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Constrained Interpolation Profile Conservative Semi-Lagrangian Scheme Based on Third-Order Polynomial Functions and Essentially Non-Oscillatory (CIP-CSL3ENO) Scheme

Part of: Partial differential equations, initial value and time-dependent initial-boundary value problems Hyperbolic equations and systems Two-phase and multiphase flows

Published online by Cambridge University Press:  06 July 2017

Qijie Li ,
Syazana Omar ,
Xi Deng  and
Kensuke Yokoi
Qijie Li*
Affiliation:
School of Engineering, Cardiff University, Cardiff, CF24 3AA, UK
Syazana Omar*
Affiliation:
School of Engineering, Cardiff University, Cardiff, CF24 3AA, UK
Xi Deng*
Affiliation:
School of Engineering, Cardiff University, Cardiff, CF24 3AA, UK Department of Energy Sciences, Tokyo Institute of Technology, Yokohama, 226-8502, Japan
Kensuke Yokoi*
Affiliation:
School of Engineering, Cardiff University, Cardiff, CF24 3AA, UK
*
*Corresponding author. Email addresses:YokoiK@cardiff.ac.uk (K. Yokoi), liq33@cardiff.ac.uk (Q. Li), omars2@cardiff.ac.uk (S. Omar), deng.x.aa@m.titech.ac.jp (X. Deng)
*Corresponding author. Email addresses:YokoiK@cardiff.ac.uk (K. Yokoi), liq33@cardiff.ac.uk (Q. Li), omars2@cardiff.ac.uk (S. Omar), deng.x.aa@m.titech.ac.jp (X. Deng)
*Corresponding author. Email addresses:YokoiK@cardiff.ac.uk (K. Yokoi), liq33@cardiff.ac.uk (Q. Li), omars2@cardiff.ac.uk (S. Omar), deng.x.aa@m.titech.ac.jp (X. Deng)
*Corresponding author. Email addresses:YokoiK@cardiff.ac.uk (K. Yokoi), liq33@cardiff.ac.uk (Q. Li), omars2@cardiff.ac.uk (S. Omar), deng.x.aa@m.titech.ac.jp (X. Deng)
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Abstract

We propose a fully conservative and less oscillatory multi-moment scheme for the approximation of hyperbolic conservation laws. The proposed scheme (CIP-CSL3ENO) is based on two CIP-CSL3 schemes and the essentially non-oscillatory (ENO) scheme. In this paper, we also propose an ENO indicator for the multimoment framework, which intentionally selects non-smooth stencil but can efficiently minimize numerical oscillations. The proposed scheme is validated through various benchmark problems and a comparison with an experiment of two droplets collision/separation. The CIP-CSL3ENO scheme shows approximately fourth-order accuracy for smooth solution, and captures discontinuities and smooth solutions simultaneously without numerical oscillations for solutions which include discontinuities. The numerical results of two droplets collision/separation (3D free surface flow simulation) show that the CIP-CSL3ENO scheme can be applied to various types of fluid problems not only compressible flow problems but also incompressible and 3D free surface flow problems.

Keywords

CIP-CSL schemeENO schemeconservation lawsfree surface flows

MSC classification

Secondary: 35L65: Conservation laws 65M06: Finite difference methods 65M08: Finite volume methods 76T10: Liquid-gas two-phase flows, bubbly flows
Type
Research Article
Information
Communications in Computational Physics , Volume 22 , Issue 3 , September 2017 , pp. 765 - 788
Copyright
Copyright © Global-Science Press 2017 

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