Nicolas Vasset

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Optimal retrofit of district heating network to lower temperature levels

Energy

Solving the transport equation by the use of 6D spectral methods in spherical geometry

arXiv (Cornell University), Apr 28, 2011

We present a numerical method for handling the resolution of a general transport equation for rad... more We present a numerical method for handling the resolution of a general transport equation for radiative particles, aimed at physical problems with a doubly spherical geometry. Having in mind the computational time difficulties encountered in problems such as neutrino transport in astrophysical supernovae, we propose a scheme based on full spectral methods in 6d spherical coordinates. This approach, known to be suited when the characteristic length of the dynamics is much smaller than the domain size, has the potential advantage of a global speedup with respect to usual finite difference schemes. An analysis of the properties of the Liouville operator expressed in our coordinates is necessary in order to handle correctly the numerical behaviour of the solution. This reflects on a specific (spherical) geometry of the computational domain. The numerical tests, performed under several different regimes for the equation, prove the robustness of the scheme: their performances also point out to the suitability of such an approach to large scale computations involving transport physics for massless radiative particles. We wish to point out that the algorithm presented here, is particularly suitable to treat problems in which matter has high velocities, such as the neutrino transport in supernovae.

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Reduction of supply temperature in existing district heating: A review of strategies and implementations

Energy

Gestion optimale d'un système de production géothermique

HAL (Le Centre pour la Communication Scientifique Directe), Feb 23, 2022

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Formulation and assessment of multi-objective optimal sizing of district heating network

Energy

The efficiency of a District Heating (DH) network depends among other things on the quality of it... more The efficiency of a District Heating (DH) network depends among other things on the quality of its design and more precisely on the sizing of the distribution network pipes. Providing DH designers with relevant methodology to select appropriate pipes is crucial to maximize the utility of those systems. This paper presents a methodology focusing on the optimal sizing of pipe diameters in DH networks: the methodology uses a genetic algorithm to generate a set of Pareto-optimal sizing choices. An implementation of the methodology is presented, and is validated on three test cases, each of them corresponding to an elementary configuration, which can be encountered in real-world DH network. As a result, the performance of the results provided by the optimization for each test case are as good or better than the best reference solutions we could provide. The last part of this paper addresses the scalability of the proposed sizing methodology. The interest of the presented methodology is lies in the typology of optimal solutions provided for the test cases that could not be devised with traditional sizing methods and by the scalability of the method that makes it suitable for optimal sizing at city scale.

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Solving the transport equation by the use of 6D spectral methods in spherical coordinates

We present a numerical method for handling the resolution of a general transport equation for rad... more We present a numerical method for handling the resolution of a general transport equation for radiative particles, aime d at physical problems with a doubly spherical geometry. Having in mind the computational time diffi culties encountered in problems such as neutrino transport in astrophysical supernovae, we propose a scheme based on full spectral methods in 6d spherical coordinates. This approach, known to be suited when the characteristic length of the dynamics is much smaller than the domain size, has the potential advantage of a global speedup with respect to usual finite di fference schemes. An analysis of the properties of the Liouville operator expressed in our coordinates is necessary in order to handle correctly the numerical behaviour of the solution. This refl ects on a specific (spherical) geometry of the computational domain. The numerical tests, performed under several different regimes for the equation, prove the robustness of the scheme: their performances also poi...

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Validation of a multi-objective optimization framework for the sizing of pipes in DH Networks

Energy Reports, 2021

Sizing distribution equipment of a district heating (DH) network is a complex yet decisive proces... more Sizing distribution equipment of a district heating (DH) network is a complex yet decisive process to target techno-economic optimality for these systems. This paper describes and validates a framework that uses multi-objective optimization to support decisions regarding the sizing of a DH network. A genetic algorithm (NSGA2) is employed to generate optimal pipe diameters with respect to the operational and investment cost. This framework is then validated using an elementary toy problem consisting of a straight horizontal two-tube network, with a set of identical consumers equally distributed in the network and supplied by a unique heat source. We show that the framework, on the aforementioned problem, reaches very good convergence and diversity for the optimal solutions. This sizing method is then compared to typical local sizing method. We demonstrate a significant decrease of global cost by 40% by using DH network system simulation to take into account local interactions inside the DH system.

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Precise computations of dynamical black hole spacetimes using quasilocal horizon structures

Quelques aspects des horizons de trous noirs en relativité numérique

Http Www Theses Fr, 2009

Une approche de la modelisation numerique des espaces-temps de trous noirs, basee sur le formalis... more Une approche de la modelisation numerique des espaces-temps de trous noirs, basee sur le formalisme des horizons quasilocaux, est presentee. Le contexte est celui d'une formulation contrainte des equations (3+1) d'Einstein en jauge de Dirac generalisee, Apres avoir situe les aspects principaux du probleme, nous presentons un nouvel outil pour l'etude numerique d'equations tensorielles et vectorielles avec une contrainte de divergence nulle, utilisant des methodes spectrales. Cet outil s'applique directement aux champs tensoriels en jauge de Dirac. Nous presentons ensuite la theorie mathematique des trous noirs, avec un accent sur les differentes notions d'horizon. La theorie des horizons quasilocaux stationnaires et dynamiques de trous noirs est aussi developpee, Nous l'appliquons a l'etude numerique d'espaces-temps de trous noirs stationnaires en jauge de Dirac. Le cas d'un seul horizon isole permet de recuperer la solution globale de Kerr sans hypothese de symetrie supplementaire ou de restriction pour la geometrie conforme sur l'horizon, Le developpement d'outils numeriques pour l'etude geometrique d'un horizon permet une analyse physique precise des donnees obtenues. Nous appliquons aussi ces outils a l'etude d'inegalites geometriques pour les horizons, liees a l'inegalite de Penrose et a la censure cosmique. Nous presentons enfin les perspectives de cette approche dans le contexte d'un espace-temps totalement dynamique, permettant de modeliser numeriquement l'evolution temporelle des horizons de trous noirs, et pouvant s'appliquer a l'etude de l'effondrement critique de coeurs denses d'etoiles et la coalescence de binaires.

Application of initial data sequences to the study of Black Hole dynamical trapping horizons

AIP Conference Proceedings, 2009

Non-continuous "jumps" of Apparent Horizons occur generically in 3+1 (binary) black hole evolutio... more Non-continuous "jumps" of Apparent Horizons occur generically in 3+1 (binary) black hole evolutions. The dynamical trapping horizon framework suggests a spacetime picture in which these "Apparent Horizon jumps" are understood as spatial cuts of a single spacetime hypersurface foliated by (compact) marginally outer trapped surfaces. We present here some work in progress which makes use of uni-parametric sequences of (axisymmetric) binary black hole initial data for exploring the plausibility of this spacetime picture. The modelling of Einstein evolutions by sequences of initial data has proved to be a successful methodological tool in other settings for the understanding of certain qualitative features of evolutions in restricted physical regimes.

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Excision technique in constrained formulations of Einstein equations: collapse scenario

Journal of Physics: Conference Series, 2015

We present a new excision technique used in constrained formulations of Einstein equations to dea... more We present a new excision technique used in constrained formulations of Einstein equations to deal with black hole in numerical simulations. We show the applicability of this scheme in several scenarios. In particular, we present the dynamical evolution of the collapse of a neutron star to a black hole, using the CoCoNuT code and this excision technique.

Numerical study of stationary black holes: local horizon properties and the Kerr solution

This work focuses on a numerical implementation of the local physics of black hole astrophysical ... more This work focuses on a numerical implementation of the local physics of black hole astrophysical spacetimes. This is done by imposing boundary conditions on a certain formulation of Einstein Equations, namely the fully constrained formalism(FCF) of Bonazzola et al.(2004). We here make use of the Isolated Horizon formalism of Ashtekar et al. (1999), aiming at a local characterization of a black hole region. This horizon can be seen as an intuitive physical object (contrary to, e.g., the event horizon). We thus solve the Einstein Equations, using 3+1 formalism, on 3-slices of spacetime excised by marginally trapped surfaces. We are then able to recover the Kerr spacetime outside the black hole region only by prescribing that our grid boundary behaves indeed like an Isolated Horizon. Contrary to some earlier works, we take into account the non-conformal part of our 3-metric, making use of a no-boundary method on the horizon. Our spacetime is then perfectly stationary.We compare our res...

A numerical study of Penrose-like inequalities in a family of axially symmetric initial data

EAS Publications Series, 2008

Our current picture of black hole gravitational collapse relies on two assumptions: i) the result... more Our current picture of black hole gravitational collapse relies on two assumptions: i) the resulting singularity is hidden behind an event horizon-weak cosmic censorship conjecture-and ii) spacetime eventually settles down to a stationarity state. In this setting, it follows that the minimal area containing an apparent horizon is bound by the square of the total ADM mass (Penrose inequality conjecture). Following Dain et al. 2002, we construct numerically a family of axisymmetric initial data with one or several marginally trapped surfaces. Penrose and related geometric inequalities are discused for these data. As a by-product, it is shown how Penrose inequality can be used as a diagnosis for an apparent horizon finder numerical routine.

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Isolated Horizons in Numerical Relativity: Constructing the Excised Kerr Spacetime in Dirac Gauge

The Twelfth Marcel Grossmann Meeting - On Recent Developments in Theoretical and Experimental General Relativity Astrophysics and Relativistic Field Theories - Proceedings of the MG12 Meeting on General Relativity, 2012

Excision scheme for black holes in constrained evolution formulations: Spherically symmetric case

Physical Review D, 2014

Excision techniques are used in order to deal with black holes in numerical simulations of Einste... more Excision techniques are used in order to deal with black holes in numerical simulations of Einstein's equations and consist in removing a topological sphere containing the physical singularity from the numerical domain, applying instead appropriate boundary conditions at the excised surface. In this work we present recent developments of this technique in the case of constrained formulations of Einstein's equations and for spherically symmetric spacetimes. We present a new set of boundary conditions to apply to the elliptic system in the fully constrained formalism of Bonazzola et al. [Phys. Rev. D 70, 104007 (2004)], at an arbitrary coordinate sphere inside the apparent horizon. Analytical properties of this system of boundary conditions are studied and, under some assumptions, an exponential convergence toward the stationary solution is exhibited for the vacuum spacetime. This is verified in numerical examples, together with the applicability in the case of the accretion of a scalar field onto a Schwarzschild black hole. We also present the successful use of the excision technique in the collapse of a neutron star to a black hole, when excision is switched on during the simulation, after the formation of the apparent horizon. This allows the accretion of matter remaining outside the excision surface and for the stable long-term evolution of the newly formed black hole.

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Excised black hole spacetimes: Quasilocal horizon formalism applied to the Kerr example

Physical Review D, 2009

MAGNETOROTATIONALLY DRIVEN SUPERNOVAE AS THE ORIGIN OF EARLY GALAXY r -PROCESS ELEMENTS?

The Astrophysical Journal, 2012

We examine magnetorotationally driven supernovae as sources of r-process elements in the early Ga... more We examine magnetorotationally driven supernovae as sources of r-process elements in the early Galaxy. On the basis of thermodynamic histories of tracer particles from a three-dimensional magnetohydrodynamical core-collapse supernova model with approximated neutrino transport, we perform nucleosynthesis calculations with and without considering the effects of neutrino absorption reactions on the electron fraction (Y e) during post-processing. We find that the peak distribution of Y e in the ejecta is shifted from ∼ 0.15 to ∼ 0.17 and broadened toward higher Y e due to neutrino absorption. Nevertheless, in both cases the second and third peaks of the solar r-process element distribution can be well reproduced. The rare progenitor configuration that was used here, characterized by a high rotation rate and a large magnetic field necessary for the formation of bipolar jets, could naturally provide a site for the strong r-process in agreement with observations of the early galactic chemical evolution.

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A spectral method for the wave equation of divergence-free vectors and symmetric tensors inside a sphere

Journal of Computational Physics, 2010

The wave equation for vectors and symmetric tensors in spherical coordinates is studied under the... more The wave equation for vectors and symmetric tensors in spherical coordinates is studied under the divergence-free constraint. We describe a numerical method, based on the spectral decomposition of vector/tensor components onto spherical harmonics, that allows for the evolution of only those scalar fields which correspond to the divergence-free degrees of freedom of the vector/tensor. The full vector/tensor field is recovered at each time-step from these two (in the vector case), or three (symmetric tensor case) scalar fields, through the solution of a first-order system of ordinary differential equations (ODE) for each spherical harmonic. The correspondence with the poloidal-toroidal decomposition is shown for the vector case. Numerical tests are presented using an explicit Chebyshev-tau method for the radial coordinate.

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A mathematical description of the IDSA for supernova neutrino transport, its discretization and a comparison with a finite volume scheme for Boltzmann’s equation

ESAIM: Proceedings, 2012

In this paper we give an introduction to the Boltzmann equation for neutrino transport used in co... more In this paper we give an introduction to the Boltzmann equation for neutrino transport used in core collapse supernova models as well as a detailed mathematical description of the Isotropic Diffusion Source Approximation (IDSA) established in [6]. Furthermore, we present a numerical treatment of a reduced Boltzmann model problem based on time splitting and finite volumes and revise the discretization of the IDSA in [6] for this problem. Discretization error studies carried out on the reduced Boltzmann model problem and on the IDSA show that the errors are of order one in both cases. By a numerical example, a detailed comparison of the reduced model and the IDSA is carried out and interpreted. For this example the IDSA modeling error with respect to the reduced Boltzmann model is numerically determined and localized. Résumé. Dans cet article, nous donnons une introductionà l'équation de Boltzmann pour le transport des neutrinos dans les modèles de supernovaeà effondrement de coeur ainsi qu'une description détaillée de l'Isotropic Diffusion Source Approximation (IDSA) développée dans [6]. De plus, nous présentons le traitement numérique d'un modèle de Boltzmann simplifié basé sur une décomposition en temps de l'opérateur et sur un algorithme de volumes finis ainsi que l'adaptation de la discrétisation de l'IDSA de [6]à notre modèle. Lesétudes de l'erreur de discrétisation faites sur le modèle de Boltzmann simplifié et sur l'IDSA montrent que les erreurs sont d'ordre un dans les deux cas. A l'aide d'un exemple numérique, nous comparons et interprétons en détail les deux modèles. Pour cet exemple, l'erreur de modélisation de l'IDSA par rapport au modèle de Boltzmann simplifié est déterminée numériquement et localisée.

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Nicolas Vasset

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