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Sloshing simulation of standing wave with time-independent finite difference method for Euler equations

Sloshing simulation of standing wave with time-independent finite difference method for Euler equations
Sloshing simulation of standing wave with time-independent finite difference method for Euler equations
The numerical solutions of standing waves for Euler equations with the nonlinear free surface boundary condition in a two-dimensional (2D) tank are studied. The irregular tank is mapped onto a fixed square domain through proper mapping functions. A staggered mesh system is employed in a 2D tank to calculate the elevation of the transient fluid. A time-independent finite difference method, which is developed by Bangfuh Chen, is used to solve the Euler equations for incompressible and inviscid fluids. The numerical results agree well with the analytic solutions and previously published results. The sloshing profiles of surge and heave motion with initial standing waves are presented. The results show very clear nonlinear and beating phenomena.
euler equation, finite difference method, numerical simulation, crank-nicolson scheme
0253-4827
1475-1488
Luo, Zhi-qiang
78de99d1-a88b-4f1f-9c56-4fa8bc1dea71
Chen, Zhi-Min
e4f81e6e-5304-4fd6-afb2-350ec8d1e90f
Luo, Zhi-qiang
78de99d1-a88b-4f1f-9c56-4fa8bc1dea71
Chen, Zhi-Min
e4f81e6e-5304-4fd6-afb2-350ec8d1e90f

Luo, Zhi-qiang and Chen, Zhi-Min (2011) Sloshing simulation of standing wave with time-independent finite difference method for Euler equations. Applied Mathematics and Mechanics, 32 (11), 1475-1488. (doi:10.1007/s10483-011-1516-6).

Record type: Article

Abstract

The numerical solutions of standing waves for Euler equations with the nonlinear free surface boundary condition in a two-dimensional (2D) tank are studied. The irregular tank is mapped onto a fixed square domain through proper mapping functions. A staggered mesh system is employed in a 2D tank to calculate the elevation of the transient fluid. A time-independent finite difference method, which is developed by Bangfuh Chen, is used to solve the Euler equations for incompressible and inviscid fluids. The numerical results agree well with the analytic solutions and previously published results. The sloshing profiles of surge and heave motion with initial standing waves are presented. The results show very clear nonlinear and beating phenomena.

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More information

Published date: 2011
Keywords: euler equation, finite difference method, numerical simulation, crank-nicolson scheme
Organisations: Fluid Structure Interactions Group

Identifiers

Local EPrints ID: 204423
URI: http://eprints.soton.ac.uk/id/eprint/204423
ISSN: 0253-4827
PURE UUID: 323c75d0-986b-4746-a0b5-9b708b8a19b6

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Date deposited: 28 Nov 2011 14:54
Last modified: 07 Jan 2022 21:06

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Contributors

Author: Zhi-qiang Luo
Author: Zhi-Min Chen

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