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The Lie-group shooting method for steady-state Burgers equation with high Reynolds number

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Abstract

The steady-state Burgers equation with high Reynolds number is a singularly perturbed boundary value problem. In order to depress the singularity we consider a coordinate transformation from the z-domain to the t-domain. Then we construct a very effective Lie-group shooting method to search a missing initial condition of slope through a weighting factor r ∈ (0,1). Furthermore, a closed-form formula is derived to calculate the unknown slope in terms of r in a more refined range identified. Numerical examples were examined to show that the new approach has high efficiency and high accuracy.

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Authors and Affiliations

  1. Department of Mechanical and Mechatronic Engineering, National Taiwan Ocean University, Keelung, 202, China

    Chein-Shan Liu, Jiang-Ren Chang & Chih-Wen Chang

  2. Department of Systems Engineering and Naval Architecture, National Taiwan Ocean University, Keelung, 202, China

    Chein-Shan Liu, Jiang-Ren Chang & Chih-Wen Chang

Authors
  1. Chein-Shan Liu
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  2. Jiang-Ren Chang
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  3. Chih-Wen Chang
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Corresponding author

Correspondence to Chein-Shan Liu.

Additional information

Project supported by the National Science Council of Taiwan (Grant No: NSC 94-2212-E-019-005).

Biography : LIU Chein-Shan (1958-05), Male, Professor

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Liu, CS., Chang, JR. & Chang, CW. The Lie-group shooting method for steady-state Burgers equation with high Reynolds number. J Hydrodyn 18 (Suppl 1), 359–364 (2006). https://doi.org/10.1007/BF03400473

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  • DOI: https://doi.org/10.1007/BF03400473

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