Development and validation of a SUPG finite element scheme for the compressible Navier–Stokes equations using a modified inviscid flux discretization

This paper considers the streamline‐upwind Petrov–Galerkin (SUPG) method applied to the unsteady compressible Navier–Stokes equations in conservation‐variable form. The spatial discretization, including a modified approach for interpolating the inviscid flux terms in the SUPG finite element formulation, and the second‐order accurate time discretization are presented. The numerical method is discussed in detail. The performance of the algorithm is then investigated by considering inviscid flow past a circular cylinder. Validation of the finite element formulation via comparisons with experimental data for high‐Mach number perfect gas laminar flows is presented, with a specific focus on comparisons with experimentally measured skin friction and convective heat transfer on a 15° compression ramp. Copyright © 2007 John Wiley & Sons, Ltd.     

Aircraft and crew scheduling for fractional ownership programs

Fractional aircraft ownership programs, where individuals or corporations own a fraction of an aircraft, have revolutionized the corporate aviation industry. Fractional management companies (FMC) manage all aspects of aircraft operations enabling the owners to enjoy the benefits of private aviation without the associated responsibilities. We describe here the development of a scheduling decision support tool for a leading FMC. We present mathematical models, exact and heuristic solution methods. Our computational results using real and randomly generated data indicate that these models are quite effective in finding optimal or near-optimal solutions. The first phase of the implementation of one of these models at the FMC led to a significant improvement in effective utilization of the aircraft, reduction of costs due to reduced empty moves, and hence increased profits.     

On the theory of the shear-induced isotropic-to-nematic phase transition of side chain liquid-crystalline polymers

The shear-induced isotropic-to-nematic phase transition of side chain liquid-crystalline polymers is studied theoretically. A modification of the previous models of main-chain liquid crystals to the case of side chain liquid-crystalline polymers is proposed. Orientational and rheological properties of the model are studied in plane-shear flow. Predictions of the present model agree qualitatively with experimental results (Pujolle-Robic, Noirez in Nature 409:167, 2001).     

Evaluation of adaptive mesh refinement and coarsening for the computation of compressible flows on unstructured meshes

The compressible gas flows of interest to aerospace applications often involve situations where shock and expansion waves are present. Decreasing the characteristic dimension of the computational cells in the vicinity of shock waves improves the quality of the computed flows. This reduction in size may be accomplished by the use of mesh adaption procedures. In this paper an analysis is presented of an adaptive mesh scheme developed for an unstructured mesh finite volume upwind computer code. This scheme is tailored to refine or coarsen the computational mesh where gradients of the flow properties are respectively high or low. The refinement and coarsening procedures are applied to the classical gas dynamic problems of the stabilization of shock waves by solid bodies. In particular, situations where oblique shock waves interact with an expansion fan and where bow shocks arise around solid bodies are considered. The effectiveness of the scheme in reducing the computational time, while increasing the solution accuracy, is assessed. It is shown that the refinement procedure alone leads to a number of computational cells which is 20% larger than when alternate passes of refinement and coarsening are used. Accordingly, a reduction of computational time of the same order of magnitude is obtained. Copyright © 2005 John Wiley & Sons, Ltd.     

Asymptotic behavior of vortices in axisymmetric flow without swirl

We investigate the confinement properties of bounded, nonnegative, compactly supported vortices of axisymmetric incompressible Euler flows without swirl. We show that along one direction of the symmetry axis, its support can grow no faster than O[(t log t)^1/2]. The rate at which it approaches the symmetry axis is also estimated. Together with the result of Maffei–Marchioro on the radial growth rate of the support, it is contained in a slowly expanding tubular region. The techniques of the above‐mentioned authors, Iftimie–Lopes–Nussenzveig and Iftimie–Sideris–Gamblin, are used. Copyright © 2008 John Wiley & Sons, Ltd.     

An adaptive cut‐cell method for environmental fluid mechanics

In this work we present a numerical method for solving the incompressible Navier–Stokes equations in an environmental fluid mechanics context. The method is designed for the study of environmental flows that are multiscale, incompressible, variable‐density, and within arbitrarily complex and possibly anisotropic domains. The method is new because in this context we couple the embedded‐boundary (or cut‐cell) method for complex geometry with block‐structured adaptive mesh refinement (AMR) while maintaining conservation and second‐order accuracy. The accurate simulation of variable‐density fluids necessitates special care in formulating projection methods. This variable‐density formulation is well known for incompressible flows in unit‐aspect ratio domains, without AMR, and without complex geometry, but here we carefully present a new method that addresses the intersection of these issues. The methodology is based on a second‐order‐accurate projection method with high‐order‐accurate Godunov finite‐differencing, including slope limiting and a stable differencing of the nonlinear convection terms. The finite‐volume AMR discretizations are based on two‐way flux matching at refinement boundaries to obtain a conservative method that is second‐order accurate in solution error. The control volumes are formed by the intersection of the irregular embedded boundary with Cartesian grid cells. Unlike typical discretization methods, these control volumes naturally fit within parallelizable, disjoint‐block data structures, and permit dynamic AMR coarsening and refinement as the simulation progresses. We present two‐ and three‐dimensional numerical examples to illustrate the accuracy of the method. Copyright © 2008 John Wiley & Sons, Ltd.     

An accurate finite element scheme with moving meshes for computing 3D‐axisymmetric interface flows

An accurate finite element scheme for computing 3D‐axisymmetric incompressible free surface and interface flows is proposed. It is based on the arbitrary Lagrangian Eulerian (ALE) approach using free surface/interface‐resolved moving meshes. Key features like the surface force, consisting of surface tension and the local curvature, and jumps in the density and viscosity over different fluid phases are precisely incorporated in the finite element formulation. The local curvature is approximated by using the Laplace–Beltrami operator technique combined with a boundary approximation by isoparametric finite elements. A new approach is used to derive the 3D‐axisymmetric form from the variational form in 3D‐Cartesian coordinates. Several test examples show the high accuracy and the robustness of the proposed scheme. Copyright © 2007 John Wiley & Sons, Ltd.     

Shear viscosity of polymer and surfactant monolayers

The surface shear viscosity of monolayers formed at the surface of water by adsorbed polyethyl- eneoxyde and by stearic acid is measured as a function of the surface pressure of the monolayer using a new surface viscometer. The principle of the viscometer is the measurement of the drag force on a circular disk undergoing a uniform translation at the water surface: a hydrodynamic model based on the lubrication approximation allows a calculation of the surface viscosities from the absolute measurement of the drag forces. Received: 26 August 1999     

Dynamic simulation of the hydrodynamic interaction among immersed particles in Stokes flow

A numerical method for the dynamic simulation of the hydrodynamic interaction among particles in Stokes flow is developed. The method couples the quasi-static Stokes equations for the fluid with the equilibrium equations for the particles. The boundary element method is used to represent the velocity at a general field point in terms of surface velocities and stresses. However, neither the stresses nor the velocities are assumed to be known on the surface of the particles. Kinematic equations relating the linear and angular velocities at the centroids of the particles to the surface velocities are combined with the discretized boundary element equations and the equilibrium equations to generate a system of linear equations. The associated coefficient matrix is correspondent to the grand resistance matrix which relates the velocities of the particles to a given geometry.