Retrospective time integral scheme and its applications to the advection equation
To put more information into a difference scheme of a differential equation for making an accurate prediction, a new kind of time integration scheme, known as the retrospective (RT) scheme, is proposed on the basis of the memorial dynamics. Stability criteria of the scheme for an advection equation in certain conditions are derived mathematically. The computations for the advection equation have been conducted with its RT scheme. It is shown that the accuracy of the scheme is much higher than that of the leapfrog (LF) difference scheme.
Key wordstime integration memorization numerical weather prediction difference scheme advection equation
Unable to display preview. Download preview PDF.
- 2.Robert A. A stable numerical integration scheme for the primitive meteorological equations.Atmos-Ocean, 1981, 19(1): 35–46Google Scholar
- 3.O'Brien JJ. Time Integration Schemes Advanced Physical Oceanographic Numerical Modeling. Amsterdam: Reidel Press, 1986. 155–164Google Scholar
- 6.Zhang HX, Guo C, Zong, WG. Problems about gird and height order schemes.Acta Mechanica Sinica, 1999, 31 (4): 398–405 (in Chinese)Google Scholar
- 10.Cao HX, Feng GL. Self-memorial model of climate prediction and its preliminary application.Chinese J Comput Phys, 1999, 16 (2): 206–210 (in Chinese)Google Scholar
- 12.ECMWF. ECMWF Forecast Model. ECMWF Research Department, 1987Google Scholar
- 13.Haltiner GJ. Numerical Weather Prediction. New York: John Wiley & Son Inc, 1971. 78–101Google Scholar