Modification of 2-D Time-Domain Shallow Water Wave Equation using Asymptotic Expansion Method

4th International Conference on Operational Research

Khairuman, Teuku^1,4 ; Nasruddin, M.N.^1 ; Tulus^2 ; Ramli, Marwan^3

Department of Physics, Faculty of Science, University of Sumatera Utara, Medan, Indonesia^1

Department of Mathematics, Faculty of Science, University of Sumatera Utara, Medan, Indonesia^2

Department of Mathematics, Faculty of Science, Syiah Kuala University, Aceh, Indonesia^3

Department of Physics, Faculty of Science, Syiah Kuala University, Aceh, Indonesia^4

关键词: Asymptotic expansion method;    Boussinesq equations;    Computational time and memory;    Dispersion relations;    Linear modeling;    Nonlinear partial differential equations;    Shallow water theory;    Shallow water wave equation;   

Others  :  https://iopscience.iop.org/article/10.1088/1757-899X/300/1/012049/pdf
DOI  :  10.1088/1757-899X/300/1/012049

来源: IOP

【 摘 要 】

Generally, research on the tsunami wave propagation model can be conducted by using a linear model of shallow water theory, where a non-linear side on high order is ignored. In line with research on the investigation of the tsunami waves, the Boussinesq equation model underwent a change aimed to obtain an improved quality of the dispersion relation and non-linearity by increasing the order to be higher. To solve non-linear sides at high order is used a asymptotic expansion method. This method can be used to solve non linear partial differential equations. In the present work, we found that this method needs much computational time and memory with the increase of the number of elements.