Jeffery-hamel flow with maple: a case study of integration of elliptic functions in a cas

ABSTRACT

This paper takes a classical problem in two-dimensional fluid flow-namely, flow into or out of a wedge-shaped channel with a sink or source at the vertex, which flow is known as Jeffery-Hamel flow and has "well-known" solutions containing elliptic functions-and tries to duplicate, or even extend, the classical solutions by using a CAS, in this instance Maple. The purposes of this case study include examining just how good CAS can be at elliptic functions; and, more importantly, identifying needs for improvement. Another purpose is to compare the analytical solution with modern numerical solutions. Finally, we believe that this work will motivate improvements to CAS facilities for automatic case analysis. As an aside, we present some simple methods for integration of elliptic functions that seem not to be widely known.

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INDEX TERMS

Primary Classification:
  I. Computing Methodologies
  I.1 SYMBOLIC AND ALGEBRAIC MANIPULATION
      I.1.4 Applications

General Terms:
Algorithms, Performance

Keywords:
elliptic functions, integration