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

The newly developed unifying discontinuous formulation named the correction procedure via reconstruction (CPR) for conservation laws is extended to solve the Navier-Stokes equations for 3D mixed grids. In the current development, tetrahedrons and triangular prisms are considered. The CPR method can unify several popular high order methods including the discontinuous Galerkin and the spectral volume methods into a more efficient differential form. By selecting the solution points to coincide with the flux points, solution reconstruction can be completely avoided. Accuracy studies confirmed that the optimal order of accuracy can be achieved with the method. Several benchmark test cases are computed by solving the Euler and compressible Navier-Stokes equations to demonstrate its 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 smoothness estimate which is suited as a control input to a shock capture mechanism. Using an artificial viscosity in the latter role, we obtain a DG scheme for the numerical solution of nonlinear systems of conservation laws. Building on work by Persson and Peraire, we thoroughly justify the detector’s design and analyze its performance on a number of benchmark problems. We further explain the scaling and smoothing steps necessary to turn the output of the detector into a local, artificial viscosity. We close by providing an extensive array of numerical tests of the detector in use.

There is a growing interest in high-order finite and spectral/hp element methods using continuous and discontinuous Galerkin formulations. In this paper we investigate the effect of h- and p-type refinement on the relationship between runtime performance and solution accuracy. The broad spectrum of possible domain discretisations makes establishing a performance-optimal selection non-trivial. Through comparing the runtime of different implementations for evaluating operators over the space of discretisations with a desired solution tolerance, we demonstrate how the optimal discretisation and operator implementation may be selected for a specified problem. Furthermore, this demonstrates the need for codes to support both low- and high-order discretisations.

Theoretical studies and numerical experiments suggest that unstructured high-order methods can provide solutions to otherwise intractable fluid flow problems within complex geometries. However, it remains the case that existing high-order schemes are generally less robust and more complex to implement than their low-order counterparts. These issues, in conjunction with difficulties generating high-order meshes, have limited the adoption of high-order techniques in both academia (where the use of low-order schemes remains widespread) and industry (where the use of low-order schemes is ubiquitous). In this short review, issues that have hitherto prevented the use of high-order methods amongst a non-specialist community are identified, and current efforts to overcome these issues are discussed. Attention is focused on four areas, namely the generation of unstructured high-order meshes, the development of simple and efficient time integration schemes, th e development of robust and accurate shock capturing algorithms, and finally the development of high-order methods that are intuitive and simple to implement. With regards to this final area, particular attention is focused on the recently proposed flux reconstruction approach, which allows various well known high-order schemes (such as nodal discontinuous Galerkin methods and spectral difference methods) to be cast within a single unifying framework. It should be noted that due to the experience of the authors the review is directed somewhat towards aerodynamic applications and compressible flow. However, many of the discussions have a wider applicability. Moreover, the tone of the review is intended to be generally accessible, such that an extended scientific community can gain insight into factors currently pacing the adoption of unstructured high-order methods.

An exploratory study is performed to investigate the use of a time-dependent discrete adjoint methodology for design optimization of a high-lift wing configuration augmented with an active flow control system. The location and blowing parameters associated with a series of jet actuation orifices are used as design variables. In addition, a geometric parameterization scheme is developed to provide a compact set of design variables describing the wing shape. The scaling of the implementation is studied using several thousand processors and it is found that asynchronous file operations can greatly improve the overall performance of the approach in such massively parallel environments. Three design examples are presented which seek to maximize the mean value of the lift coefficient 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 than three times the incremental lift provided by the non-optimized actuation.

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

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 numerical flux function, with acoustic wave improvement. The method is implemented on an unstructured hybrid mesh in three dimensions. A solution of higher order accuracy is obtained by reconstruction, using an iteratively corrected least squares process, and by a new limiting procedure. The numerical performance of the complete approach is demonstrated by considering its application to the simulation of steady turbulent transonic flow over an ONERA M6 wing and to a steady inviscid supersonic flow over a modern military aircraft configuration.

For flows with strong periodic content, time-spectral methods can be used to obtain time-accurate solutions at substantially reduced cost compared to traditional time-implicit methods which operate directly in the time domain. However, these methods are only applicable in the presence of fully periodic flows, which represents a severe restriction for many aerospace engineering problems. This paper presents an extension of the time-spectral approach for problems that include a slow transient in addition to strong periodic behavior, suitable for applications such as transient turbofan simulation or maneuvering rotorcraft calculations. The formulation is based on a collocation method which makes use of a combination of spectral and polynomial basis functions and results in the requirement of solving coupled time instances within a period, similar to the time spectral approach, although multiple successive periods must be solved to capture the transient 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 which minimizes the modifications required to an existing steady-state solver. For dynamically deforming mesh cases, a formulation which preserves discrete conservation as determined by the Geometric Conservation Law is derived and implemented. A fully implicit approach which takes into account the coupling between the various time instances is implemented and shown to preserve the baseline steady-state multigrid convergence rate as the number of time instances is increased. Accuracy and efficiency are demonstrated for periodic and non-periodic problems by comparing the performance of the method with a traditional time-stepping approach using a simple two-dimensional pitching airfoil problem, a three-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 been studied at Central Aerohydrodynamic Institute (TsAGI) where a computational code has been designed for numerical solution of the 3-D Euler and Navier-Stokes equations. Our discussion is mainly based on the results of the DG study conducted in TsAGI in collaboration with the NUMECA International. The capacity of a DG scheme to tackle challenging computational problems is demonstrated and its potential advantages over FV schemes widely used in modern computational aerodynamics are highlighted.