A transform method for linear evolution PDEs on a finite interval

We study initial boundary value problems for linear scalar evolutionpartial differential equations, with spatial derivatives ofarbitrary order, posed on the domain {t > 0, 0 < x <L}. We show that the solution can be expressed as an integralin the complex k-plane. This integral is defined in terms ofan x-transform of the initial condition and a t-transform ofthe boundary conditions. The derivation of this integral representationrelies on the analysis of the global relation, which is an algebraicrelation defined in the complex k-plane coupling all boundaryvalues of the solution. For particular cases, such as the case of periodic boundaryconditions, or the case of boundary value problems for even-orderPDEs, it is possible to obtain directly from the global relationan alternative representation for the solution, in the formof an infinite series. We stress, however, that there existinitial boundary value problems for which the only representationis an integral which cannot be written as an infinite series.An example of such a problem is provided by the linearized versionof the KdV equation. Similarly, in general the solution of odd-orderlinear initial boundary value problems on a finite intervalcannot be expressed in terms of an infinite series.     

A numerical and experimental investigation of the interactions between a non‐uniform planar array of incompressible free jets

The interaction between multiple incompressible air jets has been studied numerically and experimentally. The numerical predictions have been first validated using experimental data for a single jet configuration. The spreading features of five unequal jets in the configuration of one larger central jet surrounded by four smaller equi‐distant jets, have been studied, for different lateral spacing ratios of 1.5, 2.0 and 2.5 and a central jet Reynolds number of 1.24×105 (corresponding to a Mach number of 0.16). Flow of five equal jets has also been simulated, for the sake of comparison. The jet interactions commence at an axial distance of about 3–4 diameters and complete by an axial distance of about 10 diameters for the lowest spacing ratio of 1.5. For larger spacing ratios, the length required for the start and completion of jet interaction increase. Peripheral jets bend more towards the central jet and merge at a smaller distance, when their sizes are smaller than that of the central jet. The entrainment ratio for multiple jets is higher than that for a single jet. Excellent agreement is observed between the experimental data and theoretical predictions for both mean flow field and turbulent quantities, at regions away from the jet inlet. The potential core length and initial jet development, however, are not predicted very accurately due to differences in the assumed and actual velocity profiles at the jet inlet. Copyright © 2004 John Wiley & Sons, Ltd.     

LES of turbulent heat transfer: proper convection numerical schemes for temperature transport

Large eddy simulations of two basic configurations (decay of isotropic turbulence, and the academic plane channel flow) with heat transfer have been performed comparing several convection numerical schemes, in order to discuss their ability to evaluate temperature fluctuations properly. Results are compared with the available incompressible heat transfer direct numerical simulation data. It is shown that the use of regularizing schemes (such as high order upwind type schemes) for the temperature transport equation in combination with centered schemes for momentum transport equation gives better results than the use of centred schemes for both equations. Copyright © 2004 John Wiley & Sons, Ltd.     

High‐order accurate numerical solutions of incompressible flows with the artificial compressibility method

A high‐order accurate, finite‐difference method for the numerical solution of incompressible flows is presented. This method is based on the artificial compressibility formulation of the incompressible Navier–Stokes equations. Fourth‐ or sixth‐order accurate discretizations of the metric terms and the convective fluxes are obtained using compact, centred schemes. The viscous terms are also discretized using fourth‐order accurate, centred finite differences. Implicit time marching is performed for both steady‐state and time‐accurate numerical solutions. High‐order, spectral‐type, low‐pass, compact filters are used to regularize the numerical solution and remove spurious modes arising from unresolved scales, non‐linearities, and inaccuracies in the application of boundary conditions. The accuracy and efficiency of the proposed method is demonstrated for test problems. Copyright © 2004 John Wiley & Sons, Ltd.     

Robust handling of non‐linear constraints for GA optimization of aerodynamic shapes

A new approach to the robust handling of non‐linear constraints for GAs (genetic algorithms) optimization is proposed. A specific feature of the approach consists of the change in the conventional search strategy by employing search paths which pass through both feasible and infeasible points (contrary to the traditional approach where only feasible points may be included in a path). The method (driven by full Navier–Stokes computations) was applied to the problem of multiobjective optimization of aerodynamic shapes subject to various geometrical and aerodynamic constraints. The results demonstrated that the method retains high robustness of conventional GAs while keeping CFD computational volume to an acceptable level, which allowed the algorithm to be used in a demanding engineering environment. Copyright © 2004 John Wiley & Sons, Ltd.