Weak local residuals as smoothness indicators for the shallow water equations

作者：Mungkasi Sudi^*; Li Zhenquan; Roberts Stephen Gwyn

来源：Applied Mathematics Letters, 2014, 30: 51-55.

DOI：10.1016/j.aml.2013.12.007

• Weak local residual
• Smoothness indicator
• Shock detector
• Finite volume method
• Shallow water equations
• Conservation laws

The system of shallow water equations admits infinitely many conservation laws. This paper investigates weak local residuals as smoothness indicators of numerical solutions to the shallow water equations. To get a weak formulation, a test function and integration are introduced into the shallow water equations. We use a finite volume method to solve the shallow water equations numerically. Based on our numerical simulations, the weak local residual of a simple conservation law with a simple test function is identified to be the best as a smoothness indicator.

• 出版日期2014-4