Accurately Model the Kuramoto--Sivashinsky Dynamics with Holistic Discretization
نویسندگان
چکیده
منابع مشابه
Accurately Model the Kuramoto-Sivashinsky Dynamics with Holistic Discretization
We analyse the nonlinear Kuramoto–Sivashinsky equation to develop accurate discretisations modeling its dynamics on coarse grids. The analysis is based upon centre manifold theory so we are assured that the discretisation accurately models the dynamics and may be constructed systematically. The theory is applied after dividing the physical domain into small elements by introducing isolating int...
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We analyse the nonlinear Kuramoto-Sivashinsky equation to develop an accurate finite difference approximation to its dynamics. The analysis is based upon centre manifold theory so we are assured that the finite difference model accurately models the dynamics and may be constructed systematically. The theory is applied after dividing the physical domain into small elements by introducing insulat...
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We analyze a Crank–Nicolson–type finite difference scheme for the Kuramoto– Sivashinsky equation in one space dimension with periodic boundary conditions. We discuss linearizations of the scheme and derive second–order error estimates.
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We undertake an exploration of recurrent patterns in the antisymmetric subspace of the one-dimensional Kuramoto-Sivashinsky system. For a small but already rather "turbulent" system, the long-time dynamics takes place on a low-dimensional invariant manifold. A set of equilibria offers a coarse geometrical partition of this manifold. The Newton descent method enables us to determine numerically ...
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ژورنال
عنوان ژورنال: SIAM Journal on Applied Dynamical Systems
سال: 2006
ISSN: 1536-0040
DOI: 10.1137/050627733