Results 1  10
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11
A smooth transition model between kinetic and diffusion equations
, 2004
"... Abstract. This paper presents a model which provides a smooth transition between a kinetic and a hydrodynamic domain. The idea is to use a buffer zone, in which both diffusion and kinetic equations will be solved. The solution of the original kinetic equation will be recovered as the sum of the solu ..."
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Cited by 24 (11 self)
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Abstract. This paper presents a model which provides a smooth transition between a kinetic and a hydrodynamic domain. The idea is to use a buffer zone, in which both diffusion and kinetic equations will be solved. The solution of the original kinetic equation will be recovered as the sum of the solutions of these two equations. We use an artificial connecting function which makes the equation on each domain degenerate at the end of the buffer zone, thus no boundary condition is needed at the transition point. Consequently this model avoids the delicate issue of finding the interface condition in a typical domain decomposition method that couples a kinetic equation with hydrodynamic equations. A simple kinetic scheme is developed to discretize our model, and numerical examples are used to validate the method. Key words. KineticFluid coupling, Kinetic equation, Hydrodynamic approximation AMS subject classifications. 82B40, 82B80, 82C40, 82C80, 76P05
Asymptoticpreserving & wellbalanced schemes for radiative transfer and the Rosseland approximation
, 2003
"... We are concerned with efficient numerical simulation of the radiative transfer equations... ..."
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Cited by 18 (2 self)
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We are concerned with efficient numerical simulation of the radiative transfer equations...
A Domain Decomposition Analysis For A TwoScale Linear Transport Problem
, 2002
"... We present a domain decomposition theory on an interface problem for the linear transport equation between a diffusive and a nondiffusive region. To leading order, i.e. up to an error of the order of the mean free path in the diffusive region, the solution in the nondiffusive region is independen ..."
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Cited by 15 (8 self)
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We present a domain decomposition theory on an interface problem for the linear transport equation between a diffusive and a nondiffusive region. To leading order, i.e. up to an error of the order of the mean free path in the diffusive region, the solution in the nondiffusive region is independent of the density in the diffusion region. However, the diffusive and the nondiffusive regions are coupled at the interface at the next order of approximation. In particular, our algorithm avoids interating the diffusion and transport solutions as is done in most other methods — see for example BalMaday [Math. Modelling and Numer. Anal. to appear]. Our analysis is based instead on an accurate description of the boundary layer at the interface matching the phasespace density of particles leaving the nondiffusion region to the bulk density that solves the diffusive equation.
Machnumber uniform asymptoticpreserving gauge schemes for compressible flows
 Bulletin of the Institute of Mathematics, Academia Sinica, New Series
"... We present novel algorithms for compressible flows that are efficient for all Mach numbers. The approach is based on several ingredients: semiimplicit schemes, the gauge decomposition of the velocity field and a second order formulation of the density equation (in the isentropic case) and of the en ..."
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Cited by 8 (6 self)
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We present novel algorithms for compressible flows that are efficient for all Mach numbers. The approach is based on several ingredients: semiimplicit schemes, the gauge decomposition of the velocity field and a second order formulation of the density equation (in the isentropic case) and of the energy equation (in the full NavierStokes case). Additionally, we show that our approach corresponds to a micromacro decomposition of the model, where the macro field corresponds to the incompressible component satisfying a perturbed low Mach number limit equation and the micro field is the potential component of the velocity. Finally, we also use the conservative variables in order to obtain a proper conservative formulation of the equations when the Mach number is order unity. We successively consider the isentropic case, the full NavierStokes case, and the isentropic NavierStokesPoisson case. In this work, we only concentrate on the question of the time discretization and show that the proposed method leads to Asymptotic Preserving schemes for
Numerical study of a domain decomposition method for a twoscale linear transport equation, Netw
 Heterog. Media
, 2006
"... Abstract. We perform a numerical study on a domain decomposition method proposed in [13] for the linear transport equation between a diffusive and a nondiffusive region. This method avoids iterating the diffusion and transport solutions as in a typical domain decomposition method. Our numerical res ..."
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Cited by 6 (3 self)
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Abstract. We perform a numerical study on a domain decomposition method proposed in [13] for the linear transport equation between a diffusive and a nondiffusive region. This method avoids iterating the diffusion and transport solutions as in a typical domain decomposition method. Our numerical results, in both one and two space dimensions, confirm the theoretical analysis of [13]. We also provide an improved second order method that provides a more accurate numerical solution than that proposed in [13].
Splitting schemes for the simulation of non equilibrium radiative flows
, 2006
"... Abstract. This paper is devoted to the numerical investigation of radiative hydrodynamics equations. We focus on non–equilibrium regimes and we design asymptotic preserving schemes which can handle the corresponding stiff equations. Our study includes relativistic effects and Doppler corrections. ..."
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Cited by 5 (2 self)
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Abstract. This paper is devoted to the numerical investigation of radiative hydrodynamics equations. We focus on non–equilibrium regimes and we design asymptotic preserving schemes which can handle the corresponding stiff equations. Our study includes relativistic effects and Doppler corrections.
A FUNCTIONAL LIMIT THEOREM FOR THE POSITION OF A PARTICLE IN A LORENTZ TYPE MODEL
, 2006
"... Abstract. Consider a particle moving through a random medium, which consists of spherical obstacles, randomly distributed in R d. The particle is accelerated by a constant external field; when colliding with an obstacle, the particle inelastically reflects. We study the asymptotics of X(t), which de ..."
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Abstract. Consider a particle moving through a random medium, which consists of spherical obstacles, randomly distributed in R d. The particle is accelerated by a constant external field; when colliding with an obstacle, the particle inelastically reflects. We study the asymptotics of X(t), which denotes the position of the particle at time t, as t → ∞. The result is a functional limit theorem for X(t). Key words and phrases: Lorentz model, motion in random medium, functional central limit theorem for Markov chains, limit theorems.
On the Asymptotic Preserving property of the Unified Gas Kinetic Scheme for the diffusion limit of linear kinetic models
, 2013
"... Abstract. The unified gas kinetic scheme (UGKS) of K. Xu et al. [37], originally developed for multiscale gas dynamics problems, is applied in this paper to a linear kinetic model of radiative transfer theory. While such problems exhibit purely diffusive behavior in the optically thick (or small Knu ..."
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Abstract. The unified gas kinetic scheme (UGKS) of K. Xu et al. [37], originally developed for multiscale gas dynamics problems, is applied in this paper to a linear kinetic model of radiative transfer theory. While such problems exhibit purely diffusive behavior in the optically thick (or small Knudsen) regime, we prove that UGKS is still asymptotic preserving (AP) in this regime, but for the free transport regime as well. Moreover, this scheme is modified to include a time implicit discretization of the limit diffusion equation, and to correctly capture the solution in case of boundary layers. Contrary to many AP schemes, this method is based on a standard finite volume approach, it does neither use any decomposition of the solution, nor staggered grids. Several numerical tests demonstrate the properties of the scheme. Key words. Transport equations, diffusion limit, asymptotic preserving schemes, stiff terms 1
Hydrodynamics Radiative Transfert Models Numerical Scheme for radiative transfert
"... Numerische Mathematik manuscript No. (will be inserted by the editor) ..."