关于浅水线性化矩方程的双曲随机伽辽金投影
On Hyperbolic Stochastic Galerkin Projections of Shallow Water Linearised Moment Equations
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中文总结 AI 辅助
研究浅水线性化矩方程的双曲随机伽辽金投影，用伪谱乘积进行广义多项式混沌展开，推导能量方程并分析双曲性，引入正则化，通过数值测试表明该方法精度高且运行快。
中文摘要 AI 辅助
在这项工作中，我们提出了一种用保守变量表示的一维浅水线性化矩方程的侵入式随机伽辽金公式，使用伪谱乘积进行广义多项式混沌展开。浅水线性化矩方程构成了一个具有任意数量方程的双曲偏微分方程组，提高了标准浅水方程的精度。不失一般性，我们在理论分析和模拟中都假设不确定参数为摩擦系数。对于新的随机伽辽金浅水线性化矩方程，我们推导了能量方程，分析了双曲性，并引入正则化以确保浅水线性化矩方程线性情况的双曲性。通过数值测试，我们展示了新的随机伽辽金公式与非侵入式蒙特卡罗方法相比的准确性，表明随机伽辽金方法实现了相当的精度且运行时间显著更快。
英文摘要
In this work, we present an intrusive stochastic Galerkin formulation of the one-dimensional shallow water linearised moment equations expressed in conservative variables, using the pseudospectral product for generalised polynomial chaos expansions. The shallow water linearised moment equations constitute a hyperbolic system of partial differential equations with an arbitrary number of equations that enhance the accuracy of the standard shallow water equations. Without loss of generality, we assume for both the theoretical analysis and the simulations that the uncertain parameter is the friction coefficient. For the new stochastic Galerkin shallow water linearised moment equations, we derive an energy equation, analyse the hyperbolicity - since this property is not preserved by the stochastic Galerkin projection - and introduce a regularisation to ensure hyperbolicity for the linear case of the shallow water linearised moment equations. Through numerical tests, we demonstrate the accuracy of the new stochastic Galerkin formulation in comparison with a non-intrusive Monte Carlo method, showing that the stochastic Galerkin approach achieves comparable accuracy with significantly faster run times.
