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The present paper deals with the implementation of non-penetration boundary conditions at solid walls for three-dimensional inviscid flow computations on Cartesian grids. The crux of the method is the curvature-corrected symmetry technique (CCST) developed by the present authors for body-fitted grids. The method introduces ghost cells near the boundaries whose values are developed from an assumed flow-field model in vicinity of the wall consisting of a vortex flow, with locally symmetric distribution of entropy and total enthalpy. In three dimensions this procedure is implemented in the so-called “osculating plane”. This method was shown to be substantially more accurate than traditional surface boundary condition approaches. This improved boundary condition is adapted to a Cartesian mesh formulation, which we have termed the “ghost-cell method”. In this approach, all cell centers exterior to the body are computed with fluxes at the six surrounding cell faces, without any cut cell. A multiple-valued point technique is used to compute sharp edges. The merits of the ghost-cell method for three-dimensional inviscid flow computations are established by computing compressible and transonic flows about a sphere, an oblate and a prolate spheroid, a cylindrical wing with an end-plate, the ONERA M6 wing and detailed comparison to body-fitted grid computations and to published data. The computed results show the surface non-penetration condition to be satisfied in the limit of vanishing cell size and the method to be second-order accurate in space. The comparison with body-fitted results proves that the accuracy is comparable to the accuracy of CCST computations on body-fitted grids and remarkably superior to body-fitted computations based on traditional pressure extrapolation, non-penetration boundary conditions. In addition, we prove that the results are independent of the position of the body with respect to the grid. Finally, we show that the ONERA M6 wing results compare very well with published data. [Copyright &y& Elsevier]

Abstract: Different sources of uncertainty in CFD simulations are illustrated by a detailed study of two-dimensional, turbulent, transonic flow in a converging–diverging channel. Runs were performed with the commercial CFD code GASP using different turbulence models, grid levels, and flux-limiters to see the effect of each on the CFD simulation uncertainties. Two flow conditions were studied by changing the exit pressure ratio: the first is a complex case with a strong shock and a separated flow region, the second is the weak shock case with no separation. The uncertainty in CFD simulations has been studied in terms of four contributions: (1) discretization error, (2) error in geometry representation, (3) turbulence model, and (4) the downstream boundary condition. In this paper, we have quantified the relative contribution and the importance of each source of uncertainty and shown the level of scatter in results that a well informed CFD user may obtain in a typical design activity. The nozzle efficiency results obtained in this study showed that the range of variation for the strong shock case was much larger than that observed in the weak shock case. The discretization errors were up to 6% and the relative uncertainty originating from the selection of different turbulence models was as large as 9% for the strong shock case. Furthermore, the results demonstrated that grid convergence is not achieved with grid levels that have moderate mesh sizes and showed that highly refined grids are required to obtain solutions with an acceptable level of accuracy in design problems that involve simulations of complex flow fields. The results illustrated the interaction of different sources of uncertainty and showed that the magnitudes of numerical errors are influenced by the physical models used. [Copyright &y& Elsevier]

Abstract: Vorticity confinement methods have been shown to be very effective in the computation of flows involving the convection of thin vortical layers. These are the only Eulerian methods whereby simulations of these layers remain very thin and persist long distances without significant dissipation. Initially developed by Steinhoff and co-workers for incompressible flow, these methods have been used successfully to predict complex flows, particularly involving helicopter rotors. Recently, the method has been extended to a compressible finite-volume form, which will enable the methods to be used for a much broader class of problems. In this paper, we examine the ability of the compressible vortex confinement methodology to handle an important class of vortex-dominated flows involving massive separation from bluff bodies. We evaluate the effectiveness of the method by comparisons with experimental data and available state-of-the-art computations. An important conclusion of the present work is that vortex confinement applied to massively separated flows, without modeling the viscous terms and on an essentially inviscid grid, can result in a reasonable approximation to turbulent separated flows. The computed flow structures and velocity profiles were in good agreement with time-averaged values of the data and with LES simulations even though the confinement approach utilized more than a factor of 50 fewer cells in the computation (20,000 compare to more the 1 million). The success of the method for these classes of flows may be attributed to the accurate calculation of the rotational inviscid flow which dominates the convection of the large-scale flow structures. [Copyright &y& Elsevier]

A new procedure for robust and efficient design optimization of inviscid flow problems has been developed and implemented on a wide variety of test problems. The methodology involves the use of an accurate flow solver to calculate the objective function and an approximate, dissipative flow solver, which is used only in the solution of the discrete quasi-time-dependent adjoint problem. The resulting design sensitivities are very robust even in the presence of noise or other non-smoothness associated with objective functions in many high-speed flow problems. The design problem is solved using what we term progressive optimization, whereby a sequence of a partially converged flow solution, followed by a partially converged adjoint solution followed by an optimization step is performed. This procedure is performed using a sequence of progressively finer grids for the solution of the flow field, while only using coarser grids for the adjoint equation solution.This approach has been tested on numerous inverse and direct (constrained) design problems involving two- and three-dimensional transonic nozzles and airfoils as well as supersonic blunt bodies. The methodology is shown to be robust and highly efficient, with a converged design optimization produced in no more than the amount of computational work to perform from 0.5 to 2.5 fine-mesh flow analyses. [Copyright &y& Elsevier]