Time accurate local time stepping for the unsteady shallow water equations

• Published in: International journal for numerical methods in fluids Vol. 48; no. 7; pp. 775 - 799
• Main Authors: Crossley, A. J., Wright, N. G.
• Format: Journal Article
• Language: English
• Published: Chichester, UK John Wiley & Sons, Ltd 10.07.2005; Wiley
• Subjects: Applied fluid mechanics; Computational methods in fluid dynamics; Exact sciences and technology; Fluid dynamics; Fundamental areas of phenomenology (including applications); Hydrodynamics, hydraulics, hydrostatics; local time stepping; open channel; Physics; Roe's approximate Riemann solver; shallow water; unsteady flow; upwind source terms; upwind source terms; Source terms; Computational fluid dynamics; Hydraulics; Open channel flow; Digital simulation; open channel; Unsteady flow; Euler equations; local time stepping; shallow water; Finite volume methods; Upwind scheme; Roe's approximate Riemann solver; Riemann function; Shallow-water equations
• ISSN: 0271-2091; 1097-0363
• DOI: 10.1002/fld.956

Two time accurate local time stepping (LTS) strategies originally developed for the Euler equations are presented and applied to the unsteady shallow water equations of open channel flow. Using the techniques presented allows individual cells to be advanced to different points in time, in a time accurate fashion. The methods shown are incorporated into an explicit finite volume version of Roe's scheme which is implemented in conjunction with an upwind treatment for the source terms. A comparison is made between the results obtained using the conventional time stepping approach and the two LTS methods through a series of test cases. The results illustrate a number of benefits of using LTS which included reduced run times and improved solution accuracy. In addition it is shown how using an upwind source term treatment can be beneficial for flows dominated by the geometry. Copyright © 2005 John Wiley & Sons, Ltd.