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

  • Qijie Li (a1), Syazana Omar (a1), Xi Deng (a1) (a2) and Kensuke Yokoi (a1)

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.

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Corresponding author

*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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