| CHEN Jianzhong,SHI Zhongke,HU Yanmei. 2005. High-resolution central difference scheme for the shallow water equations. Acta Oceanologica Sinica, (5):39－45 |
| High-resolution central difference scheme for the shallow water equations |
| High-resolution central difference scheme for the shallow water equations |
| Received:May 21, 2005 Revised:July 12, 2005 |
| DOI： |
| Key words:shallow water equations central difference scheme high-resolution scheme |
| 中文关键词: shallow water equations central difference scheme high-resolution scheme |
| 基金项目: |
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| Abstract: |
| A two-dimensional nonoscillatory central difference scheme was extended to the shallow water equations.A high-resolution numerical method for solving the shallow water equations was presented.In order to prevent oscillation, the nonlinear limiter is employed to approximate the discrete slopes.The main advantage of the presented method is simplicity comparable with the upwind schemes.This method does not require Riemann solvers or some form of flux difference splitting methods.Furthermore, the discrete derivatives of flux can be approximated by the component-wise approach and thus the computation of Jacobian can be avoided.The method retains high resolution and high accuracy similar to the upwind results.It is applied to simulating several tests, including circular dam-break problem, shock focusing problem and partial dam-break problem.The results are in good agreement with the numerical results obtained by other methods.The simulated results also demonstrate that the presented method is stable and efficient. |
| 中文摘要: |
| A two-dimensional nonoscillatory central difference scheme was extended to the shallow water equations.A high-resolution numerical method for solving the shallow water equations was presented.In order to prevent oscillation, the nonlinear limiter is employed to approximate the discrete slopes.The main advantage of the presented method is simplicity comparable with the upwind schemes.This method does not require Riemann solvers or some form of flux difference splitting methods.Furthermore, the discrete derivatives of flux can be approximated by the component-wise approach and thus the computation of Jacobian can be avoided.The method retains high resolution and high accuracy similar to the upwind results.It is applied to simulating several tests, including circular dam-break problem, shock focusing problem and partial dam-break problem.The results are in good agreement with the numerical results obtained by other methods.The simulated results also demonstrate that the presented method is stable and efficient. |
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