Scientific Research and Essays

  • Abbreviation: Sci. Res. Essays
  • Language: English
  • ISSN: 1992-2248
  • DOI: 10.5897/SRE
  • Start Year: 2006
  • Published Articles: 2748

Full Length Research Paper

Semi-analytic solutions to Riemann problem for one-dimensional gas dynamics

Emad A. Az-Zo?bi
  • Emad A. Az-Zo?bi
  • Department of Mathematics and Statistics, Mutah University, Mutah P. O. Box 7, Al-Karak, Jordan.
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Kamal Al Dawoud
  • Kamal Al Dawoud
  • Department of Mathematics and Statistics, Mutah University, Mutah P. O. Box 7, Al-Karak, Jordan.
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  •  Received: 10 August 2014
  •  Accepted: 17 October 2014
  •  Published: 30 October 2014

Abstract

This work deals with the implementation of reduced differential transform method (RDTM) for solving the Riemann problem for gas dynamics in one dimension. The RDTM is an analytical method that can be applied to many linear and nonlinear partial differential equations and is capable of reducing the size of computations. Using this method, the solution is calculated in the form of convergent power series with easily computable components. The definition and basic properties of RDTM are investigated. Some new generalized formulas of reduced differential transforms are derived. The Riemann problem that describes the isentropic flow of an inviscid gas is considered to demonstrate the effectiveness and promising of the proposed algorithm.
 
Key words: Reduced differential transform method, gas dynamics, isentropic flow of an inviscid gas equations, conservation law.