Integral transform solution for the lid‐driven cavity flow problem in streamfunction‐only formulation

The basic ideas in the generalized integral transform technique are further advanced to allow for the hybrid numerical‐analytical solution of the two‐dimensional steady Navier‐Stokes equations in streamfunction‐only formulation. The classical lid‐driven square cavity problem is selected for illustration of the approach. The corresponding biharmonic‐type non‐linear partial differential equation for the streamfunction is integral transformed in one of the co‐ordinates and an infinite system of coupled non‐linear ODEs for the transformed potential results in the other independent variable. Upon truncation to an appropriate finite order, the ODE system is numerically solved by well‐established algorithms with automatic error control devices. The convergence behaviour of the eigenfunction expansion is demonstrated and reference results are provided for typical values of Reynolds number.