The vector potential in the numerical solution of three-dimensional fluid dynamics problems in multiply connected regions

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Abstract

The numerical solution of three-dimensional fluid flow problems in multiply connected regions using the vector potential formulation is reviewed. The major difficulty in such a formulation is the determination of boundary conditions for the vector potential. Two existing boundary formulations are examined, and it is shown that whilst one of the formulations leads to indeterminate vector potential boundary conditions for multiply connected solutions, the other presents well-defined conditions but is numerically not implementable. A new alternative is then proposed, and its validity and practicability are demonstrated with the solution of several annular cavity problems.

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