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- W261567132 abstract "We study a projective integration scheme for a kinetic equation in both the diffusive and hydrodynamic scaling, on which a limiting diffusion or advection equation exists. 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, macroscopic time step. 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 limiting equation, whereas the required number of inner steps does not depend on the small-scale parameter. The presented method is asymptotic-preserving, in the sense that the method converges to a standard finite volume scheme for the limiting equation in the limit of vanishing small parameter. We show how to obtain arbitrary-order, general, explicit schemes for kinetic equations as well as for systems of nonlinear hyperbolic conservation laws, and provide numerical results." @default.
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- W261567132 date "2014-10-31" @default.
- W261567132 modified "2023-10-18" @default.
- W261567132 title "High-Order Asymptotic-Preserving Projective Integration Schemes for Kinetic Equations" @default.
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- W261567132 doi "https://doi.org/10.1007/978-3-319-10705-9_38" @default.
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