Multistage Schemes With Multigrid for Euler and Navier-Stokes Equations Components and Analysis

A class of explicit multistage time-stepping schemes with centered spatial di erencing and multigrid is considered for the compressible Euler and Navier-Stokes equations. These schemes are the basis for a family of computer programs ( ow codes with multigrid (FLOMG) series) currently used to solve a wide range of uid dynamics problems, including internal and external ows. In this paper, the components of these multistage time-stepping schemes are de ned, discussed, and in many cases analyzed to provide additional insight into their behavior. Special emphasis is given to numerical dissipation, stability of Runge-Kutta schemes, and the convergence-acceleration techniques of multigrid and implicit residual smoothing. Both the Baldwin and Lomax algebraic equilibrium model and the Johnson and King one-half equation nonequilibrium model are used to establish turbulence closure. Implementation of these models is described.