Space-Time Spectral Element Methods for One-Dimensional Nonlinear Advection-Diffusion Problems

Pinhas Bar-Yoseph, Eduard Moses, Uzi Zrahia, Alexander L. Yarin

Research output: Contribution to journalArticlepeer-review

42 Citations (Scopus)


The following space-time Galerkin spectral element methods are developed and applied to solve the Burgers equation with small viscosity: (a) coupled methods, consisting of an explicit method for hyperbolic dominated equations and an implicit method for parabolic dominated equations; (b) two splitting methods which solve the hyperbolic substep explicitly and the parabolic one implicitly (one uses spectral elements in the explicit part and the other uses the Adams-Bashforth multistep method). A subcycling technique, in which several convective steps are taken for each implicit viscous step was also investigated for the two splitting methods. A stability analysis of the four methods is performed and subsequent results are debated. A convergence study and a comparison of computer execution time for the four methods is made and the results are discussed. Comparative study leads to the conclusion that the space-time spectral element splitting method with subcycling is superior to the other methods presented in terms of robustness and computer execution time. The number of subcycles should be kept low (2-3) in order to avoid significant loss of accuracy. The coupled explicit method is also applied to the solution of the one-dimensional coupled continuity, momentum, and energy equations for non-isothermal flow of an ideal gas with temperature dependent properties in a cylindrical duct of variable radius.

Original languageEnglish
Pages (from-to)62-74
Number of pages13
JournalJournal of Computational Physics
Issue number1
Publication statusPublished - 1995 Jun

ASJC Scopus subject areas

  • Numerical Analysis
  • Modelling and Simulation
  • Physics and Astronomy (miscellaneous)
  • Physics and Astronomy(all)
  • Computer Science Applications
  • Computational Mathematics
  • Applied Mathematics


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