The generalized Riemann problem method for the shallow water equations with bottom topography

International Journal for Numerical Methods in Engineering - Tập 65 Số 6 - Trang 834-862 - 2006
Jiequan Li1, Guoxian Chen1,2
1Department of Mathematics, Capital Normal University, Beijing 100037, People’s Republic of China
2LMAM, School of Mathematical Sciences, Peking University, Beijing, 100871, People’s Republic of China

Tóm tắt

AbstractThis paper extends the generalized Riemann problem method (GRP) to the system of shallow water equations with bottom topography. The main contribution is that the generalized Riemann problem method (J. Comput. Phys. 1984; 55(1):1–32) is used to evaluate the midpoint values of solutions at each cell interface so that the bottom topography effect is included in numerical fluxes, and at the same step the source term is discretized with an interface method in which only mid‐point values are plugged in. This scheme is well balanced between the flux gradient and bottom topography when incorporating the surface gradient method (SGM) (J. Comput. Phys. 2001; 168(1):1–25) into data reconstruction step, and it is also suitable for both steady and unsteady flow simulations. We illustrate the accuracy of this scheme by several 1‐D and 2‐D numerical experiments. Copyright © 2005 John Wiley & Sons, Ltd.

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International Journal for Numerical Methods in Engineering

Tập 65 Số 6

834-862

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