD). In particular, he is interested in the observation of so-called non-classical gas dynamics wave-fields in the vapour phase of complex organic compounds and in the near-critical region of pure, common substances. He is the coordinator of the Laboratory of Compressible-fluid dynamics for Renewable Energy Applications (CREA, crealab.polimi.it). He is the recipient of a ERC Consolidator Grant 2013, aimed at performing unique measurements of NCIFD flows in the Test-Rig for Organic Vapours (TROVA) facility in Milano. He is contributing as co-PI to two Marie Sk?odowska-Curie networks, the Joint European Doctorate NITROS (nitros-edj.eu) and the Training Network UTOPIAE (utopia.eu), in the field of in-flight icing prediction.
The subsurface is being increasingly utilised both as a resource and as an energy and waste repository. Historically, there have been few issues of concern related to competition between resources, with groundwater contamination being a notable exception. However, with increasing exploitation, resource conflicts are becoming increasingly common and complex. Current issues in this regard include, for example, the long-range impact of mechanical, chemical and thermal energy storage on groundwater resources, and the complex effects surrounding hydraulic fracturing in both geothermal and shale gas production.
To analyse and predict the mutual influence of subsurface projects and their impact on groundwater reservoirs, advanced numerical models are necessary. In general, these subsurface systems include processes of varying complexity occurring in different parts of the domain of interest. These processes mostly take place on different spatial and temporal scales. It is extremely challenging to model such systems in an adequate way, accounting for the spatially varying and scale-dependent character of these processes.
In this seminar, we will give an overview of possible utilisation conflicts in subsurface systems and of how the groundwater is affected and review several model coupling concepts with a focus on the lecturer’s work in this field. The concepts are divided into temporal and spatial coupling concepts, where the latter are sub-divided into multi-process, multi-scale, multi-dimensional, and multi-compartment coupling strategies. We will present a large-scale simulation showing the general applicability of the modelling concepts of such complicated natural systems, especially the impact on the groundwater of simultaneously using geothermal energy and storing chemical and thermal energy. At the same time, we will show that such real large-scale systems provide a good environment for balancing the efficiency potential and possible weaknesses of the approaches discussed.
Contact: anna.scotti@polimi.it
Prof. Helmig is head of the Department of Hydromechanics and Modelling of Hydrosystems at the University of Stuttgart. In 1995, he was awarded the renowned “Dresdner Grundwasserforschungspreis” for his doctoral thesis on “Theory and numerics of multiphase flow through fractured porous media”. He was co-founder and, from 2009 to 2011, President of the International Society for Porous Media “InterPore”; he is spokesman of the International Research Training Group “NUPUS – Nonlinearities and upscaling in porous media” with partner universities in Delft, Utrecht, Eindhoven, Wageningen and Bergen, and he is a member of the Executive Board of Directors of the Cluster of Excellence Simulation Technology at the University of Stuttgart. He is on the editorial boards of a number of journals and has been selected as Darcy Lecturer 2015 by the US National Ground Water Association.
The well-known hidden Markov model (HMM) is a two-dimensional stochastic process (X,Y), where Y is a Markov chain and conditionally on Y, the X-process consists of independent random variables, the distribution of the random variable X_t depending on Y_t, only. Over the last decades, HMM's have become very popular stochastic models with applications to speech recognition, signal processing, linguistic, computational molecular biology and so on. Often the Y-process is unobserved (hidden) and the goal of the inference is to estimate its unobserved realization based on a realization of X-process. This task is called the segmentation problem and the standard ways to solve it is to use either maximum likelihood (so-called Viterbi) path or pointwise maximum likelihood (so-called PMAP) path.
A trivial but important property of HMM is that the process Z=(X,Y) is itself a Markov process with a product state space. This observation allows naturally enlarge the class of HMM's to the class of pairwise Markov models (PMM) as follows: Z=(X,Y) is a PMM if Z has Markov property. Now it is clear that PMM's are a much larger class of models whose HMM's is just a little subclass. We briefly discuss several PMM's like Markov switching models and HMM's with dependent noise. It is important to note that if (X,Y) is a Markov process, then neither X nor Y need to have Markov property, but conditionally on X, the Y-process is Markov and vice versa.
It turns out that many good properties of HMM's are mainly due to the Markov property of Z and hence these properties carry on to PMM's as well. In particular the well-known Viterbi and forward-backward algorithms apply and so standard segmentation approaches can be applied in the case of PMM's. Moreover, PMM-models provide a rather flexible and realistic model for the homology of random sequences. A triplet Markov model (TMM), introduced by W. Pieczynski, is a three-dimensional Markov process (X,Y,U), where, as previously, X stands for observations and Y is the hidden state sequence of interest. But in addition, there is another hidden component U. Since conditionally on U, the pair (X,Y) is an inhomogeneous PMM, the U-component models now the change of environment. It turns out that adding the U-component makes the model really flexible.
We give a general approach to the risk-based segmentation problem that also applies for PMM's and TMM's, discuss the weaknesses standard approaches and introduce a way to overcome these problems. We also discuss the asymptotics of Viterbi segmentation for PMM's.
Prof. Helmig is head of the Department of Hydromechanics and Modelling of Hydrosystems at the University of Stuttgart. In 1995, he was awarded the renowned “Dresdner Grundwasserforschungspreis” for his doctoral thesis on “Theory and numerics of multiphase flow through fractured porous media”. He was co-founder and, from 2009 to 2011, President of the International Society for Porous Media “InterPore”; he is spokesman of the International Research Training Group “NUPUS – Nonlinearities and upscaling in porous media” with partner universities in Delft, Utrecht, Eindhoven, Wageningen and Bergen, and he is a member of the Executive Board of Directors of the Cluster of Excellence Simulation Technology at the University of Stuttgart. He is on the editorial boards of a number of journals and has been selected as Darcy Lecturer 2015 by the US National Ground Water Association.
In the talk we deal with the so-called mean field planning problem: a coupled system of two PDEs, a forward continuity equation and a backward Hamilton-Jacobi equation. This problem has been introduced by P-L. Lions in a series of lectures held at Collège de France and can be viewed as a modification of the mean field games system as well as a generalization of the optimal transportation problem in its dynamic formulation à la Benamou-Brenier. We concentrate on the variational structure of the problem, from which a notion of "weak variational" solution can be given. In particular, we provide a well-posedness result for the system on the whole space in a $L^p$ framework under general assumptions on the coupling term.
The talk is based on a joint work with G. Savaré and A. Porretta.
Prof. Helmig is head of the Department of Hydromechanics and Modelling of Hydrosystems at the University of Stuttgart. In 1995, he was awarded the renowned “Dresdner Grundwasserforschungspreis” for his doctoral thesis on “Theory and numerics of multiphase flow through fractured porous media”. He was co-founder and, from 2009 to 2011, President of the International Society for Porous Media “InterPore”; he is spokesman of the International Research Training Group “NUPUS – Nonlinearities and upscaling in porous media” with partner universities in Delft, Utrecht, Eindhoven, Wageningen and Bergen, and he is a member of the Executive Board of Directors of the Cluster of Excellence Simulation Technology at the University of Stuttgart. He is on the editorial boards of a number of journals and has been selected as Darcy Lecturer 2015 by the US National Ground Water Association.
In the talk we deal with the so-called mean field planning problem: a coupled system of two PDEs, a forward continuity equation and a backward Hamilton-Jacobi equation. This problem has been introduced by P-L. Lions in a series of lectures held at Collège de France and can be viewed as a modification of the mean field games system as well as a generalization of the optimal transportation problem in its dynamic formulation à la Benamou-Brenier. We concentrate on the variational structure of the problem, from which a notion of "weak variational" solution can be given. In particular, we provide a well-posedness result for the system on the whole space in a $L^p$ framework under general assumptions on the coupling term.
The talk is based on a joint work with G. Savaré and A. Porretta.
Prof. Helmig is head of the Department of Hydromechanics and Modelling of Hydrosystems at the University of Stuttgart. In 1995, he was awarded the renowned “Dresdner Grundwasserforschungspreis” for his doctoral thesis on “Theory and numerics of multiphase flow through fractured porous media”. He was co-founder and, from 2009 to 2011, President of the International Society for Porous Media “InterPore”; he is spokesman of the International Research Training Group “NUPUS – Nonlinearities and upscaling in porous media” with partner universities in Delft, Utrecht, Eindhoven, Wageningen and Bergen, and he is a member of the Executive Board of Directors of the Cluster of Excellence Simulation Technology at the University of Stuttgart. He is on the editorial boards of a number of journals and has been selected as Darcy Lecturer 2015 by the US National Ground Water Association.
In the talk we deal with the so-called mean field planning problem: a coupled system of two PDEs, a forward continuity equation and a backward Hamilton-Jacobi equation. This problem has been introduced by P-L. Lions in a series of lectures held at Collège de France and can be viewed as a modification of the mean field games system as well as a generalization of the optimal transportation problem in its dynamic formulation à la Benamou-Brenier. We concentrate on the variational structure of the problem, from which a notion of "weak variational" solution can be given. In particular, we provide a well-posedness result for the system on the whole space in a $L^p$ framework under general assumptions on the coupling term.
The talk is based on a joint work with G. Savaré and A. Porretta.
Prof. Helmig is head of the Department of Hydromechanics and Modelling of Hydrosystems at the University of Stuttgart. In 1995, he was awarded the renowned “Dresdner Grundwasserforschungspreis” for his doctoral thesis on “Theory and numerics of multiphase flow through fractured porous media”. He was co-founder and, from 2009 to 2011, President of the International Society for Porous Media “InterPore”; he is spokesman of the International Research Training Group “NUPUS – Nonlinearities and upscaling in porous media” with partner universities in Delft, Utrecht, Eindhoven, Wageningen and Bergen, and he is a member of the Executive Board of Directors of the Cluster of Excellence Simulation Technology at the University of Stuttgart. He is on the editorial boards of a number of journals and has been selected as Darcy Lecturer 2015 by the US National Ground Water Association.
Numerical meshes are essential components for forecasting the physical behavior of subsurface domains. Structured grids are often used for this purpose, but they lack flexibility to accurately represent complex subsurface geometry and to provide local level of detail in heterogeneous media. Unstructured meshes can, in principle, address these two gaps. In spite of much progress, challenges still exist to easily create unstructured meshes whose features are compatible with geological heterogeneities, with the physics to be simulated and with the selected numerical method. In this talk, I will review some recent and ongoing work RING to address these problems and discuss some of the remaining challenges. I will also highlight some features of the RINGMesh library, which is as a platform to address mesh-related problems.
Contact: luca.formaggia@polimi.it
Prof. Helmig is head of the Department of Hydromechanics and Modelling of Hydrosystems at the University of Stuttgart. In 1995, he was awarded the renowned “Dresdner Grundwasserforschungspreis” for his doctoral thesis on “Theory and numerics of multiphase flow through fractured porous media”. He was co-founder and, from 2009 to 2011, President of the International Society for Porous Media “InterPore”; he is spokesman of the International Research Training Group “NUPUS – Nonlinearities and upscaling in porous media” with partner universities in Delft, Utrecht, Eindhoven, Wageningen and Bergen, and he is a member of the Executive Board of Directors of the Cluster of Excellence Simulation Technology at the University of Stuttgart. He is on the editorial boards of a number of journals and has been selected as Darcy Lecturer 2015 by the US National Ground Water Association.
Seminari Matematici al
Politecnico di Milano
- Analisi
- Cultura Matematica
- Seminari FDS
- Geometria e Algebra
- Probabilità e Statistica Matematica
- Probabilità Quantistica