Publications related to Positive Solutions of Transport Equations and Classical Nonuniqueness of Characteristic curves

Anomalous dissipation and other non-smooth phenomena in fluids

The thesis is dedicated to the study of two main partial differential equations (PDEs) in fluid dynamics: the Navier-Stokes equations, which describe the motion of incompressible fluids, and the transport equation with divergence-free velocity fields, whic ...

EPFL2024

Mean-field transport equations and energy theorem for plasma edge turbulent transport

Reinart Andreas J. Coosemans

This paper establishes a mean-field equation set and an energy theorem to provide a theoretical basis in view of the development of self-consistent, physics-based turbulent transport models for mean-field transport codes. A rigorous averaging procedure ide ...

Cambridge University Press2024

A cut-cell method for the numerical simulation of 3D multiphase flows with strong interfacial effects

Alexandre Caboussat, Alexandre Masserey, Marco Picasso, Julien Hess

We present a numerical model for the approximation of multiphase flows with free surfaces and strong interfacial effects. The model relies on the multiphase incompressible Navier-Stokes equations, and includes surface tension effects on the interfaces betw ...

Academic Press Inc Elsevier Science2024

ALMOST EVERYWHERE NONUNIQUENESS OF INTEGRAL CURVES FOR DIVERGENCE-FREE SOBOLEV VECTOR FIELDS

Massimo Sorella

We construct divergence-free Sobolev vector fields in C([0,1];W-1,W-r(T-d;Rd)) with r < d and d\geq 2 which simultaneously admit any finite number of distinct positive solutions to the continuity equation. These vector fields are then shown to have at leas ...

Siam Publications2023

LDP and CLT for SPDEs with transport noise

Lucio Galeati

In this work we consider solutions to stochastic partial differential equations with transport noise, which are known to converge, in a suitable scaling limit, to solution of the corresponding deterministic PDE with an additional viscosity term. Large devi ...

SPRINGER2023

Investigation of the Time Resolution Set Up Used to Compute the Full Load Vortex Rope in a Francis Turbine

François Avellan, Andres Müller, Cécile Münch-Alligné, Arthur Tristan Favrel

The flow in a Francis turbine at full load is characterised by the development of an axial vortex rope in the draft tube. The vortex rope often promotes cavitation if the turbine is operated at a sufficiently low Thoma number. Furthermore, the vortex rope ...

2021

Direct numerical simulation of phase change in the presence of non-condensable gases

Lubomír Bures, Yohei Sato

This paper describes a new numerical method for the simulation of phase change phenomena between a liquid and a vapour in the presence of non-condensable gases. The method is based on an interface-tracking approach in the framework of single-fluid modellin ...

2020

Generalization of Fourier’s Law into Viscous Heat Equations

Nicola Marzari, Andrea Cepellotti, Michele Simoncelli

Heat conduction in dielectric crystals originates from the dynamics of atomic vibrations, whose evolution is well described by the linearized Boltzmann transport equation for the phonon populations. Recently, it was shown that thermal conductivity can be r ...

American Physical Society2020

Continuously-fed density currents over impermeable and porous substrates

Sara Venuleo

Gravity currents are buoyancy-driven flows having a significant impact on the environment and human life. They can be observed in a vast range of natural and anthropogenic scenarios, such as seawater and freshwater, the atmosphere, or industrial processes. ...

EPFL2020

An adaptive algorithm for the transport equation with time dependent velocity

Marco Picasso, Samuel Dubuis

An a posteriori error estimate is derived for the approximation of the transport equation with a time dependent transport velocity. Continuous, piecewise linear, anisotropic finite elements are used for space discretization, the Crank-Nicolson scheme schem ...

2020

Multi space reduced basis preconditioners for parametrized partial differential equations

Niccolò Dal Santo

The multiquery solution of parametric partial differential equations (PDEs), that is, PDEs depending on a vector of parameters, is computationally challenging and appears in several engineering contexts, such as PDE-constrained optimization, uncertainty qu ...

EPFL2018

Numerical Modelling of Two-Phase Flow with Moving Boundary Fitted Meshes

Erik Gros

In this thesis, a computational approach is used to study two-phase flow including phase change by direct numerical simulation. This approach follows the interface with an adaptive moving mesh. The incompressible Navier-Stokes equations are solved, in tw ...

EPFL2018

A semi-Lagrangian splitting method for the numerical simulation of sediment transport with free surface flows

Alexandre Caboussat, Marco Picasso, Gilles Steiner, Arwa Mrad

We present a numerical model for the simulation of 3D poly-dispersed sediment transport in a Newtonian flow with free surfaces. The physical model is based on a mixture model for multiphase flows. The Navier-Stokes equations are coupled with the transport ...

PERGAMON-ELSEVIER SCIENCE LTD2018

Tokamak equilibrium reconstruction code LIUQE and its real time implementation

Basil Duval, Jean-Marc Moret, Holger Reimerdes, Stefano Coda, Federico Alberto Alfredo Felici, Hoang Bao Le

Equilibrium reconstruction consists in identifying, from experimental measurements, a distribution of the plasma current density that satisfies the pressure balance constraint. The LIUQE code adopts a computationally efficient method to solve this problem, ...

Elsevier2015

Numerical simulation of 3D free surface flows, with multiple incompressible immiscible phases. Applications to impulse waves

Alexandre Caboussat, Marco Picasso

A numerical method for the solution to the density-dependent incompressible Navier-Stokes equations modeling the flow of N immiscible incompressible liquid phases with a free surface is proposed. It allows to model the flow of an arbitrary number of liquid ...

Wiley-Blackwell2014

Accuracy of momentum and gyrodensity transport in global gyrokinetic particle-in-cell simulations

Laurent Villard, Ben McMillan

Gyrokinetic Particle-In-Cell (PIC) simulations based on conservative Lagrangian formalisms admit transport equations for conserved quantities such as gyrodensity and toroidal momentum, and these can be derived for arbitrary wavelength, even though previous ...

Amer Inst Physics2014

Microwave gas breakdown in elliptical waveguides

Michael Mattes, Francisco Edén Sorolla Rosario, Ioannis Koufogiannis

This paper analyzes the microwave gas discharge within elliptical waveguides excited by the fundamental mode. The Rayleigh-Ritz method has been applied to solve the continuity equation. The eigenvalue problem defined by the breakdown condition has been sol ...

American Institute of Physics (AIP)2014

Thermodynamics of continuous media with intrinsic rotation and magnetoelectric coupling

Jean-Philippe Ansermet, Sylvain Bréchet

The thermodynamics of an electrically charged, multicomponent continuous medium with intrinsic rotation is analysed in the presence of electromagnetic fields with a weak linear magnetoelectric coupling in the non-relativistic limit. Taking into account the ...

Springer Verlag2013

A bio-chemo-hydro-mechanical model for microbially induced calcite precipitation in soils

Lyesse Laloui

Microbial Induced Calcite Precipitation (MICP) is an innovative technique for soil grouting involving a bacterial reactive grout. A comprehensive research work is carried out to better understand and consequently describe the phenomenon of multispecies rea ...

Elsevier Sci Ltd2012

Convergence Analysis For Spectral Approximation To A Scalar Transport Equation With A Random Wave Speed

This paper is concerned with the initial-boundary value problems of scalar transport equations with uncertain transport velocities. It was demonstrated in our earlier works that regularity of the exact solutions in the random spaces (or the parametric spac ...

Vsp Bv2012