Vanel, J. M.; Peyret, R.; Bontoux, P. 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. Cited in 27 Documents MSC: 76B47 Vortex flows for incompressible inviscid fluids 76M99 Basic methods in fluid mechanics Keywords:unsteady two-dimensional incompressible flows; Chebyshev polynomial expansions; boundary conditions; accuracy; stability; iterative solution procedure; influence matrix technique; two-dimensional formulation Citations:Zbl 0591.00024 PDFBibTeX XML