A variational principle governing the dynamics of a vortex filament in unbounded incompressible inviscid fluid flow was suggested by Rasetti and Regge [Physica A 80, 217 (1975)]. This variational principle holds in the approximation taking into account the logarithmically large terms, on the order of ln(La) , L and a being the length and the cross-section radius of the filament, respectively. I...

An approximate theoretical formula for the distribution of aerodynamic load over arbitrary thick wings in incompressible flow is developed by combining three-dimensional results from thin-wing theory with two-dimensional results from thick-aerofoil theory. The formula is applied to two wings of identical planform, with 60 degrees trailing-edge sweepback and differing aerofoil thickness, which h...

We study the inviscid limit problem of the incompressible flows in the presence of both impermeable regular boundaries and a hypersurface transversal to the boundary across which the inviscid flow has a discontinuity jump. In the former case, boundary layers have been introduced by Prandtl as correctors near the boundary between the inviscid and viscous flows. In the latter case, the viscosity ...

This paper presents a simple and computationally-efficient algorithm for solving steady two-dimensional subsonic and transonic compressible flow over an airfoil. This work uses an interactive viscous-inviscid solution by incorporating the viscous effects in a thin shear-layer. Boundary-layer approximation reduces the Navier-Stokes equations to a parabolic set of coupled, non-linear partial diff...

A fractional step lattice Boltzmann scheme is presented to greatly improve the stability of the lattice Boltzmann method (LBM) in modelling incompressible flows at high Reynolds number. This method combines the good features of the conventional LBM and the fractional step technique. Through the fractional step, the flow at an extreme case of infinite Reynolds number (inviscid flow) can be effec...

We show that, for solutions of a model of two-dimensional, viscous, compressible fluid flow, curves which are initially transverse to the spatial boundary and across which the fluid density is discontinuous become tangent to the boundary instantaneously in time. We also show by similar techniques that, for the Euler equations of two-dimensional, inviscid, incompressible flow and for a large cla...

An inviscid actuator disk model is embedded in a three-dimensional low-order panel method code for inviscid incompressible flow in order to study the propeller effects on an arbitrary body. The actuator disk model predicts the time–averaged induced velocities in the slipstream of a propeller with an arbitrary radial distribution of load. The model is constructed by superposition of four vortici...

This paper presents the development of a 2D high-order solver with unstructured spectral difference method for unsteady incompressible Navier-Stokes equations. Timemarching methods cannot be applied directly to incompressible flows because the governing equations are not hyperbolic. An artificial compressibility method (ACM) is employed in order to treat the inviscid fluxes using the traditiona...

Steady, incompressible flow solutions are found numerically for a radially expanding liquid sheet in order to confirm analytical results for inviscid flow and to investigate viscous and nonlinear effects. An hp-finite element method is used to perform the numerical simulations. Comparisons are made to theoretical predictions of the radius where the sheet becomes unstable. To determine the criti...