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Similarity Analysis of Boundary Value Problems with Finite Boundaries

In: Group Invariance in Engineering Boundary Value Problems

Author

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  • R. Seshadri

    (Syncrude Canada Limited)

  • T. Y. Na

    (University of Michigan—Dearborn, Department of Mechanical Engineering)

Abstract

It is commonly believed that similarity analysis of boundary value problems in science and engineering is domain-and-boundary condition limited, in that semi-infinite or infinite domains are required. A review of literature on similarity would, indeed, reveal that similarity solutions are mostly available for boundary value problems that lack a characteristic length in one or more coordinate directions. In his book, Hansen 1 points out that problems with finite boundaries associated with finite, non-zero values do not usually possess similarity solutions. Therefore, he suggests that a lack of characteristic length in a coordinate direction could be used as a hint to proceed with similarity analysis and seek possible solutions.

Suggested Citation

  • R. Seshadri & T. Y. Na, 1985. "Similarity Analysis of Boundary Value Problems with Finite Boundaries," Springer Books, in: Group Invariance in Engineering Boundary Value Problems, chapter 0, pages 91-102, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4612-5102-6_5
    DOI: 10.1007/978-1-4612-5102-6_5
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