Kinetic and hyperbolic equations: modeling, analysis and numerics

Liste des contributions

23. Global entropy stability for a class of unlimited high-order schemes for hyperbolic systems of conservation laws

Christophe BERTHON

12/12/2022 14:15

3. Vlasov-Poisson-Fokker-Planck equation in the adiabatic asymptotics

Etienne LEHMAN

12/12/2022 15:30

The main concern of this article is the study of a nonlinear Vlasov-Poisson-Fokker-
Planck equation describing the electron dynamics in a thermonuclear fusion plasma, in the regime of a small electron-to-ion mass ratio (ε ≪ 1). The first part of this work focuses on the rigorous ε → 0 asymptotic study, based on hypocoercive techniques, permitting to understand the transition from the kinetic...

5. A mass-conserving sparse grid combination technique with biorthogonal hierarchical basis functions

Katharina KORMANN

12/12/2022 16:15

Grid-based solvers for the simulation of kinetic equations suffer from
the curse of dimensionality. The sparse grid combination technique is a
means to reduce the number of degrees of freedom in high dimensions,
however, the hierarchical representation for the combination step with
the state-of-the-art hat functions suffers from poor conservation
properties and numerical instability.
We...

6. Numerical methods for the Vlasov-Poisson system under the quasi neutral and fluid scalings.

Giacomo DIMARCO

13/12/2022 09:00

In this talk we will discuss the development and the analysis of asymptotic stable and consistent schemes in the joint quasi-neutral and fluid limits for the collisional Vlasov Poisson system. 
We will first introduce the quasi neutral scaling and its formal limit and then we will discuss different numerical approaches based on splitting techniques for dealing with the stiffness of the...

7. A numerical framework for hypocoercivity in the context of kinetic equations.

Alain BLAUSTEIN

13/12/2022 09:45

We propose a numerical method for a Vlasov-Fokker-Planck model with external applied force field and prove quantitative results ensuring that it is Asymptotic-Preserving for  both the macroscopic regime and the long time behavior simultaneously. We illustrate these results with various numerical experiments in which we observe, among others, transition phase between macroscopic and long time...

8. Multi-fidelity method for a class of kinetic models with uncertainties

Liu LIU

13/12/2022 11:00

In this talk, we will discuss some recent development on the multi-
fidelity methods for solving a class of kinetic equations with multi-
dimensional uncertainties and different scalings. The Boltzmann
equation, linear transport equation and epidemic transport system will
be particularly studied, followed by some formal error estimates. We
will also briefly discuss applying deep learning...

9. Monte Carlo Stochastic Galerkin methods for collisional plasmas

Lorenzo PARESCHI

13/12/2022 14:00

10. A kinetic model of plasma-probe interaction : theory and numerics

Mehdi BADSI

13/12/2022 14:45

We are interested in the modeling of a cylindrical Langmuir probe interacting with two species electrostatic plasma. We consider the stationary Vlasov-Poisson equations written in polar coordinates with absorbing boundary conditions at the probe. We will present the general methodology based on a phase-space analysis to construct stationary solutions and explain how to deal with unpopulated...

4. From collisional kinetic models to sprays: internal energy exchanges

Frédérique CHARLES

13/12/2022 16:00

We are interested in models describing the evolution of particles (such as solid dust particles or droplets) in a rarefied gas. We present here a derivation of a fluid-kinetic system in which the gas and the disperse phase are coupled not only by the drag force, but also by the exchange of temperature between the gas and the droplets/dust specks.
We start from a kinetic collisional model,...

11. Derivation of a two-phase flow model with surface tension

Hélène MATHIS

13/12/2022 16:45

This talk deals with the derivation of a compressible two-phase flow model by means of the Least Action Principle (LAP).
The key point of this method is to provide an appropriate Lagrangian functional which depicts the behaviour of the fluid system.
It is composed of a kinetic energy, taking into account small scales features, and a potential energy.

The latter corresponds to the...

13. Analysis of discontinuous Galerkin/Hermite spectral methods for the Vlasov-Poisson system

Marianne BESSEMOULIN-CHATARD

14/12/2022 09:00

In this talk, I present some recent results obtained in collaboration with Francis Filbet. We study discontinuous Galerkin approximations for the Vlasov-Poisson system written as an hyperbolic system using Hermite polynomials. We introduce a new $L^2$ weighted space, with a time dependent weight, allowing to prove global stability. Moreover, we prove the convergence of the proposed method by...

14. An asymptotic preserving scheme for the full Euler equations in the low Mach limit

Paola ALLEGRINI

14/12/2022 09:45

This work is in collaboration with Marie-Hélène Vignal, Institut de Mathéma-
tiques de Toulouse, UT3-Paul Sabatier.

In this work, we develop and study an asymptotic preserving (AP) scheme for
the compressible Euler system in the low Mach number regime. For subsonic
flows, the acoustic waves are very fast compared to the velocity of the fluid,
we are in an incompressible regime. From a...

15. A Conservative Low Rank Tensor Approach with Discontinuous Galerkin discretization for Nonlinear Vlasov Equations

Jingmei QIU

14/12/2022 11:00

In this paper, we propose a novel Local Macroscopic Conservative (LoMaC) low rank tensor method with discontinuous Galerkin (DG) discretization for the physical and phase spaces for simulating the Vlasov-Poisson (VP) system. The LoMaC property refers to the exact local conservation of macroscopic mass, momentum and energy at the discrete level. The LoMaC low rank tensor algorithm (recently...

16. Dynamical low-rank methods for high-dimensional collisional kinetic equations

Jingwei HU

14/12/2022 14:00

Kinetic equations describe the nonequilibrium dynamics of a complex system using a probability density function. Despite of their important role in multiscale modeling to bridge microscopic and macroscopic scales, numerically solving kinetic equations is computationally demanding as they lie in the six-dimensional phase space. Dynamical low-rank method is a dimension-reduction technique that...

17. An averaged model for thick sprays

Victor FOURNET

14/12/2022 14:45

Sprays describe particles in interaction with a surrounding gas. We are interested in the so-called “thick” sprays with a coupling through a drag force and the volume fraction of the gas.
The usual model has several problems at the level of the mathematical analysis. Those problems, and physical consideration, lead us to propose a new averaged model.
The obtained system is conservative and...

18. Modified Lawson schemes for Vlasov equations

Nicolas CROUSEILLES

14/12/2022 15:50

20. Large-magnetic field regimes and asymptotic preserving schemes for plasmas in a torus configuration

Luis Miguel RODRIGUES

15/12/2022 10:30

Even in highly-oscillating dynamics may persist quantities that are evolving on slower scales and, at first-order, uncouple from fast oscillations. Thus asymptotically the slow dynamics obeys a closed system of uncoupled equations, which may be thought as averaged equations.

That is typically the case for plasmas subject to strong magnetic fields. In this case, the task of identifying a...

24. Quantum Computation of nonlinear partial differential equations and Uncertainty Quantification

Shi JIN

15/12/2022 11:15

Nonlinear partial differential equations (PDEs) are crucial to modelling important problems in science but they are computationally expensive and suffer from the curse of dimensionality. Since quantum algorithms have the potential to resolve the curse of dimensionality in certain instances, some quantum algorithms for nonlinear PDEs have been developed. However, they are fundamentally bound...

21. An implicit, conservative, asymptotic-preserving electrostatic particle-in-cell algorithm for arbitrarily magnetized plasmas

Luis CHACON

15/12/2022 14:00

We propose a new electrostatic particle-in-cell algorithm able to use large timesteps compared to particle gyro-period under a (to begin, uniform) large external magnetic field [1]. The algorithm extends earlier electrostatic fully implicit PIC implementations [2] with a new asymptotic- preserving (AP) particle-push scheme [3] that allows timesteps much larger than particle gyroperiods. In the...

22. Sparse grid reconstructions for Particle-In-Cells methods

Clément GUILLET

15/12/2022 14:45

Based on a mixed discretization (composed of mesh and particles) of the Vlasov-Maxwell system, Particle-In-Cell (PIC) methods are among the most successful models for the simulation of kinetic plasmas.  Including simplicity, ease of parallelization and robustness,
PIC schemes still contain a main drawback with the statistical error associated to the
particle noise, depending on the average...

2. Topological states in a swarmalator model

Pierre DEGOND

15/12/2022 15:50

Swarmalators are agents that combine the features of swarming particles and
oscilla tors hence the name, contraction of ‘swarmer’ and ‘oscillator’. Each
particle is endowed with a phase which modulates its interaction force with
the other particles. In return, relative positions modulate phase
synchronization between interacting particles. In the talk, I will present a
model whree there...

19. Numerical approximation of 3D magnetized Vlasov equation with moment methods

Bruno DESPRES

15/12/2022 16:35

Moment methods for the approximation of Valsov equations regain a lot of interest, in particular with Hermite polynomials which reveal particularly adpapted to Gaussian profiles. However the application of moment methods to
 Vlasov equation with a non constant strong 3D forcing magnetic field is less evident. We will review the recent advances made within the MUFFIN project.

25. High order structure preserving Generalized Finite Difference schemes for Particle In Cell simulations on structured grids

Eric SONNENDRUCKER

16/12/2022 09:00

Semi-Discrete schemes for the Vlasov-Maxwell equations based on a Particle in Cell method combined with techniques from Finite Element Exterior Calculus yield a finite dimensional hamiltonian system which after time discretization with classical geometric numerical methods have very good long time properties and preserve exactly important invariants of the system. We will propose in this talk...

26. Numerical schemes for the collisional Vlasov equation in the finite Larmor radius regime

Anaïs CRESTETTO

16/12/2022 09:45

This work is devoted to the construction of multiscale numerical schemes efficient in the finite Larmor radius approximation of the collisional Vlasov equation. Following the paper of Bostan and Finot (2019), the system involves two different regimes, a highly oscillatory and a dissipative regimes, whose asymptotic limits do not commute. In this work, we consider a Particle-In-Cell...

27. Entropy stable, positivity preserving and well-balanced Godunov-type schemes for multidimensional hyperbolic system of equations

Raphaël LOUBERE

16/12/2022 10:50

A class of cell centered Finite Volume schemes has been introduced to discretize the equations of
Lagrangian hydrodynamics on moving mesh [4]. In this framework, the numerical fluxes are evaluated
by means of an approximate Riemann solver, based at the nodes of the mesh, which provides the
nodal velocity required to move the mesh in a compatible manner. In this presentation, we...

12. Talk 11