Journal of Fluid Mechanics

Numerical solution of free-boundary problems in fluid mechanics. Part 1. The finite-difference technique

G.  Ryskin a1p1 and L. G.  Leal a1
a1 Department of Chemical Engineering, California Institute of Technology, Pasadena, California 91125

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We present here a brief description of a numerical technique suitable for solving axisymmetric (or two-dimensional) free-boundary problems of fluid mechanics. The technique is based on a finite-difference solution of the equations of motion on an orthogonal curvilinear coordinate system, which is also constructed numerically and always adjusted so as to fit the current boundary shape. The overall solution is achieved via a global iterative process, with the condition of balance between total normal stress and the capillary pressure at the free boundary being used to drive the boundary shape to its ultimate equilibrium position.

(Published Online April 20 2006)
(Received April 11 1983)
(Revised April 27 1984)

p1 Present address: Department of Chemical Engineering, Northwestern University, Evanston, Illinois 60201.