An efficient multigrid approach to solving highly recirculating flows

A multigrid solution strategy is presented for the efficient and economic solution of highly recirculating incompressible laminar flows. This paper emphasizes the importance of using high order discretizations for the governing equations of motion, in particular the inertia terms, and the enhancement of the overall stability and efficiency of the method through the use of defect correction. The latter enables solutions to an accuracy equivalent to machine round-off to be found easily with solutions to 'engineering accuracy' being obtained very rapidly on extremely fine grids. These ideas are demonstrated for the solution of two commonly encountered test problems-flow in a lid-driven cavity and flow through a suddenly expanding channel. Results show that proceeding in this way leads to a robust methodology for the solution of a whole class of problems of this type, which is readily extended to three dimensions.