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Incremental unknowns method based on the θ-scheme for time-dependent convection–diffusion equations

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  • Song, Lunji
  • Wu, Yujiang

Abstract

A θ-scheme using two-level incremental unknowns is presented for solving time-dependent convection–diffusion equations in two-dimensional case. The IMG algorithm (Inertial Manifold–Multigrid algorithm) including the second-order incremental unknowns is convergent. The incremental unknowns method based on the θ-scheme needs a stability condition as 0≤θ<1/2 and is unconditionally stable as 1/2≤θ≤1. By the GMRES method in the iteration at each time step, numerical results of the convection–diffusion equations are investigated and confirm that oscillations can be controlled by the incremental unknowns method.

Suggested Citation

  • Song, Lunji & Wu, Yujiang, 2009. "Incremental unknowns method based on the θ-scheme for time-dependent convection–diffusion equations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 79(7), pages 2001-2012.
    • Handle: RePEc:eee:matcom:v:79:y:2009:i:7:p:2001-2012
    DOI: 10.1016/j.matcom.2008.08.001
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    Cited by:

    1. Garcia, Salvador, 2011. "Aperiodic, chaotic lid-driven square cavity flows," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 81(9), pages 1741-1769.
    2. Garcia, Salvador, 2017. "Chaos in the lid-driven square cavity," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 142(C), pages 98-112.

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