Application of an upwind algorithm to the three-dimensional parabolized Navier-Stokes equations

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

“…The PNS method [26,37,38] can be used to accurately compute supersonic viscous flows that contain no separated regions and produce negligible upstream influence. The PNS equations (with MHD effects included) expressed in a general nonorthogonal coordinate system are given by Eq.…”

“…The 3-D FBIPNS algorithm has been incorporated into NASA's upwind parabolized NS (UPS) code originally developed by Lawrence et al [37,38]. The UPS code solves the parab olized Navier-Stokes equations using a fully conservative, finite-volume approach in a general nonorthogonal coordinate system.…”

Computation of the integrated aerodynamic and propulsive flowfields of a generic hypersonic space plane

“…The UPS code has been rigorously validated by comparing results with other codes and experimental results for a wide range of flow conditions [28,30,32,[34][35][36].…”

“…Lawrence et al [31,32] have developed a robust upwind (perfect gas) PNS code (UPS code) which solves the PNS equations using a finite-volume, upwind TVD (Total Variation Diminishing) method based on Roe's approximate Riemann solver [33]. The dissipation term associated with this scheme is sufficiently adaptive to various flow conditions so that no user-specified smoothing is required.…”

“…This eliminates the problem of determining the correct amount of smoothing which "plagued" many of the previous centrally-differenced PNS codes. The two-dimensional (2-D) [31] and three-dimensional (3-D) [32] versions of the UPS code have been extended to permit both equilibrium [22,28] and nonequilibrium [23,30] (finite-rate, chemically reacting) airflow computations. For nonequilibrium flows, the fluid dynamic and species continuity equations are solved in a loosely-coupled manner.…”