Multigrid Convergence Acceleration of the Preconditioned Compressible flow Equations

In this paper, the preconditioned nonlinear multigrid algorithm is used with aim of improving convergence rates,reducing CPUtime for solving compressible flow equations. MultiGrid (MG) methods are a group of algorithms that are used for acceleratingconvergence of differential equations using a series of discretizations. This method is based upon the principle that explains whenthe global (low-frequency) error of a fine mesh is represented on a coarse mesh, it retains the same characteristics as of the local(high-frequency) error, thus the same method for removing high frequency errors is also applicable in such situation. When thenonlinear multigrid algorithm drives the external iterations, the choice of smoother on each grid level plays an important role in theperformance. In this research, a preconditioning method has been used to reduce instabilities of the linear system that arise in eachiteration. Some important results of this research are: choosing the best preconditioning scheme to be coupled with MG method,assessment of MG method performance in equations of turbulence, laminar,inviscid flows,analysis of different cyclingschemes.