International Journal of
Science and Technology Education Research

  • Abbreviation: Int. J. Sci. Technol. Educ. Res.
  • Language: English
  • ISSN: 2141-6559
  • DOI: 10.5897/IJSTER
  • Start Year: 2010
  • Published Articles: 79

Full Length Research Paper

Implicit total variation diminishing (TVD) and essentially non-oscillatory (ENO) algorithms applied to the euler equations in three-dimensions

  Edisson Sávio de Góes Maciel  
  Rua Demócrito Cavalcanti, 152, Afogados, Recife, Pernambuco 50750-080, Brazil.
Email: [email protected]

  •  Accepted: 25 October 2011
  •  Published: 31 December 2011



In the present work, the Yee, Warming and Harten and the Yang schemes are implemented, on a finite volume context and using a structured spatial discretization, to solve the Euler equations in three-dimensions. The former is a TVD (Total Variation Diminishing) high resolution scheme, whereas the latter is a TVD or ENO (Essentially Non-Oscillatory) high resolution algorithm. All three schemes are flux difference splitting ones. An implicit formulation is employed to solve the Euler equations. A spatially variable time step procedure is employed to accelerate the convergence of the numerical schemes. This technique has provided excellent gains in terms of convergence acceleration, as observed by Maciel. The physical problems of the transonic flow along a convergent-divergent nozzle, the low supersonic flow along a ramp, and the moderate supersonic flow along a compression corner are studied. The results have demonstrated that more severe pressure fields are obtained by the Yee, Warming and Harten scheme, although better pressure distributions and accuracy are obtained by the Yang’s schemes.


Key Words: Yee, Warming and Harten algorithm, total variation diminishing high resolution scheme, Yang algorithms, TVD/ENO high resolution schemes, Euler equations.

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