arXiv subjects

A. Vasseur

Publications and source records attributed to A. Vasseur.

6 recordsLinked to original sources

arXiv2009

A Discontinuous Galerkin Method for Viscous Compressible Multifluids

We present a generalized discontinuous Galerkin method for a multicomponent compressible barotropic Navier-Stokes system of equations. The system presented has a functional viscosity nu which depends on the pressure p=p(rho,mu_i) of the flow, with the density rho and the local concentration mu_i. High order Runge-Kutta time discretization techniques are employed, and different methods of dealing with arbitrary coupled boundary conditions are discussed. Analysis of the energy consistency of the scheme is performed in addition to inspection of the relative error of the solution compared to exact analytic test cases. Finally several examples, comparisons, generalizations and physical applications are presented.

physics.comp-ph↗

arXiv2009

Quantum Hydrodynamics with Trajectories: The Nonlinear Conservation Form Mixed/Discontinuous Galerkin Method with Applications in Chemistry

We present a solution to the conservation form (Eulerian form) of the quantum hydrodynamic equations which arise in chemical dynamics by implementing a mixed/discontinuous Galerkin (MDG) finite element numerical scheme. We show that this methodology is stable, showing good accuracy and a remarkable scale invariance in its solution space. In addition the MDG method is robust, adapting well to various initial-boundary value problems of particular significance in a range of physical and chemical applications. We further show explicitly how to recover the Lagrangian frame (or pathline) solutions.

physics.chem-ph↗

arXiv2008

Existence and Uniqueness of Strong Solutions for a Compressible Multiphase Navier-Stokes Miscible Fluid-Flow Problem in Dimension n = 1

We prove the global existence and uniqueness of strong solutions for a compressible multifluid described by the barotropic Navier-Stokes equations in dim = 1. The result holds when the diffusion coefficient depends on the pressure. It relies on a global control in time of the L2 norm of the space derivative of the density, via a new kind of entropy.

math-ph↗

arXiv2006

Drift diffusion equations with fractional diffusion and the quasi-geostrophic equation

Motivated by the critical dissipative quasi-geostrophic equation, we prove that drift-diffusion equations with L^2 initial data and minimal assumptions on the drift are locally Holder continuous. As an application we show that solutions of the quasi-geostrophic equation with initial L^2 data and critical diffusion (-Δ)^{1/2}, are locally smooth for any space dimension.

math.AP↗

arXiv2006

L^p estimates for quantities advected by a compressible flow

We consider the evolution of a quantity advected by a compressible flow and subject to diffusion. When this quantity is scalar it can be, for instance, the temperature of the flow or the concentration of some pollutants. Because of the diffusion term, one expects the equations to have a regularizing effect. However, in their Euler form, the equations describe the evolution of the quantity multiplied by the density of the flow. The parabolic structure is thus degenerate near vacuum (when the density vanishes). In this paper we show that we can nevertheless derive uniform $L^{p}$ bounds that do not depend on the density (in particular the bounds do not degenerate near vacuum). Furthermore the result holds even when the density is only a measure. We investigate both the scalar and the system case. In the former case, we obtain $L^{\infty}$ bounds. In the latter case the quantity being investigated could be the velocity field in compressible Navier-Stokes type of equations, and we derive uniform $L^p$ bounds for some $p$ depending on the ratio between the two viscosity coefficients (the main additional difficulty in that case being to deal with the second viscosity term involving the divergence of the velocity). Such estimates are, to our knowledge, new and interesting since they are uniform with respect to the density. The proof relies mostly on a method introduced by De Giorgi to obtain regularity results for elliptic equations with discontinuous diffusion coefficients.

math.AP↗

arXiv2005

Electric turbulence in a plasma subject to a strong magnetic field

We consider in this paper a plasma subject to a strong deterministic magnetic field and we investigate the effect on this plasma of a stochastic electric field. We show that the limit behavior, which corresponds to the transfer of energy from the electric wave to the particles (Landau phenomena), is described by a Spherical Harmonics Expansion (SHE) model.

math.AP↗