Assessment of Time Integration Methods in the Numerical Solution of Two-Dimensional Shallow Water Equations

Document Type : Research Paper


1 Student of Department of Hydro-Structure, Faculty of Agriculture, Tarbiat Modares University of Tehran.

2 Assistant Professor of Department of Hydro-Structure, Faculty of Agriculture, Tarbiat Modares University of Tehran, Iran

3 Full Professor of Department of Hydro-Structure, Faculty of Agriculture, Tarbiat Modares University of Tehran.


The 2D shallow water equations are used in flow simulation of rivers, floodplains, coastal currents, etc. In the research, updating or the so-called numerical integration of temporal terms of two-dimensional equations using first-order methods is more stable but less accurate. In contrast, high-order accuracy methods have numerical stability problems and cause divergence (Brouwer et al., 2014). For this reason, second-order accurate methods with median properties are widely used. Despite much research on how to deal with spatial terms, according to a review by the authors, there is less research on how to deal with the temporal terms of equations. In addition, studies on time integration methods are limited to solving 1D problems. In this research, two different time integration methods of Runge-Kutta third order (RK-3 method) and Strang splitting operator method (Strang method), which have a second-order of accuracy and are commonly used in various research (Huang et al., 2013), have been investigated. Therefore, two models have been obtained in which the applied time integration methods are different, but the ways adopted to deal with spatial and sources terms of equations are same. Then, 1D and 2D reference problems are implemented using these two models and their results are presented in order to recognize the appropriate time integration method for solving 2D shallow water equations.


Main Subjects

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Volume 43, Issue 2
July 2020
Pages 215-230
  • Receive Date: 02 May 2018
  • Revise Date: 29 December 2018
  • Accept Date: 02 February 2019
  • First Publish Date: 21 June 2020