Michael A. Park

Using an Adjoint Approach to Eliminate Mesh Sensitivities in Computational Design

An adjoint algorithm for efficiently incorporating the effects of mesh sensitivities in a computational design framework is introduced. The method eliminates the need for explicit linearizations of the mesh movement scheme with respect to the geometric parameterization variables, an expense that has hindered large-scale design optimization for practical applications. The effects of the mesh sensitivities can be accounted for through the solution of an adjoint problem equivalent in cost to a single mesh movement computation, followed by an explicit matrix-vector product whose cost scales with the number of design variables and the resolution of the parameterized surface grid. The methodology augments the current practice of using adjoints solely for the flowfield and leads to a dramatic computational savings. The accuracy of the implementation is established, and several sample design optimizations are shown.

Parallel Anisotropic Tetrahedral Adaptation

An adaptive method that robustly produces high aspect ratio tetrahedra to a general 3D metric specification without introducing hybrid semi-structured regions is presented. The grid operators and higher-level logic is described with their respective domain-decomposed parallelizations. An tetrahedral adaptation scheme is demonstrated for 1000‐1 anisotropy in a simple cube geometry. This form of adaptation is applicable to more complex domain boundaries via a cut-cell approach as demonstrated by a parallel 3D supersonic simulation of a complex fighter aircraft. To avoid the assumptions and approximations required to form a metric to specify adaptation, an approach is introduced that directly evaluates interpolation error. The grid is adapted to reduce and equidistribute this interpolation error calculation without the use of an intervening anisotropic metric. Direct interpolation error adaptation is illustrated for fifth-order elements in 1D and linear and quadratic tetrahedra in 3D.

Turbulent Output-Based Anisotropic Adaptation

Controlling discretization error is a remaining challenge for computational fluid dynamics simulation. Grid adaptation is applied to reduce estimated discretization error in drag or pressure integral output functions. To enable application to high O(10) Reynolds number turbulent flows, a hybrid approach is utilized that freezes the near-wall boundary layer grids and adapts the grid away from the no slip boundaries. The hybrid approach is not applicable to problems with under resolved initial boundary layer grids, but is a powerful technique for problems with important off-body anisotropic features. Supersonic nozzle plume, turbulent flat plate, and shock-boundary layer interaction examples are presented with comparisons to experimental measurements of pressure and velocity. Adapted grids are produced that resolve off-body features in locations that are not known a priori.

FUN3D and CFL3D Computations for the First High Lift Prediction Workshop

Workshop, held in Chicago in June 2010. The unstructured-grid code FUN3D and the structured-grid code CFL3D were applied to several different grid systems. The effects of code, grid system, turbulence model, viscous term treatment, and brackets were studied. The SST model on this configuration predicted lower lift than the Spalart-Allmaras model at high angles of attack; the Spalart-Allmaras model agreed better with experiment. Neglecting viscous cross-derivative terms caused poorer prediction in the wing tip vortex region. Output-based grid adaptation was applied to the unstructured-grid solutions. The adapted grids better resolved wake structures and reduced flap flow separation, which was also observed in uniform grid refinement studies. Limitations of the adaptation method as well as areas for future improvement were identified.

Validation of an Output-Adaptive, Tetrahedral Cut-Cell Method for Sonic Boom Prediction

A cut-cell approach to computational fluid dynamics that uses the median dual of a tetrahedral background grid is described. The discrete adjoint is also calculated for an adaptive method to control error in a specified output. The adaptive method is applied to sonic boom prediction by specifying an integral of offbody pressure signature as the output. These predicted signatures are compared to wind-tunnel measurements to validate the method for sonic boom prediction. Accurate midfield sonic boom pressure signatures are calculated with the Euler equations without the use of hybrid grid or signature propagation methods. Highly refined, shock-aligned anisotropic grids are produced by this method from coarse isotropic grids created without prior knowledge of shock locations. A heuristic reconstruction limiter provides stable flow and adjoint solution schemes while producing similar signatures to Barth―Jespersen and Venkatakrishnan limiters. The use of cut cells with an output-based adaptive scheme automates the volume grid generation task after a triangular mesh is generated for the cut surface.

An Exact Dual Adjoint Solution Method for Turbulent Flows on Unstructured Grids

An algorithm for solving the discrete adjoint system based on an unstructured-grid discretization of the Navier-Stokes equations is presented. The method is constructed such that an adjoint solution exactly dual to a direct differentiation approach is recovered at each time step, yielding a convergence rate which is asymptotically equivalent to that of the primal system. The new approach is implemented within a three-dimensional unstructured-grid framework and results are presented for inviscid, laminar, and turbulent flows. Improvements to the baseline solution algorithm, such as line-implicit relaxation and a tight coupling of the turbulence model, are also presented. By storing nearest-neighbor terms in the residual computation, the dual scheme is computationally efficient, while requiring twice the memory of the flow solution. The scheme is expected to have a broad impact on computational problems related to design optimization as well as error estimation and grid adaptation efforts.

Collaborative Software Development in Support of Fast Adaptive AeroSpace Tools (FAAST)

A collaborative software development approach is described. The software product is an adaptation of proven computational capabilities combined with new capabilities to form the Agencys next generation aerothermodynamic and aerodynamic analysis and design tools. To efficiently produce a cohesive, robust, and extensible software suite, the approach uses agile software development techniques; specifically, project retrospectives, the Scrum status meeting format, and a subset of Extreme Programmings coding practices are employed. Examples are provided which demonstrate the substantial benefits derived from employing these practices. Also included is a discussion of issues encountered when porting legacy Fortran 77 code to Fortran 95 and a Fortran 95 coding standard.

Grid-Adapted FUN3D Computations for the Second High Lift Prediction Workshop (Invited)

Contributions of the unstructured Reynolds-averaged Navier-Stokes code FUN3D to the 2 nd AIAA CFD High Lift Prediction Workshop are described, and detailed comparisons are made with experimental data. Using workshop-supplied grids, results for the clean wing conguration are compared with results from the structured code CFL3D Using the same turbulence model, both codes compare reasonably well in terms of total forces and moments, and the maximum lift is similarly over-predicted for both codes compared to experiment. By including more representative geometry features such as slat and ap brackets and slat pressure tube bundles, FUN3D captures the general eects of the Reynolds number variation, but under-predicts maximum lift on workshop-supplied grids in comparison with the experimental data, due to excessive separation. However, when output-based, o-body grid adaptation in FUN3D is employed, results improve considerably. In particular, when the geometry includes both brackets and the pressure tube bundles, grid adaptation results in a more accurate prediction of lift near stall in comparison with the wind-tunnel data. Furthermore, a rotation-corrected turbulence model shows improved pressure predictions on the outboard span when using adapted grids.

Output-Adaptive Tetrahedral Cut-Cell Validation for Sonic Boom Prediction

A cut-cell approach to Computational Fluid Dynamics (CFD) that utilizes the median dual of a tetrahedral background grid is described. The discrete adjoint is also calculated, which permits adaptation based on improving the calculation of a specified output (off-body pressure signature) in supersonic inviscid flow. These predicted signatures are compared to wind tunnel measurements on and off the configuration centerline 10 body lengths below the model to validate the method for sonic boom prediction. Accurate mid-field sonic boom pressure signatures are calculated with the Euler equations without the use of hybrid grid or signature propagation methods. Highly-refined, shock-aligned anisotropic grids were produced by this method from coarse isotropic grids created without prior knowledge of shock locations. A heuristic reconstruction limiter provided stable flow and adjoint solution schemes while producing similar signatures to Barth-Jespersen and Venkatakrishnan limiters. The use of cut-cells with an output-based adaptive scheme completely automated this accurate prediction capability after a triangular mesh is generated for the cut surface. This automation drastically reduces the manual intervention required by existing methods.

Parallel, Gradient-Based Anisotropic Mesh Adaptation for Re-entry Vehicle Configurations

Two gradient-based adaptation methodologies have been implemented into the Fun3d refine GridEx infrastructure. A spring-analogy adaptation which provides for nodal movement to cluster mesh nodes in the vicinity of strong shocks has been extended for general use within Fun3d, and is demonstrated for a 70 sphere cone at Mach 2. A more general feature-based adaptation metric has been developed for use with the adaptation mechanics available in Fun3d, and is applicable to any unstructured, tetrahedral, flow solver. The basic functionality of general adaptation is explored through a case of flow over the forebody of a 70 sphere cone at Mach 6. A practical application of Mach 10 flow over an Apollo capsule, computed with the Felisa flow solver, is given to compare the adaptive mesh refinement with uniform mesh refinement. The examples of the paper demonstrate that the gradient-based adaptation capability as implemented can give an improvement in solution quality.