Solution techniques for the vorticity–streamfunction formulation of two‐dimensional unsteady incompressible flows

A review of the authors' solution techniques for the vorticity-streamfunction formulation of two-dimensional unsteady incompressible flows is presented. While both the viscous and inviscid cases are considered, the derivation of the proper finite element formulations for multiply connected domains is emphasised. In all formulations associated with the vorticity transport equation, the streamline upwind/Petrov-Galerkin method is used. The adaptive implicit-explicit and grouped element-by-element solution strategies are employed to maximise the computational efficiency. The solutions obtained in all tests cases compare well with solutions from previously published investigations. The convergence and benchmark studies performed in this paper show that the solution techniques presented are accurate, reliable and efficient.

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