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Application of the Homotopy Analysis Method to Fluid Flow Problems

In: Nonlinear Flow Phenomena and Homotopy Analysis

Author

Listed:
  • Kuppalapalle Vajravelu

    (University of Central Florida, Department of Mathematics)

  • Robert A. van Gorder

    (University of Central Florida, Department of Mathematics)

Abstract

The equations of viscous flow have been known for more than 100 years. In their complete form, these equations are very difficult to solve, even on modern digital computers. In fact, at high Reynolds numbers (turbulent flow), the equations are impossible to solve with present mathematical techniques, because the boundary conditions become randomly time-dependent. Nevertheless, it is very instructive to present and discuss these fundamental equations because they give many insights, yield several particular solutions, and can be examined for modeling purposes. Also, these equations can then be simplified, using Prandtl boundary-layer approximations. The resulting simpler system is very practical and yields many fruitful engineering solutions.

Suggested Citation

  • Kuppalapalle Vajravelu & Robert A. van Gorder, 2012. "Application of the Homotopy Analysis Method to Fluid Flow Problems," Springer Books, in: Nonlinear Flow Phenomena and Homotopy Analysis, chapter 0, pages 101-155, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-32102-3_5
    DOI: 10.1007/978-3-642-32102-3_5
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