Exactly conservative semi-Lagrangian scheme for multi-dimensional hyperbolic equations with directional splitting technique

Takashi Nakamura, Ryotaro Tanaka, Takashi Yabe, Kenji Takizawa

Research output: Contribution to journalArticle

106 Citations (Scopus)

Abstract

A new numerical method that guarantees exact mass conservation is proposed to solve multidimensional hyperbolic equations in semi-Lagrangian form. The method is based on the constrained interpolation profile (CIP) scheme and keeps the many good characteristics of the original CIP scheme. The CIP strategy is applied to the integral form of variables. Although the advection and nonadvection terms are separately treated, mass conservation is kept in the form of a spatial profile inside a grid cell. Therefore, it retains various advantages of the semi-Lagrangian solution with exact conservation, which has been beyond the capability of conventional semi-Lagrangian schemes.

Original languageEnglish
Pages (from-to)171-207
Number of pages37
JournalJournal of Computational Physics
Volume174
Issue number1
DOIs
Publication statusPublished - 2001 Nov 20
Externally publishedYes

Fingerprint

Conservation
Interpolation
interpolation
conservation
profiles
Advection
Numerical methods
advection
grids
cells

Keywords

  • CIP-CSL2
  • Computational algorithm
  • Cubic interpolation
  • Mass conservation
  • Monotone preserving
  • Multi-dimensions
  • R-CIP-CSL2
  • Semi-Lagrangian

ASJC Scopus subject areas

  • Computer Science Applications
  • Physics and Astronomy(all)

Cite this

Exactly conservative semi-Lagrangian scheme for multi-dimensional hyperbolic equations with directional splitting technique. / Nakamura, Takashi; Tanaka, Ryotaro; Yabe, Takashi; Takizawa, Kenji.

In: Journal of Computational Physics, Vol. 174, No. 1, 20.11.2001, p. 171-207.

Research output: Contribution to journalArticle

@article{105d0930f4534f40b8319fb0cea3491f,
title = "Exactly conservative semi-Lagrangian scheme for multi-dimensional hyperbolic equations with directional splitting technique",
abstract = "A new numerical method that guarantees exact mass conservation is proposed to solve multidimensional hyperbolic equations in semi-Lagrangian form. The method is based on the constrained interpolation profile (CIP) scheme and keeps the many good characteristics of the original CIP scheme. The CIP strategy is applied to the integral form of variables. Although the advection and nonadvection terms are separately treated, mass conservation is kept in the form of a spatial profile inside a grid cell. Therefore, it retains various advantages of the semi-Lagrangian solution with exact conservation, which has been beyond the capability of conventional semi-Lagrangian schemes.",
keywords = "CIP-CSL2, Computational algorithm, Cubic interpolation, Mass conservation, Monotone preserving, Multi-dimensions, R-CIP-CSL2, Semi-Lagrangian",
author = "Takashi Nakamura and Ryotaro Tanaka and Takashi Yabe and Kenji Takizawa",
year = "2001",
month = "11",
day = "20",
doi = "10.1006/jcph.2001.6888",
language = "English",
volume = "174",
pages = "171--207",
journal = "Journal of Computational Physics",
issn = "0021-9991",
publisher = "Academic Press Inc.",
number = "1",

}

TY - JOUR

T1 - Exactly conservative semi-Lagrangian scheme for multi-dimensional hyperbolic equations with directional splitting technique

AU - Nakamura, Takashi

AU - Tanaka, Ryotaro

AU - Yabe, Takashi

AU - Takizawa, Kenji

PY - 2001/11/20

Y1 - 2001/11/20

N2 - A new numerical method that guarantees exact mass conservation is proposed to solve multidimensional hyperbolic equations in semi-Lagrangian form. The method is based on the constrained interpolation profile (CIP) scheme and keeps the many good characteristics of the original CIP scheme. The CIP strategy is applied to the integral form of variables. Although the advection and nonadvection terms are separately treated, mass conservation is kept in the form of a spatial profile inside a grid cell. Therefore, it retains various advantages of the semi-Lagrangian solution with exact conservation, which has been beyond the capability of conventional semi-Lagrangian schemes.

AB - A new numerical method that guarantees exact mass conservation is proposed to solve multidimensional hyperbolic equations in semi-Lagrangian form. The method is based on the constrained interpolation profile (CIP) scheme and keeps the many good characteristics of the original CIP scheme. The CIP strategy is applied to the integral form of variables. Although the advection and nonadvection terms are separately treated, mass conservation is kept in the form of a spatial profile inside a grid cell. Therefore, it retains various advantages of the semi-Lagrangian solution with exact conservation, which has been beyond the capability of conventional semi-Lagrangian schemes.

KW - CIP-CSL2

KW - Computational algorithm

KW - Cubic interpolation

KW - Mass conservation

KW - Monotone preserving

KW - Multi-dimensions

KW - R-CIP-CSL2

KW - Semi-Lagrangian

UR - http://www.scopus.com/inward/record.url?scp=0035923853&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0035923853&partnerID=8YFLogxK

U2 - 10.1006/jcph.2001.6888

DO - 10.1006/jcph.2001.6888

M3 - Article

VL - 174

SP - 171

EP - 207

JO - Journal of Computational Physics

JF - Journal of Computational Physics

SN - 0021-9991

IS - 1

ER -