Over the last three decades Computational Fluid Dynamics (CFD) has gradually joined thewind tunnel and flight test as a primary flow analysis tool for aerodynamic designers. CFDhas had its most favorable impact on the aerodynamic design of the high-speed cruiseconfiguration of a transport. This success has raised expectations among aerodynamiciststhat the applicability of CFD can be extended to the full flight envelope. However, thecomplex nature of the flows and geometries involved places substantially increased demandson the solution methodology and resources required. Currently most simulations involveReynolds-Averaged Navier-Stokes (RANS) codes although Large Eddy Simulation (LES) andDetached Eddy Suimulation (DES) codes are occasionally used for component analysis ortheoretical studies. Despite simplified underlying assumptions, current RANS turbulencemodels have been spectacularly successful for analyzing attached, transonic flows. Whetheror not these same models are applicable to complex flows with smooth surface separation isan open question. A prerequisite for answering this question is absolute confidence thatthe CFD codes employed reliably solve the continuous equations involved. Too often,failure to agree with experiment is mistakenly ascribed to the turbulence model ratherthan inadequate numerics. Grid convergence in three dimensions is rarely achieved. Evenresidual convergence on a given grid is often inadequate. This paper discusses issuesinvolved in residual and especially grid convergence.

The newly developed unifying discontinuous formulation named the correction procedure viareconstruction (CPR) for conservation laws is extended to solve the Navier-Stokesequations for 3D mixed grids. In the current development, tetrahedrons and triangularprisms are considered. The CPR method can unify several popular high order methodsincluding the discontinuous Galerkin and the spectral volume methods into a more efficientdifferential form. By selecting the solution points to coincide with the flux points,solution reconstruction can be completely avoided. Accuracy studies confirmed that theoptimal order of accuracy can be achieved with the method. Several benchmark test casesare computed by solving the Euler and compressible Navier-Stokes equations to demonstrateits performance.

We present a novel, cell-local shock detector for use with discontinuous Galerkin (DG)methods. The output of this detector is a reliably scaled, element-wise smoothnessestimate which is suited as a control input to a shock capture mechanism. Using anartificial viscosity in the latter role, we obtain a DG scheme for the numerical solutionof nonlinear systems of conservation laws. Building on work by Persson and Peraire, wethoroughly justify the detector’s design and analyze its performance on a number ofbenchmark problems. We further explain the scaling and smoothing steps necessary to turnthe output of the detector into a local, artificial viscosity. We close by providing anextensive array of numerical tests of the detector in use.

There is a growing interest in high-order finite and spectral/hp elementmethods using continuous and discontinuous Galerkin formulations. In this paper weinvestigate the effect of h- and p-type refinement onthe relationship between runtime performance and solution accuracy. The broad spectrum ofpossible domain discretisations makes establishing a performance-optimal selectionnon-trivial. Through comparing the runtime of different implementations for evaluatingoperators over the space of discretisations with a desired solution tolerance, wedemonstrate how the optimal discretisation and operator implementation may be selected fora specified problem. Furthermore, this demonstrates the need for codes to support bothlow- and high-order discretisations.

Theoretical studies and numerical experiments suggest that unstructured high-ordermethods can provide solutions to otherwise intractable fluid flow problems within complexgeometries. However, it remains the case that existing high-order schemes are generallyless robust and more complex to implement than their low-order counterparts. These issues,in conjunction with difficulties generating high-order meshes, have limited the adoptionof high-order techniques in both academia (where the use of low-order schemes remainswidespread) and industry (where the use of low-order schemes is ubiquitous). In this shortreview, issues that have hitherto prevented the use of high-order methods amongst anon-specialist community are identified, and current efforts to overcome these issues arediscussed. Attention is focused on four areas, namely the generation of unstructuredhigh-order meshes, the development of simple and efficient time integration schemes, th edevelopment of robust and accurate shock capturing algorithms, and finally the developmentof high-order methods that are intuitive and simple to implement. With regards to thisfinal area, particular attention is focused on the recently proposed flux reconstructionapproach, which allows various well known high-order schemes (such as nodal discontinuousGalerkin methods and spectral difference methods) to be cast within a single unifyingframework. It should be noted that due to the experience of the authors the review isdirected somewhat towards aerodynamic applications and compressible flow. However, many ofthe discussions have a wider applicability. Moreover, the tone of the review is intendedto be generally accessible, such that an extended scientific community can gain insightinto factors currently pacing the adoption of unstructured high-order methods.

An exploratory study is performed to investigate the use of a time-dependent discreteadjoint methodology for design optimization of a high-lift wing configuration augmentedwith an active flow control system. The location and blowing parameters associated with aseries of jet actuation orifices are used as design variables. In addition, a geometricparameterization scheme is developed to provide a compact set of design variablesdescribing the wing shape. The scaling of the implementation is studied using severalthousand processors and it is found that asynchronous file operations can greatly improvethe overall performance of the approach in such massively parallel environments. Threedesign examples are presented which seek to maximize the mean value of the liftcoefficient for the coupled system, and results demonstrate improvements as high as 27%relative to the lift obtained with non-optimized actuation. This lift gain is more thanthree times the incremental lift provided by the non-optimized actuation.

Physics based simulation is widely seen as a way of increasing the information aboutaircraft designs earlier in their definition, thus helping with the avoidance ofunanticipated problems as the design is refined. This paper reports on an effort to assessthe automated use of computational fluid dynamics level aerodynamics for the developmentof tables for flight dynamics analysis at the conceptual stage. These tables are then usedto calculate handling qualities measures. The methodological questions addressed area)geometry and mesh treatment for automated analysis from a high level conceptual aircraftdescription and b) sampling and data fusion to allow the timely calculation of large datatables. The test case used to illustrate the approaches is based on a refined designpassenger jet wind tunnel model. This model is reduced to a conceptual description, andthe ability of this geometry to allow calculations relevant to the final design to bedrawn is then examined. Data tables are then generated and handling qualitiescalculated.

A finite volume method for the simulation of compressible aerodynamic flows is described.Stabilisation and shock capturing is achieved by the use of an HLLC consistent numericalflux function, with acoustic wave improvement. The method is implemented on anunstructured hybrid mesh in three dimensions. A solution of higher order accuracy isobtained by reconstruction, using an iteratively corrected least squares process, and by anew limiting procedure. The numerical performance of the complete approach is demonstratedby considering its application to the simulation of steady turbulent transonic flow overan ONERA M6 wing and to a steady inviscid supersonic flow over a modern military aircraftconfiguration.

For flows with strong periodic content, time-spectral methods can be used to obtaintime-accurate solutions at substantially reduced cost compared to traditionaltime-implicit methods which operate directly in the time domain. However, these methodsare only applicable in the presence of fully periodic flows, which represents a severerestriction for many aerospace engineering problems. This paper presents an extension ofthe time-spectral approach for problems that include a slow transient in addition tostrong periodic behavior, suitable for applications such as transient turbofan simulationor maneuvering rotorcraft calculations. The formulation is based on a collocation methodwhich makes use of a combination of spectral and polynomial basis functions and results inthe requirement of solving coupled time instances within a period, similar to the timespectral approach, although multiple successive periods must be solved to capture thetransient behavior.

The implementation allows for two levels of parallelism, one in the spatial dimension,and another in the time-spectral dimension, and is implemented in a modular fashion whichminimizes the modifications required to an existing steady-state solver. For dynamicallydeforming mesh cases, a formulation which preserves discrete conservation as determined bythe Geometric Conservation Law is derived and implemented. A fully implicit approach whichtakes into account the coupling between the various time instances is implemented andshown to preserve the baseline steady-state multigrid convergence rate as the number oftime instances is increased. Accuracy and efficiency are demonstrated for periodic andnon-periodic problems by comparing the performance of the method with a traditionaltime-stepping approach using a simple two-dimensional pitching airfoil problem, athree-dimensional pitching wing problem, and a more realistic transitioning rotor problem.

We discuss the issues of implementation of a higher order discontinuous Galerkin (DG)scheme for aerodynamics computations. In recent years a DG method has intensively beenstudied at Central Aerohydrodynamic Institute (TsAGI) where a computational code has beendesigned for numerical solution of the 3-D Euler and Navier-Stokes equations. Ourdiscussion is mainly based on the results of the DG study conducted in TsAGI incollaboration with the NUMECA International. The capacity of a DG scheme to tacklechallenging computational problems is demonstrated and its potential advantages over FVschemes widely used in modern computational aerodynamics are highlighted.