ERRORS ARISING FROM IRREGULAR BOUNDARIES IN ADI SOLUTIONS OF THE SHALLOW-WATER EQUATIONS

Truncation errors introduced by operator splittingtechniques, such as the ADI scheme, are discussed in the contextof the two‐dimensional shallow‐water equations. Numericalexamples of flow along a uniform channel, with and withoutfriction, illustrate the practical significance of these errors when the boundary is not aligned with the computational gridaxes. With irregular boundaries the maximum time step aceptable ismore severely restricted than has been realized hitherto. The problem, which is shown to stem from the treatment of the boundary conditons, is inherent in any splitting scheme and is difficult to circumvent. Copyright © 1979 John Wiley & Sons, Ltd