An HP-Adaptive Predictor-Corrector Split Projection Method for Turbulent Compressible Flow

AbstractBy using the stability condition and general formulas developed by Fukushima (1998 = Paper I) we discovered that, just as in the case of the explicit symmetric multistep methods (Quinlan and Tremaine, 1990), when integrating orbital motions of celestial bodies, the implicit symmetric multistep methods used in the predictor-corrector manner lead to integration errors in position which grow linearly with the integration time if the stepsizes adopted are sufficiently small and if the number of corrections is sufficiently large, say two or three. We confirmed also that the symmetric methods (explicit or implicit) would produce the stepsize-dependent instabilities/resonances, which was discovered by A. Toomre in 1991 and confirmed by G.D. Quinlan for some high order explicit methods. Although the implicit methods require twice or more computational time for the same stepsize than the explicit symmetric ones do, they seem to be preferable since they reduce these undesirable features significantly.

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Boundary-value problems in the Fanno model for turbulent compressible flow

Proceedings of the Royal Society of Edinburgh Section A Mathematics ◽

10.1017/s0308210502000069 ◽

2002 ◽

Vol 132 (01) ◽

pp. 121

Keyword(s):

Boundary Value Problems ◽

Compressible Flow ◽

Boundary Value

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THE INFLUENCE OF THE WIND SPEED PREDICTION ERROR ON THE SIZE OF THE STORAGE CONTROLLED OPERATION ZONE IN THE SYSTEM WITH THE WIND GENERATOR

Praci Institutu elektrodinamiki Nacionalanoi akademii nauk Ukraini ◽

10.15407/publishing2020.57.035 ◽

2020 ◽

Vol 2020 (57) ◽

pp. 35-41

Author(s):

K.S. Klen ◽

◽

M.K. Yaremenko ◽

V.Ya. Zhuykov ◽

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...

Keyword(s):

Wind Speed ◽

Prediction Error ◽

Average Energy ◽

Interpolation Formula ◽

Wind Speed Prediction ◽

Wind Generator ◽

Prediction Horizon ◽

Speed Prediction ◽

Using Data ◽

Predictor Corrector

The article analyzes the influence of wind speed prediction error on the size of the controlled operation zone of the storage. The equation for calculating the power at the output of the wind generator according to the known values of wind speed is given. It is shown that when the wind speed prediction error reaches a value of 20%, the controlled operation zone of the storage disappears. The necessity of comparing prediction methods with different data discreteness to ensure the minimum possible prediction error and determining the influence of data discreteness on the error is substantiated. The equations of the "predictor-corrector" scheme for the Adams, Heming, and Milne methods are given. Newton's second interpolation formula for interpolation/extrapolation is given at the end of the data table. The average relative error of MARE was used to assess the accuracy of the prediction. It is shown that the prediction error is smaller when using data with less discreteness. It is shown that when using the Adams method with a prediction horizon of up to 30 min, within ± 34% of the average energy value, the drive can be controlled or discharged in a controlled manner. References 13, figures 2, tables 3.

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