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

作者：Li, Gang; Lu, Changna; Qiu, Jianxian^*

来源：Journal of Scientific Computing, 2012, 51(3): 527-559.

DOI：10.1007/s10915-011-9520-4

• WENO approximation
• Up-wind linear approximation
• Troubled-cell indicator
• Shallow water equations
• Hybrid schemes
• Source term

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.

• 出版日期2012-6
• 单位南京大学; 厦门大学; 南京信息工程大学; 青岛大学