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- Mounir Bennoune, Mohammed Lemou, Luc Mieussens
- J. Comput. Physics
- 2008

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)

- Mohammed Lemou, Luc Mieussens
- SIAM J. Scientific Computing
- 2008

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)

- Mohammed Lemou
- 2007

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)

- Nicolas Crouseilles, Mohammed Lemou, Florian Méhats
- J. Comput. Physics
- 2013

- Philippe Chartier, Nicolas Crouseilles, Mohammed Lemou, Florian Méhats
- Numerische Mathematik
- 2015

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)

- Mohammed Lemou
- 2000

After a recent work on spectral properties and dispersion relations of the linearized classical Fokker-Planck-Landau operator 8], we establish in this paper analogous results for two more realistic collision operators: The rst one is the Fokker-Planck-Landau collision operator obtained by relativistic calculations of binary interactions , and the second is… (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)

We consider the three dimensional gravitational Vlasov Poisson system which describes the mechanical state of a stellar system subject to its own gravity. A well-known conjecture in astrophysics is that the steady state solutions which are nonincreasing functions of their microscopic energy are nonlinearly stable by the ow. This was proved at the linear… (More)