The P1-P1NC Finite Element Method for 1D wave simulation using Shallow Water Equation
P. V. Swastika (1*), S.R. Pudjaprasetya (2), D. Adytia (3)
(1,2) Industrial and Financial Mathematics Research Group, Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung, Jl. Ganesha 10, Bandung, 40132, Indonesia
(3) School of Computing, Telkom University, Jl. Telekomunikasi, 1 Bandung 40257, Indonesia
Abstract
We study a simple numerical scheme based on a new type of Finite Element Method (FEM) to solve 1D Shallow Water Equation (SWE). In the new scheme, the surface elevation variable is approximated by a linear continuous base function (P1) and the velocity potential variable is approximated by one-dimensional discontinuous linear non-conforming base function (P1NC). Here, we implement the P1-P1NC finite element pair to solve the 1D SWE on a structured grid, whereas the the Runge Kutta method is adopted for time integration. We verified the resulting scheme by conducting several simulations such as a standing wave simulation, and a propagation of an initial hump over sloping bathymetry. The resulting scheme free from numerical damping error, conservative and both standing wave and shoaling phenomena are well simulated.
Keywords: finite element method, non-conformal base function, structured grid, shallow water equation.
Topic: Coastal and Ocean Dynamics