To accurately simulate the complex wetting and drying process involved in flooding, two widely used schemes, the thin film scheme and the minimum threshold scheme, have been incorporated into the discrete Boltzmann model for shallow water flows. Seven classical benchmarks are employed to evaluate their performance: one-dimensional steady hydraulic jump, one-dimensional ideal dam-break flow, one-dimensional dam-break flow in an inclining channel, one-dimensional dam-break flow over a triangular obstacle, two-dimensional partial dam-break flows, two-dimensional solitary wave, and tsunami runup on a beach with complex topography. It is found that thin film scheme is easy to implement but exhibits relatively lower accuracy and noticeable numerical oscillations, whereas the minimum threshold scheme shows the opposite characteristics. Generally, both schemes demonstrate satisfactory accuracy although the minimum threshold scheme shows better stability. Furthermore, selecting an appropriate characteristic water depth is crucial for achieving accurate and stable simulations.

中文翻译：

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浅水流离散玻尔兹曼建模的干湿方案

为了准确模拟洪水中涉及的复杂湿润和干燥过程，将两种广泛使用的方案，即薄膜方案和最小阈值方案，纳入浅水流的离散玻尔兹曼模型中。采用七个经典基准来评估其性能：一维稳态水力跳跃、一维理想溃坝流、倾斜渠道中的一维溃坝流、三角障碍物上的一维溃坝流、二维部分溃坝流、二维孤立波和地形复杂海滩上的海啸隆起。研究发现，薄膜方案易于实现，但精度相对较低，数值振荡明显，而最小阈值方案则表现出相反的特性。通常，两种方案都表现出令人满意的准确性，尽管最小阈值方案显示出更好的稳定性。此外，选择合适的特征水深对于实现准确和稳定的模拟至关重要。