Abstract
For the two-dimensional, incompressible Navier-Stokes equations the pure stream function formulation leads to one nonlinear fourth-order differential equation. With Newton linearization the stream function equation can be approximated either by Lagrangian or by Hermitian formulas. The system of finite difference equations is solved directly, taking into account the special structure of the matrix. The main features of the finite difference approximations are discussed with respect to accuracy, stability and computation time. Results are shown and compared with other authors for the steady flow around a circular cylinder.
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Rieger, E., Schütz, H., Wolter, D., Thiele, F. (1990). A Comparison of Finite-Difference Approximations for the Stream Function Formulation of the Incompressible Navier-Stokes Equations. In: Hackbusch, W., Rannacher, R. (eds) Numerical Treatment of the Navier-Stokes Equations. Notes on Numerical Fluid Mechanics (NNFM), vol 30 5. Vieweg+Teubner Verlag, Wiesbaden. https://doi.org/10.1007/978-3-663-14004-7_10
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DOI: https://doi.org/10.1007/978-3-663-14004-7_10
Publisher Name: Vieweg+Teubner Verlag, Wiesbaden
Print ISBN: 978-3-528-07630-6
Online ISBN: 978-3-663-14004-7
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