Numerical Simulation of Turbulent MHD Flows Using an Iterative PNS Algorithm

A new parabolized Navier-Stokes (PNS) algorithm has been developed to efficiently compute magne- tohydrodynamic (MHD) flows in the low magnetic Reynolds number regime. In this regime, the electri- cal conductivity is low and the induced magnetic field is negligible compared to the applied magnetic field. The MHD effects are modeled by introducing source terms into the PNS equation which can then be solved in a very efficient manner. To account for upstream (elliptic) effects, the flowfields are computed using multiple streamwise sweeps with an iterated PNS al- gorithm. Turbulence has been included by modify- ing the Baldwin-Lomax turbulence model to account for MHD effects. The new algorithm has been used to compute both laminar and turbulent, supersonic, MHD flows over flat plates and supersonic viscous flows in a rectangular MHD accelerator. The present results are in excellent agreement with previous com- plete Navier-Stokes calculations. Introduction