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

108 Citations (Scopus)


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
Issue number1
Publication statusPublished - 2001 Nov 20
Externally publishedYes



  • 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)

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