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首页> 外文期刊>Journal of Computational Physics >A primitive-variable Riemann method for solution of the shallow water equations with wetting and drying
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A primitive-variable Riemann method for solution of the shallow water equations with wetting and drying

机译：用干湿法求解浅水方程组的原始变量Riemann方法

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A Riemann flux that uses primitive variables rather than conserved variables is developed for the shallow water equations with nonuniform bathymetry. This primitive-variable flux is both conservative and well behaved at zero depth. The unstructured finite-volume discretization used is suitable for highly nonuniform grids that provide resolution of complex geometries and localized flow structures. A source-term discretization is derived for nonuniform bottom that balances the discrete flux integral both for still water and in dry regions. This primitive-variable formulation is uniformly valid in wet and dry regions with embedded wetting and drying fronts. A fully nonlinear implicit scheme and both nonlinear and time-linearized explicit schemes are developed for the time integration. The implicit scheme is solved by a parallel Newton-iterative algorithm with numerically computed flux Jacobians. A concise treatment of characteristic-variable boundary conditions with source terms is also given. Computed results obtained for the one-dimensional dam break on wet and dry beds and for normal-mode oscillations in a circular parabolic basin are in very close agreement with the analytical solutions. Other results for a forced breaking wave with friction interacting with a sloped bottom demonstrate a complex wave motion with wetting, drying and multiple interacting wave fronts. Finally, a highly nonuniform, coastline-conforming unstructured grid is used to demonstrate an unsteady simulation that models an artificial coastal flooding due to a forced wave entering the Gulf of Mexico.
机译：针对具有不均匀测深的浅水方程，开发了使用原始变量而不是守恒变量的黎曼通量。该原始变量通量既保守又在零深度处表现良好。所使用的非结构化有限体积离散化适用于高度不均匀的网格，这些网格可提供复杂几何形状和局部流动结构的分辨率。源项离散化是针对非均匀底部而得出的，它可以平衡静态水和干燥区域中的离散通量积分。这种原始变量的配方在具有湿润和干燥前沿的干湿地区均有效。开发了用于时间积分的完全非线性隐式方案以及非线性和时间线性化的显式方案。隐式方案通过并行牛顿迭代算法求解，该算法具有数值计算的通量雅可比矩阵。还给出了带有源项的特征变量边界条件的简洁处理。对于干，湿床的一维溃坝以及圆形抛物线形盆地中的正常模式振荡所获得的计算结果与解析解非常吻合。带有与倾斜底部相互作用的摩擦力的强迫碎波的其他结果表明，湿，干燥和多重相互作用的波前具有复杂的波运动。最后，使用高度不均匀，符合海岸线的非结构化网格来演示不稳定模型，该模型模拟了由于强迫波进入墨西哥湾而造成的人工沿海洪水。

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