A Finite Element Analysis of Mach Reflection by Using the Boussinesq Equation

by Shoichiro Kato,
Toshimitsu Takagi,
Mutsuto Kawahara,

Document Type: Proceeding Paper

Part of: North American Water and Environment Congress & Destructive Water


The numerical analysis of Mach reflection, which is the reflection of an obliquely incident solitary wave by a vertical wail, is presented in this paper. For the mathematical model in the analysis, the two dimensional Boussinesq equation is used. In order to solve the equation, the finite element method based on the linear triangular element and the conventional Galerkin method is applied in space. The combination of the explicit and the semi-implicit schemes is employed for the time integration. Moreover, one of the treatments for the open boundary condition, in which the analytical solution of the linearized Boussinesq equation in the outside domain is linked with the discrete values of velocity and water elevation in the inside domain, is applied for the modelling of the Mach reflection problem.

Subject Headings: Finite element method | Boussinesq equations | Solitary waves | Mathematical models | Water treatment | Two-dimensional models | Two-dimensional analysis

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