浅水流动计算中—阶有限体积法Osher格式的实现

Implementation of First-order Finite-volume Osher Scheme in Shallow-water Flow Computation

近年来，一阶有限体积法Ｏｓｈｅｒ格式已在二维浅水明流的一批模型问题和应用实例中获得成功。本文首次讨论其算法实现的种种问题。核心是建立单元水力模型—阶梯流，在数学上可用一类特殊的黎曼问题来描述。将该问题化作气体动力学中的黎曼问题近似求解，然后对结果加以校正。还在理论分析和数值试验的基础上详细讨论了各种外部边界条件、内部边界和动边界的处理，构成完整的算法。

In recent years, the first-order finite-volume Osher scheme has been aPPlied with success to a dozen model problems and practical cases involving two-dimensional shallow-water open flows. This paper discusses for the first time relevant techniques in itS algorithmic implementstion. A kernel lies in the setup of a cell hydraulic model-step flow, which can be described mathematically by a special type of Riemann problem. It can be solved approximately by reducing to a standard Riemann problem in gas bomaics, and correcting the results accordingly. Based on theorehcal analysis and numerical tens, a detailed description is also given about various types of outer, inner and moving boundal treatments, so that a complete and practical algorithm has been formed.