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A pseudo-spectral solution of vorticity-stream function equations using the influence matrix technique. (English) Zbl 0606.76030

Numerical methods for fluid dynamics II, Proc. Conf., Reading/UK 1985, Inst. Math. Appl. Conf. Ser., New Ser. 7, 463-475 (1986).
[For the entire collection see Zbl 0591.00024.]
We present a fast and accurate method for computing unsteady two- dimensional incompressible flows. The method makes use of the vorticity and the stream function as dependent variables approximated by means of Chebyshev polynomial expansions. When using these variables the delicate question is the derivation of proper boundary conditions for the vorticity. The treatment of these conditions must preserve accuracy, stability and should avoid the use of an iterative solution procedure. The method developed here makes use of the influence matrix technique.
Our purpose is to give a two-dimensional formulation of the method, to point out the theoretical and numerical difficulties associated with it, and finally to present numerical results illustrating the properties of the method.

MSC:

76B47 Vortex flows for incompressible inviscid fluids
76M99 Basic methods in fluid mechanics

Citations:

Zbl 0591.00024