An Efficient Time-Marching Scheme for Solving Compressible Euler Equations

Hisaaki Daiguji, Satoru Yamamoto

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)


An implicit time-marching finite-difference scheme is proposed for analysing steady two-dimensional inviscid transonic flows. The scheme is based on the well-known Beam-Warming delta-form approximate factorization scheme, but this is improved on the following two points: ( i ) In order to treat the fixed wall boundary condition without difficulty, momentum equations of contravariant velocity components as fundamental equations in curvilinear coordinates are used. (ii) To calculate stably with a sufficiently large Courant number, the central-difference of the Crank-Nicholson method is replaced by the upstream-difference of the Robert-Weiss method. The upstreaming is performed on the basis of the theory of characteristics and does not influence the accuracy of the solution. The flows through a converging-diverging nozzle and over a symmetric wing are calculated. The calcutated results agree well with the existing theories.

Original languageEnglish
Pages (from-to)248-254
Number of pages7
JournalTransactions of the Japan Society of Mechanical Engineers Series B
Issue number473
Publication statusPublished - 1986
Externally publishedYes


  • Compressible Flow
  • Numerical Analysis
  • Shock Capturing Method
  • Time-Marching Method Finite-Difference Method
  • Transonic Flow

ASJC Scopus subject areas

  • Condensed Matter Physics
  • Mechanical Engineering


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