A strongly coupled time-marching method for solving the Navier-Stokes and \(k-\omega\) turbulence model equations with multigrid (Q1815923)

The Navier-Stokes equations and two-equation turbulence model equations, in particular, the \(k\)-\(\omega\) equations, are considered as one single set of strongly coupled equations and solved with the same explicit time-marching algorithm without time-lagging. A multigrid method, together with other acceleration techniques such as local time steps and implicit residual smoothing, is applied to both the Navier-Stokes and the turbulence model equations. The method is applied to the calculation of flows through cascades as well as over isolated airfoils.