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...

13. The introduction of a second new hypothetical gas. In the foregoing sections, we have investigated some transonic fields of flow by employing a hypothetical gas which closely approximates the real gas during an isentropic flow in the transonic range. Although such a hypothetical gas has a merit that the fundamental equation governing its flow assumes a rather simple form and can be solved e...

Numerical simulations are presented in order to test airfoil optimization criteria from the aeroelastic point of view. Based on an Evolution Strategy, airfoil-shape point optimization has been performed as a lift constrained drag minimization at a given Mach/Reynolds number combination for transonic flow. Additional to the drag minimization, the propagation time of pressure disturbances from th...

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...

In the present paper, the numerical calculation of transonic equilibria, first introduced with the FLOW code in Guazzotto et al. [Phys. Plasmas 11, 604 (2004)], is critically reviewed. In particular, the necessity and effect of imposing explicit jump conditions at the transonic discontinuity are investigated. It is found that “standard” (low-b, large aspect ratio) transonic equilibria satisfy t...

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...

A full Navier-Stokes solver has been used t o model transonic flow over three airfoil sections. The method uses a two-dimensional, implicit, conservative finite difference scheme for solving the compressible Navier-Stokes equations. Results are presented as prescribed for the Viscous Transonic Airfoil Workshop to held at the AIAA 25th Aerospace Sciences Meeting. "Jones" airfoils have been inves...

present paper investigates the numerical solution of two-dimensional unsteady compressible navier-stokes equations by a new scheme based on the finite volume method. kinetic energy preserving (kep) scheme is introduced for solving the supersonic and transonic external compressible flow field on very fine grids (with a number of cells of the order of the reynolds number) without artificial dissi...

An accretion flow is necessarily transonic around a black hole. However, around a neutron star it may or may not be transonic, depending on the inner disk boundary conditions influenced by the neutron star. I will discuss various transonic behavior of the disk fluid in general relativistic (or pseudo general relativistic) framework. I will address that there are four types of sonic/critical poi...

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...