A new forward-backward sweeping parabolized Navier-Stokes algorithm with application to magnetohydrodynamic flows

A new forward-backward sweeping parabolized Navier-Stokes algorithm has been developed to efficiently compute supersonic/hypersonic flowfields with embedded separated regions. The algorithm splits the streamwise flux vector using the Steger-Warming method and employs multiple forward/backward sweeps of the flowfield in order to duplicate the results that would be obtained with the complete Navier-Stokes equations. The forward/backward sweeping of the flowfield significantly reduces the number of iterations required over previous iterative parabolized Navier-Stokes algorithms. Once a separated flow region is computed, the algorithm returns to the usual forward-space-marching mode until the next separated flow region is encountered. The new algorithm has been applied to three separated flow test cases consisting of flow over a compression ramp and two flows over a hollow-cylinder-flare geometry. The present numerical results are in excellent agreement with complete Navier-Stokes computations and experimental data. In addition, the new algorithm has been extended to efficiently compute magnetohydrodynamic (NM) flows in the low magnetic Reynolds number regime. In this regime, the electrical conductivity is low and the induced magnetic field is negligible compared to the applied magnetic field. This allows the MHD effects to be modeled by introducing source terms into the governing equations. Turbulence has been included by modifying the Baldwin-Lomax turbulence model to account for MHD effects. The new algorithm with MHD effects included has been used to compute both laminar and turbulent, supersonic, MHD flows over flat plates, and 3-D supersonic viscous flows in an experimental MHD channel. The new algorithms have been successfully incorporated into NASA's parabolized Navier-Stokes (UPS) code.