Higher-order schemes with CIP method and adaptive Soroban grid towards mesh-free scheme

Takashi Yabe; Hiroki Mizoe; Kenji Takizawa; Hiroshi Moriki; Hyo Nam Im; Youichi Ogata

doi:10.1016/j.jcp.2003.08.019

Higher-order schemes with CIP method and adaptive Soroban grid towards mesh-free scheme

Takashi Yabe^*, Hiroki Mizoe, Kenji Takizawa, Hiroshi Moriki, Hyo Nam Im, Youichi Ogata

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

65 Citations (Scopus)

Abstract

A new class of body-fitted grid system that can keep the third-order accuracy in time and space is proposed with the help of the CIP (constrained interpolation profile/cubic interpolated propagation) method. The grid system consists of the straight lines and grid points moving along these lines like abacus - Soroban in Japanese. The length of each line and the number of grid points in each line can be different. The CIP scheme is suitable to this mesh system and the calculation of large CFL (>10) at locally refined mesh is easily performed. Mesh generation and searching of upstream departure point are very simple and almost mesh-free treatment is possible. Adaptive grid movement and local mesh refinement are demonstrated.

Original language	English
Pages (from-to)	57-77
Number of pages	21
Journal	Journal of Computational Physics
Volume	194
Issue number	1
DOIs	https://doi.org/10.1016/j.jcp.2003.08.019
Publication status	Published - 2004 Feb 10
Externally published	Yes

Keywords

Curvilinear coordinate
Mesh free
Numerical algorithm
Semi-Lagrangian scheme
Third-order scheme

ASJC Scopus subject areas

Numerical Analysis
Modelling and Simulation
Physics and Astronomy (miscellaneous)
Physics and Astronomy(all)
Computer Science Applications
Computational Mathematics
Applied Mathematics

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10.1016/j.jcp.2003.08.019

Cite this

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title = "Higher-order schemes with CIP method and adaptive Soroban grid towards mesh-free scheme",

abstract = "A new class of body-fitted grid system that can keep the third-order accuracy in time and space is proposed with the help of the CIP (constrained interpolation profile/cubic interpolated propagation) method. The grid system consists of the straight lines and grid points moving along these lines like abacus - Soroban in Japanese. The length of each line and the number of grid points in each line can be different. The CIP scheme is suitable to this mesh system and the calculation of large CFL (>10) at locally refined mesh is easily performed. Mesh generation and searching of upstream departure point are very simple and almost mesh-free treatment is possible. Adaptive grid movement and local mesh refinement are demonstrated.",

keywords = "Curvilinear coordinate, Mesh free, Numerical algorithm, Semi-Lagrangian scheme, Third-order scheme",

author = "Takashi Yabe and Hiroki Mizoe and Kenji Takizawa and Hiroshi Moriki and Im, {Hyo Nam} and Youichi Ogata",

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language = "English",

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T1 - Higher-order schemes with CIP method and adaptive Soroban grid towards mesh-free scheme

AU - Yabe, Takashi

AU - Mizoe, Hiroki

AU - Takizawa, Kenji

AU - Moriki, Hiroshi

AU - Im, Hyo Nam

AU - Ogata, Youichi

PY - 2004/2/10

Y1 - 2004/2/10

N2 - A new class of body-fitted grid system that can keep the third-order accuracy in time and space is proposed with the help of the CIP (constrained interpolation profile/cubic interpolated propagation) method. The grid system consists of the straight lines and grid points moving along these lines like abacus - Soroban in Japanese. The length of each line and the number of grid points in each line can be different. The CIP scheme is suitable to this mesh system and the calculation of large CFL (>10) at locally refined mesh is easily performed. Mesh generation and searching of upstream departure point are very simple and almost mesh-free treatment is possible. Adaptive grid movement and local mesh refinement are demonstrated.

AB - A new class of body-fitted grid system that can keep the third-order accuracy in time and space is proposed with the help of the CIP (constrained interpolation profile/cubic interpolated propagation) method. The grid system consists of the straight lines and grid points moving along these lines like abacus - Soroban in Japanese. The length of each line and the number of grid points in each line can be different. The CIP scheme is suitable to this mesh system and the calculation of large CFL (>10) at locally refined mesh is easily performed. Mesh generation and searching of upstream departure point are very simple and almost mesh-free treatment is possible. Adaptive grid movement and local mesh refinement are demonstrated.

KW - Curvilinear coordinate

KW - Mesh free

KW - Numerical algorithm

KW - Semi-Lagrangian scheme

KW - Third-order scheme

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Higher-order schemes with CIP method and adaptive Soroban grid towards mesh-free scheme

Abstract

Keywords

ASJC Scopus subject areas

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