An accuracy progressive sixth-order finite difference scheme
Abstract
How to reduce the computational error is a key issue in numerical modeling and simulation. The higher the
order of the difference scheme, the less the truncation error and the more complicated the computation. For
compromise, a simple, three-point accuracy progressive (AP) finite-difference scheme for numerical calculation
is proposed. The major features of the AP scheme are three-point, high-order accuracy, and accuracy progressive.
The lower-order scheme acts as a ‘‘source’’ term in the higher-order scheme. This treatment keeps three-point
schemes with high accuracy. The analytical error estimation shows the sixth-order accuracy that the AP scheme
can reach. The Fourier analysis of errors indicates the accuracy improvement from lower-order to higher-order
AP schemes. The Princeton Ocean Model (POM) implemented for the Japan/East Sea (JES) is used to evaluate
the AP scheme. Consider a horizontally homogeneous and stably stratified JES with realistic topography.Without
any forcing, initially motionless ocean will keep motionless forever; that is to say, there is a known solution
(V 5 0). Any nonzero model velocity can be treated as an error. The stability and accuracy are compared with
those of the second-order scheme in a series of calculations of unforced flow in the JES. The three-point sixthorder
AP scheme is shown to have error reductions by factors of 10–20 compared to the second-order difference
scheme. Due to their three-point grid structure, the AP schemes can be easily applied to current ocean and
atmospheric models.
Description
Journal of Atmospheric and Oceanic Technology, American Meteorological Society, 18, 1245-1257.
Rights
This publication is a work of the U.S. Government as defined in Title 17, United States Code, Section 101. Copyright protection is not available for this work in the United States.Collections
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