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Development of a highly accurate numerical method for shallow-water flows with arbitrary boundary shapes
line and area averaged values
Construction. Civil engineering
A versatile numerical method of flows with complex boundaries is highly needed in many hydraulic practices. This paper presents a new computational approach for shallow water flows with the emphasis on the accurate modeling of complex geometries in the Cartesian coordinate system. Expanding the concept of CIP-CSL2 scheme, the present method simultaneously solves point, line and area averaged values of a computational cell to directly capture the effects of complex boundary shapes and conditions. The method is then tested against the one-dimensional dam-break problem to find good agreement with theoretical results. Further, the applicability of the method is demonstrated for two flows. In one case, hydraulic bores bounce from impermeable walls and in the other case water flows between narrow impermeable walls whose direction is arbitrary, both of which are known to be tough problems.
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Graduate School of Engineering