Showing papers by "Lorenzo Pareschi published in 2003"
TL;DR: In this paper, a Fourier spectral method for the non-cutoff Boltzmann equation without cut-off to the Fokker-Planck-Landau equation in the so-called grazing collision limit was derived.
Abstract: In this paper we study the numerical passage from the spatially homogeneous Boltzmann equation without cut-off to the Fokker-Planck-Landau equation in the so-called grazing collision limit. To this aim we derive a Fourier spectral method for the non cut-off Boltzmann equation in the spirit of [21,23]. We show that the kernel modes that define the spectral method have the correct grazing collision limit providing a consistent spectral method for the limiting Fokker-Planck-Landau equation. In particular, for small values of the scattering angle, we derive an approximate formula for the kernel modes of the non cut-off Boltzmann equation which, similarly to the Fokker-Planck-Landau case, can be computed with a fast algorithm. The uniform spectral accuracy of the method with respect to the grazing collision parameter is also proved.
37 citations
01 Jan 2003
TL;DR: The formalism of Implicit-Explicit (IMEX) Runge-Kutta methods is essential in the derivation and analysis of the schemes and the development of schemes up to order 3 that are asymptotic-preserving and strong-stability-Preserving for the limiting system of conservation laws are considered.
Abstract: In this not e we report some recent result on the time discretization of hyperbolic systems of conservation laws with stiff relaxation terms. The formalism of Implicit-Explicit (IMEX) Runge-Kutta methods is essential in the derivation and analysis of the schemes. Here we restrict to diagonally implicit schemes and consider the development of schemes up to order 3 that are asymptotic-preserving (AP) and strong-stability-preserving (SSP) for the limiting system of conservation laws.
31 citations
TL;DR: In this paper, a Fourier spectral method for the Boltzmann equation with singular kernel was introduced and the kernel modes that define the spectral method were shown to have the correct quasi-elastic limit.
Abstract: In this paper we introduce numerical schemes for a one-dimensional kinetic model of the Boltzmann equation with dissipative collisions and variable coefficient of restitution. In particular, we study the numerical passage of the Boltzmann equation with singular kernel to nonlinear friction equations in the so-called quasi elastic limit. To this aim we introduce a Fourier spectral method for the Boltzmann equation [CITE] and show that the kernel modes that define the spectral method have the correct quasi elastic limit providing a consistent spectral method for the limiting nonlinear friction equation.
18 citations
01 Jan 2003
12 citations
TL;DR: A relaxation system for the incompressible and compressible Euler and Navier-Stokes equations is considered and a numerical scheme working uniformly in the above limits is constructed using higher-order nonoscillatory upwind discretizations and higher- order implicit-explicit time discretization.
8 citations
TL;DR: In this article, a numerical simulation of the relaxation process in a three-dimensional Coulomb gas is presented, where a Runge-Kutta solver for the time intergreation of the collision phase avoids excessive small time steps included by the stiffness of the diffusive collision operator.
Abstract: A new approach for the accurate solution of the Fokker-Planck-Landau (FPL) equation has been presented recently in [1,2]. The method is based on a fast spectral solver for the efficent solution of the collision operator. The use of a suitable explicit Runge-Kutta solver for the time intergreation of the collision phase avoids excessive small time steps included by the stiffness of the diffusive collision operator. Here we present the details of a numerical simulation of the relaxation process in a three-dimensional Coulomb gas.
6 citations