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首页> 外文期刊>Journal of Hydroinformatics >Adaptation of flux-based solvers to 2D two-layer shallow flows with variable density including numerical treatment of the loss of hyperbolicity and drying/wetting fronts
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Adaptation of flux-based solvers to 2D two-layer shallow flows with variable density including numerical treatment of the loss of hyperbolicity and drying/wetting fronts

机译：将基于助焊剂的溶剂改编为2D双层浅流，可变密度，包括损失双曲性和干燥/润湿前线的数值处理

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摘要

An important feature of the two-layer shallow flow model is that the resulting system of equations cannot be expressed in conservation-law form. Here, the HLLS and ARoe solvers, derived initially for systems of conservation laws, are reformulated and applied to the two-layer shallow flows in a great variety of problems. Their resulting extension and combination allows us to overcome the loss of the hyperbolic character, ensuring energy or exactly balanced property, guarantees positivity of the solution, and provides a correct drying/wetting advance front without requiring tuning parameters. As a result, in those cases where the rich description of internal and external waves cannot be provided by the ARoe solver, HLLS is applied. Variable density is considered in each layer as a result of a bulk density driven by the mixture of different constituents. A wide variety of test cases is presented confirming the properties of this combination, including exactly balanced scenarios in subcritical and subcritical-transcritical scenarios, dam-break problems over bed variations and wet/dry fronts, non-hyperbolic conditions, transcritical exchange flow with loss of hyperbolicity. Despite the complexity of the test cases presented here, accurate and stable simulations are guaranteed, ensuring positivity of the solution without decreasing the time step.
机译：双层浅流模型的一个重要特征是，所得到的等式系统不能以保护 - 法律形式表达。在这里，最初用于保护法律系统的HLL和AROE溶剂是重新制定的，并在各种各样的问题中重新制定并应用于两层浅流。它们所产生的扩展和组合使我们能够克服双曲性特征的损失，确保能量或完全平衡的性能，保证溶液的积极性，并提供正确的干燥/润湿前锋，而不需要调节参数。结果，在可以由AROE求解器提供内部和外部波的丰富描述的情况下，施加HLL。由于由不同成分的混合物驱动的堆积密度，在每个层中考虑可变密度。提出了各种测试用例，确认了这种组合的特性，包括亚临界和亚临界跨临界场景中的完全平衡情景，床变化和湿润/干燥前的损坏问题，非双曲条件，跨临界交换流失双曲性。尽管此处提供的测试用例的复杂性，但保证了准确和稳定的模拟，确保解决方案的积极性而不会降低时间步长。

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