We present fully general relativistic equations governing viscous transonic flows in vertical equilibrium in Kerr geometry. We find the complete set of global solutions (both for Optically thick and optically thin flows) in the weak viscosity limit. We show that for a large region of parameter space, centrifugal pressure supported standing shocks can form in accretion and winds very close to th...

Transonic accretion flow with self-consistent treatment of the magnetic field is presented. My website http://www.cfa.harvard.edu/~rshcherb/.

The lag model proposed by Olsen and Coakley is incorporated into the baseline two-equation k-ω turbulence model to simulate the transonic and supersonic turbulent separated flow. The performances of the lagged k-ω turbulence model is assessed by computing two transonic airfoil flow cases, the RAE2822 Case 10 and the 18% thick double circular arc airfoil, and a separated nozzle flow. The computa...

We prove the existence of global solutions to the Euler equations of compressible isentropic gas dynamics with geometrical structure, including transonic nozzle flow and spherically symmetric flow. Due to the presence of the geometrical source terms, the existence results themselves are new, especially as they pertain to radial flow in an unbounded region, |~x| ≥ 1, and to transonic nozzle flow...

Time-dependent two-dimensional magnetohydrodynamic simulations are carried out for tokamak plasmas with edge poloidal flow. Differently from conventional equilibrium theory, a density pedestal all around the edge is obtained when the poloidal velocity exceeds the poloidal sound speed. The outboard pedestal is induced by the transonic discontinuity, the inboard one by mass redistribution. The de...

In these lectures I shall attempt to survey some of the principal recent developments in computational aerodynamics. Prior to 1960 computational methods were hardly used in aerodynamic analysis, although they were already widely used for structural analysis. The NACA 6 series of airfoils had been developed during the forties, using hand computation to perform the Theodorsen method for conformal...

where a is the speed of sound, p is the density, _ is the potential, and the subscripts denote partial deriva-The nonuniqueness problem occurring at transonic tives. In the absence of shock waves, both forms of the speeds with the conservative potential equation is in-equation are equivalent. When shock waves are present, vestigated numerically. Evidence is given supporting use of the conservat...

Multiple solutions of the small-disturbance potential equation and the full potential equation were known for the NACA0012 airfoil in a certain range of transonic Mach numbers and at zero angle of attack. However the multiple solutions for this particular airfoil were not observed using Euler or Navier-Stokes equations under the above flow conditions. In the present work, both the Unsteady Reyn...

The secular evolution of the purely general relativistic low angular momentum accretion flow around a spinning black hole is shown to exhibit hysteresis effects. This confirms that a stationary shock is an integral part of such an accretion disc in the Kerr metric. The equations describing the space gradient of the dynamical flow velocity of the accreting matter have been shown to be equivalent...