Coordinate stretching and interface location II. A new PL expansion

An alternative to the perturbation expansion of Poincaré and Lighthill is proposed, and a simple method of deriving the new expansion is given, for the case of a nonsingular boundary. The new formulation has the advantage that the process of stretching of the independent coordinate is uncoupled from the rest of the problem, which can then be handled by standard techniques and programs. The method is illustrated by a simple example of pulsational instability in a one-zone approximation to a variable star.

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Work Title Coordinate stretching and interface location II. A new PL expansion
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Open Access
Creators
  1. Peter D. Usher
Keyword
  1. Poincare
  2. Lighthill
  3. Coordinate stretching
  4. Strained coordinates
  5. Renormalization
License CC BY 4.0 (Attribution)
Work Type Article
Publisher
  1. Journal of Computational Physics
Publication Date 1968
Publisher Identifier (DOI)
  1. https://doi.org/10.1016/0021-9991(68)90003-X
Deposited May 06, 2024

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Version 1
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  • Created
  • Updated
  • Updated Description, Publication Date Show Changes
    Description
    • Abstract
    • An alternative to the perturbation expansion of Poincaré and Lighthill is proposed, and a simple method of deriving the new expansion is given, for the case of a nonsingular boundary. The new formulation has the advantage that the process of stretching of the independent coordinate is uncoupled from the rest of the problem, which can then be handled by standard techniques and programs. The method is illustrated by a simple example of pulsational instability in a one-zone approximation to a variable star.
    Publication Date
    • 1968-07
  • Added Creator Peter D. Usher
  • Added 4b2a640c-b03f-49a9-80c6-74d9ad6c1b3d.pdf
  • Updated Keyword, License Show Changes
    Keyword
    • Poincare, Lighthill, coordinate stretching, strained coordinates, renormalization
    License
    • https://creativecommons.org/licenses/by/4.0/
  • Published
  • Updated
  • Updated Keyword, Publisher, Publisher Identifier (DOI), and 2 more Show Changes
    Keyword
    • Poincare, Lighthill, coordinate stretching, strained coordinates, renormalization
    • Poincare, Lighthill, Coordinate stretching, Strained coordinates, Renormalization
    Publisher
    • Journal of Computational Physics
    Publisher Identifier (DOI)
    • https://doi.org/10.1016/0021-9991(68)90003-X
    Description
    • Abstract
    • An alternative to the perturbation expansion of Poincaré and Lighthill is proposed, and a simple method of deriving the new expansion is given, for the case of a nonsingular boundary. The new formulation has the advantage that the process of stretching of the independent coordinate is uncoupled from the rest of the problem, which can then be handled by standard techniques and programs. The method is illustrated by a simple example of pulsational instability in a one-zone approximation to a variable star.
    Publication Date
    • 1968-07
    • 1968