Hybrid Well-balanced WENO Schemes with Different Indicators for Shallow Water Equations

Authors:
Gang Li;Changna Lu;Jianxian Qiu
Affiliations:
Department of Mathematics, Nanjing University, Nanjing, P.R. China 210093 and School of Mathematical Science, Qingdao University, Qingdao, P.R. China 266071;College of Mathematics & Physics, Nanjing University of Information Science & Technology, Nanjing, P.R. China 210044;Department of Mathematics, Nanjing University, Nanjing, P.R. China 210093 and School of Mathematical Sciences, Xiamen University, Xiamen, P.R. China 361005
Venue:
Journal of Scientific Computing
Year:
2012

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Abstract

In (J. Comput. Phys. 229: 8105---8129, 2010), Li and Qiu investigated the hybrid weighted essentially non-oscillatory (WENO) schemes with different indicators for Euler equations of gas dynamics. In this continuation paper, we extend the method to solve the one- and two-dimensional shallow water equations with source term due to the non-flat bottom topography, with a goal of obtaining the same advantages of the schemes for the Euler equations, such as the saving computational cost, essentially non-oscillatory property for general solution with discontinuities, and the sharp shock transition. Extensive simulations in one- and two-dimensions are provided to illustrate the behavior of this procedure.