A Meshfree Method for the Analysis of Planar Flows of Inviscid Fluids
A variant of a vortex particle-in-cell method is proposed for computing 2D inviscid incompressible flows in a closed domain. The governing equations are the 2D Euler equations in terms of the stream function and the vorticity, or geophysical models of the atmosphere. The approach is based on an approximation of the vorticity field using its values at a set of fluid particles and the stream function is computed by a Galerkin method. The flow domain is divided into rectangular cells. Vorticity in every cell is interpolated by a third order polynomial. The resultant piecewise continuous polynomial approximation of the vorticity is employed to derive analytically Galerkin’s coefficients of the stream function expansion. A parallel algorithm of the proposed method is also presented. The performance of the method is illustrated by some numerical results dealing with flows trough channels and the dynamics of the multipoles vortex patch calculation.
KeywordsIncompressible inviscid flows Vortices in cells method Vortex dynamics
The author would like to acknowledge the grants 11-01-00708 and 12-01-00668 from the Russian Foundation for Basic Research.
- 10.Z. Kizner, R. Khvoles, J.C. McWilliams, Rotating multipoles on the f- and \(\gamma \)-planes. Phys. Fluid 19(1), 016603, 13 (2007)Google Scholar
- 11.P. Koumoutsakos, Inviscid axisymmetrization of an elliptical vortex. J. Comput. Phys. 138, 821–857Google Scholar
- 12.H. Lamb, Hydrodynamics. Reprint of the 1932 6th edn. (Cambridge University Press, Cambridge, 1993)Google Scholar