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An improved numerical scheme for the approximate solution of the Parabolic wave model

机译：抛物线模型近似解的改进数值格式

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摘要

in this paper, the main features and performances of a new numerical scheme, ILILPM (Improved Locally and Instantaneously Linearized Parabolic Model) are described. ILILPM is an improved version of the Parabolic and Backwater (PAB) and Linearized Parabolic Model (LPM) schemes, proposed in literature for the approximate solution of the Parabolic Wave model. The algorithm presented is able to take into account transcritical flow regime and transitions from free-surface to pressurized flow in tree-like channel networks. Due to its unconditional stability, the model allows large computational time steps, leading to very fast simulations during transients for a class of flow conditions larger than those solved by the parent schemes. The model is demonstrated by comparing its results with experimental observations and with the results provided by the numerical solution of the full De Saint-Venant equations.
机译：本文介绍了一种新的数值方案ILILPM（改进的局部和瞬时线性化抛物线模型）的主要特征和性能。 ILILPM是抛物线和回水（PAB）和线性化抛物线模型（LPM）方案的改进版本，在文献中提出了抛物线波浪模型的近似解。提出的算法能够考虑跨临界流态以及树状通道网络中从自由表面到增压流的过渡。由于其无条件的稳定性，该模型允许大量的计算时间步长，从而在瞬态过程中对一类大于母体方案所求解的流量条件进行了非常快速的仿真。通过将其结果与实验观察结果以及由完整的De Saint-Venant方程的数值解提供的结果进行比较来证明该模型。

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