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Simulation of Incompressible Free Surface Flow Using the Volume Preserving Level Set Method

Part of: Incompressible viscous fluids Basic methods in fluid mechanics Equations of mathematical physics and other areas of application

Published online by Cambridge University Press:  15 October 2015

Ching-Hao Yu  and
Tony Wen-Hann Sheu
Ching-Hao Yu
Affiliation:
Department of Ocean Science and Engineering, Zhejiang University, Yuhangtang Road, Hangzhou, Zhejiang, P.R.China
Tony Wen-Hann Sheu*
Affiliation:
Department of Engineering Science and Ocean Engineering, National Taiwan University, No. 1, Sec. 4, Roosevelt Road, Taipei, Taiwan Institute of Applied Mathematical Sciences, National Taiwan University, Taiwan Center of Advanced Study in Theoretical Sciences (CASTS), National Taiwan University, Taiwan
*
*Corresponding author. Email address: [email protected] (T. W.-H. Sheu)
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Abstract

This study aims to develop a numerical scheme in collocated Cartesian grids to solve the level set equation together with the incompressible two-phase flow equations. A seventh-order accurate upwinding combined compact difference (UCCD7) scheme has been developed for the approximation of the first-order spatial derivative terms shown in the level set equation. Developed scheme has a higher accuracy with a three-point grid stencil to minimize phase error. To preserve the mass of each phase all the time, the temporal derivative term in the level set equation is approximated by the sixth-order accurate symplectic Runge-Kutta (SRK6) scheme. All the simulated results for the dam-break, Rayleigh-Taylor instability, bubble rising, two-bubble merging, and milkcrown problems in two and three dimensions agree well with the available numerical or experimental results.

Keywords

Level set equationupwinding combined compact difference schemethree-point grid stencilminimize phase errorsymplectic Runge-Kutta

MSC classification

Secondary: 35Q30: Navier-Stokes equations 76D05: Navier-Stokes equations 76D27: Other free-boundary flows; Hele-Shaw flows 76M20: Finite difference methods
Type
Research Article
Information
Communications in Computational Physics , Volume 18 , Issue 4 , October 2015 , pp. 931 - 956
Copyright
Copyright © Global-Science Press 2015 

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