Numerical Solution of the Viscous Flow Past a Cylinder with a Non-global Yet Spectrally Convergent Meshless Collocation Method
The flow of a viscous fluid past a cylinder is a classical problem in fluid-structure interaction and a benchmark for numerical methods in computational fluid dynamics. We solve it with the recently introduced radial basis function-based partition of unity method (RBF-PUM), which is a spectrally convergent collocation meshless scheme well suited to this kind of problem. The resulting discrete system of nonlinear equations is tackled with a trust-region algorithm, whose performance is much enhanced by the analytic Jacobian which is provided alongside. Preliminary results up to Re = 60 with just 1292 nodes are shown.
F. Bernal acknowledges support from FCT grant SFRH/BPD/79986/2011 and INESC-ID. A. Heryudono is partially supported by NSF Grant DMS 1552238.
- 1.G.G. Stokes, On the effect of the internal friction of fluids on the motion of pendulums. Trans. Camb. Philos. Soc. 9, 8–106 (1851)Google Scholar
- 3.F. Mandujano, R. Peralta-Fabi, On the viscous steady flow around a circular cylinder. Revista Mexicana de Física 51(1), 87–99 (2005)Google Scholar
- 7.I. Tominec, Parallel localized radial basis function methods for the shallow water equations on the sphere. MSc thesis, Technische Universitaet Muenchen (2017)Google Scholar