Numerical study of an inviscid incompressible flow through a channel of finite length

Vasily Govorukhin, Konstantin Ilin

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A two-dimensional inviscid incompressible flow in a rectilinear channel of finite length is studied numerically. Both the normal velocity and the vorticity are given at the inlet, and only the normal velocity is specified at the outlet. The flow is described in terms of the stream function and vorticity. To solve the unsteady problem numerically, we propose a version of the vortex particle method. The vorticity field is approximated using its values at a set of fluid particles. A pseudo-symplectic integrator is employed to solve the system of ordinary differential equations governing the motion of fluid particles. The stream function is computed using the Galerkin method. Unsteady flows developing from an initial perturbation in the form of an elliptical patch of vorticity are calculated for various values of the volume flux of fluid through the channel. It is shown that if the flux of fluid is large, the initial vortex patch is washed out of the channel, and when the flux is reduced, the initial perturbation evolves to a steady flow with stagnation regions.
Original languageEnglish
Pages (from-to)1315-1333
Number of pages19
JournalInternational Journal for Numerical Methods in Fluids
Issue number12
Publication statusPublished - 1 Oct 2009


  • Fluid Dynamics
  • particle methods;
  • Galerkin method;
  • partial differential equations;
  • time integration;
  • Euler flow;
  • incompressible flow;
  • flow through a given domain

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