Asymptotic-preserving Projective Integration Schemes for Kinetic Equations in the Diffusion Limit
نویسندگان
چکیده
منابع مشابه
Asymptotic-preserving Projective Integration Schemes for Kinetic Equations in the Diffusion Limit
We investigate a projective integration scheme for a kinetic equation in the limit of vanishing mean free path, in which the kinetic description approaches a diffusion phenomenon. The scheme first takes a few small steps with a simple, explicit method, such as a spatial centered flux/forward Euler time integration, and subsequently projects the results forward in time over a large time step on ...
متن کاملAsymptotic preserving schemes for the Wigner-Poisson-BGK equations in the diffusion limit
This work focusses on the numerical simulation of the Wigner-Poisson-BGK equation in the diffusion asymptotics. Our strategy is based on a “micro-macro” decomposition, which leads to a system of equations that couple the macroscopic evolution (diffusion) to a microscopic kinetic contribution for the fluctuations. A semi-implicit discretization provides a numerical scheme which is stable with re...
متن کاملAnalysis of an Asymptotic Preserving Scheme for Linear Kinetic Equations in the Diffusion Limit
We present a mathematical analysis of the asymptotic preserving scheme proposed in [M. Lemou and L. Mieussens, SIAM J. Sci. Comput., 31, pp. 334–368, 2008] for linear transport equations in kinetic and diffusive regimes. We prove that the scheme is uniformly stable and accurate with respect to the mean free path of the particles. This property is satisfied under an explicitly given CFL conditio...
متن کاملA High-Order Asymptotic-Preserving Scheme for Kinetic Equations Using Projective Integration
We investigate a high-order, fully explicit, asymptotic-preserving scheme for a kinetic equation with linear relaxation, both in the hydrodynamic and diffusive scalings in which a hyperbolic, resp. parabolic, limiting equation exists. The scheme first takes a few small (inner) steps with a simple, explicit method (such as direct forward Euler) to damp out the stiff components of the solution an...
متن کاملEfficient Asymptotic-Preserving (AP) Schemes For Some Multiscale Kinetic Equations
Many kinetic models of the Boltzmann equation have a diiusive scaling that leads to the Navier-Stokes type parabolic equations as the small scaling parameter approaches zero. In practical applications, it is desirable to develop a class of numerical schemes that can work uniformly with respect to this relaxation parameter, from the rareeed kinetic regimes to the hydrodynamic diiusive regimes. A...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: SIAM Journal on Scientific Computing
سال: 2012
ISSN: 1064-8275,1095-7197
DOI: 10.1137/100795954