Comment on “A modified leapfrog scheme for shallow water equations” by Wen-Yih Sun and Oliver M.T. Sun
Williams, P. (2012) Comment on “A modified leapfrog scheme for shallow water equations” by Wen-Yih Sun and Oliver M.T. Sun. Computers & Fluids, 62. p. 91. ISSN 0045-7930
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To link to this article DOI: 10.1016/j.compfluid.2012.02.023
A recent paper published in this journal considers the numerical integration of the shallow-water equations using the leapfrog time-stepping scheme [Sun Wen-Yih, Sun Oliver MT. A modified leapfrog scheme for shallow water equations. Comput Fluids 2011;52:69–72]. The authors of that paper propose using the time-averaged height in the numerical calculation of the pressure-gradient force, instead of the instantaneous height at the middle time step. The authors show that this modification doubles the maximum Courant number (and hence the maximum time step) at which the integrations are stable, doubling the computational efficiency. Unfortunately, the pressure-averaging technique proposed by the authors is not original. It was devised and published by Shuman  and has been widely used in the atmosphere and ocean modelling community for over 40 years.