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- W1966352008 abstract "Proposed is a method of finding unstable steady solutions based on relaxation to a running mean. It works for moderate supercriticality, when the growth rates of the instabilities do not exceed their frequencies. To calculate the running mean one should use the decaying exponential function as a kernel in the convolution formula, it offers a combination of necessary stabilization properties with the efficiency of numerical implementation. The method requires specification of the relaxation T R and averaging T A time scales, such that in the transformed eigenspectrum frequencies above the cutoff 1/ T A experience additional damping with 1/ T R rate. All originally decaying modes remain decaying. The zero frequency remains unchanged, which implies that the steady states are invariant under the transformation. The acceptable values for T R and T A can be obtained from an estimate of the frequencies and growth rates of the modes leading to instability. For faster convergence to the steady state T R should be set as large as possible, provided it causes sufficient damping of the instability. The numerical implementation of this method requires only very simple modifications to the program used for time integration of the original system." @default.
- W1966352008 created "2016-06-24" @default.
- W1966352008 creator A5088030924 @default.
- W1966352008 date "2003-01-01" @default.
- W1966352008 modified "2023-09-26" @default.
- W1966352008 title "A method of finding unstable steady solutions by forward time integration: relaxation to a running mean" @default.
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- W1966352008 doi "https://doi.org/10.1016/s1463-5003(02)00017-3" @default.
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