A modified Mohapatra—Chaudhry two-four finite difference scheme for the shallow water equations

2015 International Conference on Mathematics, its Applications, and Mathematics Education

数学;教育

Budiasih, L.K.^1,2 ; Wiryanto, L.H.^2 ; Mungkasi, S.^1

Department of Mathematics, Faculty of Science and Technology, Sanata Dharma University, Mrican, Tromol Pos 29, Yogyakarta

55002, Indonesia^1

Department of Mathematics, Faculty of Mathematics and Natural Sciences, Bandung Institute of Technology, Jalan Ganesha 10, Bandung

40132, Indonesia^2

关键词: Boussinesq equations;    Conserved quantity;    Finite difference scheme;    Momentum equation;    Numerical results;    Shallow water equations;    Spurious oscillations;    Wetting and drying process;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/693/1/012012/pdf
DOI  :  10.1088/1742-6596/693/1/012012

学科分类：发展心理学和教育心理学

来源: IOP

【 摘 要 】

A two-four finite difference scheme for Boussinesq equations was developed by Mohapatra and Chaudhry in 2004. This scheme is of course also applicable to solve the shallow water equations. However this scheme is not robust to deal with dry bed, that is, spurious oscillations appear around wet-dry areas. In this paper we propose a modified two-four finite difference scheme to solve the shallow water equations involving (almost) dry bed. The modified scheme has fewer number of divisions by zero or almost zero, and at the same time, only conserved quantities (mass and momentum) are used in the evolution of the new scheme. The modification lies on the discretisation of the momentum equation. We discretise the momentum equation using the momentum variable itself rather than using the velocity variable as done by Mohapatra and Chaudhry. Numerical results show that our proposed scheme is more robust for wetting and drying processes of the shallow water equations.