Abstract
AbstractA recent article by Leonard and Mokhtari (1990) discusses the order of accuracy of discrete equations used for numerical simulation. They maintain that discrete operators derived for the finite‐volume method should be Taylor‐series‐analysed using the various points that appear in a finite‐volume discrete equation. The current paper argues that any discrete scheme must be analysed from a single point. It is shown that while Leonard's finite‐difference QUICK scheme is O(h3)‐accurate, his implementation of QUICK for the finite‐volume method is only O(h2). An alternative finite‐volume formulation is shown to yield a locally third‐order‐accurate operator in the final discrete equation. Also, third‐order‐accurate formulae are discussed for various numerical implementations. Numerical examples are included to demonstrate actual rates of convergence for various operators.
Published Version
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