Accuracy and stability analysis of numerical schemes for the shallow water model

✍ Scribed by Yue-Kuen Kwok

• Publisher: John Wiley and Sons
• Year: 1996
• Tongue: English
• Weight: 647 KB
• Volume: 12
• Category: Article
• ISSN: 0749-159X
• DOI: 10.1002/(sici)1098-2426(199601)12:1<85::aid-num5>3.0.co;2-j

✦ Synopsis

The accuracy and stability properties of several two-level and three-level difference schemes for solving the shallow water model are analyzed by the linearized Fourier Method. The effects of explicit or implicit treatments of the gravity, Coriolis, convective and friction terms on accuracy and stability are examined. The use of Miller's properties on von Neumann polynomial plays a crucial role to resolve the tedious mathematical procedures in the Fourier analysis. As a best compromise between efficiency and stability, we recommend the semi-implicit schemes, where the surface elevation and friction terms are treated implicitly while the convective and Coriolis terms are treated explicitly. 0 1996 John Wiley & Sons, Inc.

H ( x , y , t )

= z ( x , . y , t ) + h ( x , y ) is the water depth measured from the undisturbed water surface. The hydrostatic model studies the effects of gravity wave, Coriolis forces, advection, and friction in shallow water flows. Other formulations of the shallow water