Title: Primitive variable regularization to derive novel Hyperbolic Shallow Water Moment Equations Show Chinese title

Title: 原始变量正则化推导新的双曲浅水层模方程

Abstract: Shallow Water Moment Equations are reduced-order models for free-surface flows that employ a vertical velocity expansion and derive additional so-called moment equations for the expansion coefficients. Among desirable analytical properties for such systems of equations are hyperbolicity, accuracy, correct momentum equation, and interpretable steady states. In this paper, we show analytically that existing models fail at different of these properties and we derive new models overcoming the disadvantages. This is made possible by performing a hyperbolic regularization not in the convective variables (as done in the existing models) but in the primitive variables. Via analytical transformations between the convective and primitive system, we can prove hyperbolicity and compute analytical steady states of the new models. Simulating a dam-break test case, we demonstrate the accuracy of the new models and show that it is essential for accuracy to preserve the momentum equation. Show Chinese abstract

Abstract: 浅水矩量方程是用于自由表面流的降阶模型，采用垂直速度展开并推导出附加的所谓矩方程作为展开系数。对于这类方程系统，理想分析性质包括双曲性、精确性、正确的动量方程以及可解释的定态。本文中，我们分析表明现有模型在这些性质中的不同方面存在不足，并且我们推导出了新的模型来克服这些缺点。这是通过对流变量（现有模型中所做）而非原始变量进行双曲正则化得以实现的。通过在对流系统和原始系统之间进行分析变换，我们可以证明新模型的双曲性并计算出其解析定态。通过模拟大坝破裂测试案例，我们展示了新模型的精确性，并表明保持动量方程是确保精度的关键。