Implementation of First-order Finite-volume Osher Scheme in Shallow-water Flow Computation
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摘要: 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。Abstract: 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 implementation. 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 dynmaics, and correcting the results accordingly. Based on theoretical analysis and numerical tests, a detailed description is also given about various types of outer, inner and moving boundary treatments, so that a complete and practical algorithm has been formed.
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[1] 谭维炎, 胡四一二维浅水流动的一种普适的高性能格式.水科学进展.1991, 2(3):154-161 [2] 谭维炎, 胡四一计算浅水动力学的新方向水科学进展.1992, 3(4); 310-318 [3] H Decomick, et al.Consistent Boundary Conditions for CeV-centered Upwind. Finite Volume Solvers: K W Morton et al. eds. Numerical Methods for Fluid Dynamics. Clarendon, 1988: 464-470
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