Asymptotic solutions of numerical transport problems in optically thick, diffusive regimes
Journal of Computational Physics
An Asymptotic-Induced Scheme for Nonstationary Transport Equations in the Diffusive Limit
SIAM Journal on Numerical Analysis
Diffusive Relaxation Schemes for Multiscale Discrete-Velocity Kinetic Equations
SIAM Journal on Numerical Analysis
A Numerical Method for Kinetic Semiconductor Equations in the Drift-Diffusion Limit
SIAM Journal on Scientific Computing
The Convergence of Numerical Transfer Schemes in Diffusive Regimes I: Discrete-Ordinate Method
SIAM Journal on Numerical Analysis
An Asymptotic Preserving Numerical Scheme for Kinetic Equations in the Low Mach Number Limit
SIAM Journal on Numerical Analysis
Efficient Asymptotic-Preserving (AP) Schemes For Some Multiscale Kinetic Equations
SIAM Journal on Scientific Computing
Discrete Kinetic Schemes for Multidimensional Systems of Conservation Laws
SIAM Journal on Numerical Analysis
Uniformly Accurate Diffusive Relaxation Schemes for Multiscale Transport Equations
SIAM Journal on Numerical Analysis
Projective Methods for Stiff Differential Equations: Problems with Gaps in Their Eigenvalue Spectrum
SIAM Journal on Scientific Computing
Explicit Time-Stepping for Stiff ODEs
SIAM Journal on Scientific Computing
Coarse projective kMC integration: forward/reverse initial and boundary value problems
Journal of Computational Physics
Asymptotic preserving and positive schemes for radiation hydrodynamics
Journal of Computational Physics
Second-order accurate projective integrators for multiscale problems
Journal of Computational and Applied Mathematics
Accuracy analysis of acceleration schemes for stiff multiscale problems
Journal of Computational and Applied Mathematics
Journal of Computational Physics
Numerical Schemes of Diffusion Asymptotics and Moment Closures for Kinetic Equations
Journal of Scientific Computing
Journal of Computational Physics
SIAM Journal on Scientific Computing
SIAM Journal on Numerical Analysis
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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 the diffusion time scale. We show that with an appropriate choice of the inner step size, the time-step restriction on the outer time step is similar to the stability condition for the diffusion equation, whereas the required number of inner steps does not depend on the mean free path. We also provide a consistency result. The presented method is asymptotic-preserving in the sense that the method converges to a standard finite volume scheme for the diffusion equation in the limit of vanishing mean free path. The analysis is illustrated with numerical results, and we present an application to the Su-Olson test.