Mohammed Lemou

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In this paper we develop a numerical method to solve Boltzmann like equations of kinetic theory which is able to capture the compressible Navier-Stokes dynamics at small Knudsen numbers. Our approach is based on the micro/macro decomposition technique, which applies to general collision operators. This decomposition is performed in all the phase space and(More)
We propose a new numerical scheme for linear transport equations. It is based on a decomposition of the distribution function into equilibrium and non-equilibrium parts. We also use a projection technique that allows to reformulate the kinetic equation into a coupled system of an evolution equation for the macroscopic density and a kinetic equation for the(More)
In this work, we extend the micro-macro decomposition based numerical schemes developed in [3] to the collisional Vlasov-Poisson model in the diffusion and high-field asymptotics. In doing so, we first write the Vlasov-Poisson model as a system that couples the macroscopic (equilibrium) part with the remainder part. A suitable discretization of this(More)
abstract We present fast numerical algorithms to solve the non linear Fokker-Planck-Landau equation in 3-D velocity space. The discretization of the collision operator preserves the properties required by the physical nature of the Fokker-Planck-Landau equation, such as the conservation of mass, momentum and energy, the decay of the entropy, and the fact(More)
We give a sequence of operators approximating the Fokker-Planck-Landau collision operator. This sequence is obtained by aplying the fast multipole method based on the work by Greengard and Rocklin 17], and tends to the exact Fokker-Planck-Landau operator with an arbitrary accuracy. These operators satisfy the physical properties such as the conservation of(More)
This work is devoted to the numerical simulation of nonlinear Schrödinger and Klein-Gordon equations. We present a general strategy to construct numerical schemes which are uniformly accurate with respect to the oscillation frequency. This is a stronger feature than the usual so called “Asymptotic preserving” property, the last being also satisfied by our(More)
and σN is the area of the unit sphere in R (σ3 = 4π and σ4 = 2π). This nonlinear transport equation describes in dimension N = 3 the mechanical state of a stellar system subject to its own gravity (see for instance [3, 14]). Classical calculations show that this model should be correct only for low velocities, and if high velocities occur, special(More)