A Local Timestepping Runge–Kutta Discontinuous Galerkin Method for Hurricane Storm Surge Modeling

  • Clint DawsonEmail author
Part of the The IMA Volumes in Mathematics and its Applications book series (IMA, volume 157)


In this paper, we describe a local timestepping (LTS) approach within the Runge–Kutta discontinuous Galerkin (RKDG) method, and the application of this method to the modeling of hurricane storm surge. Modeling storm surge requires the numerical solution of the shallow water equations with wind and atmospheric pressure forcing, over complex domains which include wet and dry regions. The RKDG method is well suited for these applications; however, well-resolved simulations of storm surge can require highly graded meshes, which can lead to severe global CFL constraints. The LTS approach allows for elements to use timesteps which approximately satisfy only local CFL conditions. We describe a fully parallel implementation of the LTS method within an RKDG shallow water simulator, developed by the author and collaborators over a period of several years. We demonstrate that, for a specific hurricane, namely Hurricane Ike, the LTS method can reduce parallel run-times by nearly a factor of two with no degradation in accuracy.


Local timestepping Multirate methods Shallow water equations Runge–Kutta discontinuous Galerkin methods Hurricane storm surge 



The author acknowledges the support of National Science Foundation grant DMS-0915118.


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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  1. 1.The Institute for Computational Science and EngineeringThe University of Texas at AustinAustinUSA

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