A characteristic space-time conservation element and solution element method for conservation laws II. Multidimensional extension

Hua Shen, Chih-yung Wen

Research output: Journal article publicationJournal articleAcademic researchpeer-review

28 Citations (Scopus)


The characteristic space-time conservation element and solution element (CE/SE) schemes proposed by Shen et al. (2015) [15] are straightforward extended to multidimensional schemes on 2D rectangular meshes which strictly follow the space-time conservation law. The schemes for solving both scalar conservation laws and compressible Euler equations with shock waves are developed. They are accurate and robust with CFL widely ranging from 0 to nearly 1. In Euler solvers, the frequently-used Harten, Lax and van Leer (HLL) Riemann solver, contact discontinuity restoring HLLC Riemann solver and Roe Riemann solver are employed to calculate the upwind fluxes as examples. When standard grid-aligned Riemann solvers are employed, the carbuncle phenomena are significantly suppressed when comparing with conventional upwind schemes. If rotated Riemann solvers are employed, nearly carbuncle-free results are obtained. Several well understood numerical examples are carried out to demonstrate that the 2D characteristic CE/SE schemes can simultaneously capture shocks and details of complex flow structures very well.
Original languageEnglish
Pages (from-to)775-792
Number of pages18
JournalJournal of Computational Physics
Publication statusPublished - 15 Jan 2016


  • Carbuncle phenomenon
  • Riemann solver
  • Shock capturing scheme
  • Space-time conservation element and solution element (CE/SE) method
  • Upwind scheme

ASJC Scopus subject areas

  • Computer Science Applications
  • Physics and Astronomy (miscellaneous)

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