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open-access-imgOpen AccessThe Pi − ${\text{P}}_{1}^{\text{NC}}$ Finite Element Method for 1D wave simulation using Shallow Water Equations
P. V. Swastika,
Sri Redjeki Pudjaprasetya,
Didit Adytia
Publication year2020
Publication title
iop conference series: earth and environmental science
PublisherIOP Publishing
We study a simple numerical scheme based on a new type of Finite Element Method (FEM) to solve the 1D Shallow Water Equations. In the new scheme, the surface elevation variable is approximated by a linear continuous basis function ( P 1 ) and the velocity potential variable is approximated by the one-dimensional discontinuous linear non-conforming basis function ( P 1 N C ). Here, we implement the P 1 − P 1 N C finite element pair to solve the 1D Shallow Water Equations on a structured grid, whereas 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 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.
Subject(s)basis (linear algebra) , basis function , biology , evolutionary biology , extended finite element method , finite element method , function (biology) , geometry , grid , mathematical analysis , mathematics , mixed finite element method , physics , shallow water equations , thermodynamics , variable (mathematics) , waves and shallow water

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