A new full multigrid algorithm in which the starting quantities are directly taken from the previous cycle is presented in the paper. This results in no restriction procedure for variables except for residuals. It simplifies the multigrid strategy and the structure of code. In combination with the SIMPLE algorithm, this algorithm is applied to solve fluid flows using collocated grid and higher order schemes for convective fluxes. Since the solution is directly taken from the previous cycle, there is no-matching problem of mass fluxes. The pressure correction equation on the coarse grid is similar to any other variables in this work, different to other works, in which so-called correction of the pressure-correction on the coarse grid is determined.
Accurate solutions are obtained for 2D / 3D complex laminar and turbulent flows such as lid-driven flows in 2D and 3D cavities, flows over backward-facing step, complex turbulent flows over hill, laminar and turbulent flows in curved ducts with strong secondary motion. The modern turbulence models are used for the complex turbulent flows. A speed-up up to about 80 for 2D cases as well as a speed-up up to about 40 for 3D cases have been obtained.