In this paper,we introduce a moment closure which is intended to provide a macroscopic approximation of the evolution of a particle distribution function,solution of a kinetic equation.This closure is of non local typ...In this paper,we introduce a moment closure which is intended to provide a macroscopic approximation of the evolution of a particle distribution function,solution of a kinetic equation.This closure is of non local type in the sense that it involves convolution or pseudo-differential operators.We show it is consistent with the diffusion limit and we propose numerical approximations to treat the non local terms.We illustrate how this approach can be incorporated in complex models involving a coupling with hydrodynamic equations,by treating examples arising in radiative transfer.We pay a specific attention to the conservation of the total energy by the numerical scheme.展开更多
In this paper we develop a class of Implicit-Explicit Runge-Kutta schemes for solving the multi-scale semiconductor Boltzmann equation.The relevant scale which characterizes this kind of problems is the diffusive scal...In this paper we develop a class of Implicit-Explicit Runge-Kutta schemes for solving the multi-scale semiconductor Boltzmann equation.The relevant scale which characterizes this kind of problems is the diffusive scaling.This means that,in the limit of zero mean free path,the system is governed by a drift-diffusion equation.Our aim is to develop a method which accurately works for the different regimes encountered in general semiconductor simulations:the kinetic,the intermediate and the diffusive one.Moreover,we want to overcome the restrictive time step conditions of standard time integration techniques when applied to the solution of this kind of phenomena without any deterioration in the accuracy.As a result,we obtain high order time and space discretization schemes which do not suffer from the usual parabolic stiffness in the diffusive limit.We show different numerical results which permit to appreciate the performances of the proposed schemes.展开更多
文摘In this paper,we introduce a moment closure which is intended to provide a macroscopic approximation of the evolution of a particle distribution function,solution of a kinetic equation.This closure is of non local type in the sense that it involves convolution or pseudo-differential operators.We show it is consistent with the diffusion limit and we propose numerical approximations to treat the non local terms.We illustrate how this approach can be incorporated in complex models involving a coupling with hydrodynamic equations,by treating examples arising in radiative transfer.We pay a specific attention to the conservation of the total energy by the numerical scheme.
文摘In this paper we develop a class of Implicit-Explicit Runge-Kutta schemes for solving the multi-scale semiconductor Boltzmann equation.The relevant scale which characterizes this kind of problems is the diffusive scaling.This means that,in the limit of zero mean free path,the system is governed by a drift-diffusion equation.Our aim is to develop a method which accurately works for the different regimes encountered in general semiconductor simulations:the kinetic,the intermediate and the diffusive one.Moreover,we want to overcome the restrictive time step conditions of standard time integration techniques when applied to the solution of this kind of phenomena without any deterioration in the accuracy.As a result,we obtain high order time and space discretization schemes which do not suffer from the usual parabolic stiffness in the diffusive limit.We show different numerical results which permit to appreciate the performances of the proposed schemes.
