论文标题
浅水方程的纯净性和均衡的随机盖尔金方法
Hyperbolicity-Preserving and Well-Balanced Stochastic Galerkin Method for Shallow Water Equations
论文作者
论文摘要
用于平衡或保护定律随机系统的随机制剂可能无法保留原始系统的超可波动性。在这项工作中，我们通过仔细选择非线性$ q^2/h $项的多项式混乱膨胀，以保守变量的多项式混乱范围来开发一维浅水方程的随机盖尔金配方。另外，在任意有限的随机维度中，我们建立了足够的条件，可以通过随机数量正交点的有限条件来确保随机盖尔金系统的双曲线。此外，我们为随机浅水模型开发了均衡的中央风向方案，并得出了相关的倍增性的CFL型条件。在许多具有挑战性的数值测试中说明了开发方法的性能。
A stochastic Galerkin formulation for a stochastic system of balanced or conservation laws may fail to preserve hyperbolicity of the original system. In this work, we develop hyperbolicity-preserving stochastic Galerkin formulation for the one-dimensional shallow water equations by carefully selecting the polynomial chaos expansion of the nonlinear $q^2/h$ term in terms of the polynomial chaos expansions of the conserved variables. In addition, in an arbitrary finite stochastic dimension, we establish a sufficient condition to guarantee hyperbolicity of the stochastic Galerkin system through a finite number of conditions at stochastic quadrature points. Further, we develop a well-balanced central-upwind scheme for the stochastic shallow water model and derive the associated hyperbolicty-preserving CFL-type condition. The performance of the developed method is illustrated on a number of challenging numerical tests.
