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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)

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. Email addresses: (K. Yokoi), (Q. Li), (S. Omar), (X. Deng)
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[6] J. M. Hyman Accurate monotonicity preserving cubic interpolation. SIAM Journal on Scientific and Statistical Computing 4, 4 (1983), 645654.

[16] C.-W. Shu Advanced Numerical Approximation of Nonlinear Hyperbolic Equations: Lectures given at the 2nd Session of the Centro Internazionale Matematico Estivo (C.I.M.E.) held in Cetraro, Italy, June 23–28, 1997. Springer Berlin Heidelberg, Berlin, Heidelberg, 1998, ch. Essentially non-oscillatory and weighted essentially non-oscillatory schemes for hyperbolic conservation laws, pp. 325432.

[20] Z. Sun , H. Teng , and F. Xiao A slope constrained 4th order multi-moment finite volume method with weno limiter. Communications in Computational Physics 18 (2015), 901930.

[30] K. Yokoi A density-scaled continuum surface force model within a balanced force formulation. Journal of Computational Physics 278 (2014), 221228.

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Communications in Computational Physics
  • ISSN: 1815-2406
  • EISSN: 1991-7120
  • URL: /core/journals/communications-in-computational-physics
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