Marian Nemec

Multipoint and Multi-Objective Aerodynamic Shape Optimization

A Newton‐Krylov algorithm is presented for the aerodynamic optimization of singleand multi-element airfoil configurations. The flow is governed by the compressible Navier‐Stokes equations in conjunction with a one-equation turbulence model. The preconditioned generalized minimum residual method is applied to solve the discreteadjoint equation, leading to a fast computation of accurate objective function gradients. Optimization constraints are enforced through a penalty formulation, and the resulting unconstrained problem is solved via a quasi-Newton method. Design examples include lift-enhancement and multi-point lift-constrained drag minimization problems. Furthermore, the new algorithm is used to compute a Pareto front for a multi-objective problem, and the results are validated using a genetic algorithm. Overall, the new algorithm provides an ecient and robust approach for addressing the issues of complex aerodynamic

Newton-Krylov Algorithm for Aerodynamic Design Using the Navier-Stokes Equations

A Newton‐Krylov algorithm is presented for two-dimensional Navier‐Stokes aerodynamic shape optimization problems. The algorithm is applied to both the discrete-adjoint and the discrete e ow-sensitivity methods for calculating the gradient of the objective function. The adjoint and e ow-sensitivity equations are solved using a novel preconditioned generalized minimum residual (GMRES)strategy. Together with a complete linearization of the discretized Navier‐Stokes and turbulence model equations, this results in an accurate and efecient evaluation of the gradient. Furthermore, fast e ow solutions are obtained using the same preconditioned GMRES strategy in conjunction with an inexact Newton approach. The performance of the new algorithm is demonstrated for several design examples,includinginversedesign,lift-constraineddragminimization, liftenhancement, and maximization of lift-to-dragratio. In all examples, the normof the gradientisreduced by several ordersof magnitude, indicating that alocalminimumhasbeen obtained. Bytheuseoftheadjoint method,thegradient isobtained infromone-e fth to one-half of the time required to converge a eow solution.

Adjoint-Based Adaptive Mesh Refinement for Complex Geometries

This paper examines the robustness and efficiency of an adjoint-based mesh adaptation method for problems with complicated geometries. The method is used to drive cell refinement in an embedded-boundary Cartesian mesh approach for the solution of the three-dimensional Euler equations. Detailed studies of error distributions and the evolution of cell-wise error histograms with mesh refinement are used to formulate an adaptation strategy that minimizes the run-time of the flow simulation. The effectiveness of this methodology for controlling discretization errors in engineering functionals of nonsmooth problems is demonstrated using several test cases in two and three dimensions. The test cases include a model problem for sonic-boom applications and parametric studies of launch-vehicle configurations over a wide range of flight conditions. The results show that the method is well-suited for the generation of aerodynamic databases of prescribed quality without user intervention.

Adjoint Error Estimation and Adaptive Refinement for Embedded-Boundary Cartesian Meshes

We present an approach for the computation of error estimates in output functionals such as lift or drag for an embedded-boundary Cartesian mesh method. The approach relies on the solution of an adjoint equation and provides error estimates that can be used to both improve the accuracy of the functional and guide a mesh refinement procedure. This is a significant step in our research toward automating the simulation process for flows in complex geometries. The accuracy of the approach is verified on an analytic model problem and validated against common results in the literature. The robustness of the approach is examined for two test cases in three dimensions, namely, an isolated wing in transonic flow and a canard-controlled missile in supersonic flow. The results demonstrate that the approach is tolerant of coarse initial meshes. A practical advantage of the approach is that the adaptive mesh refinement may be performed with a fixed surface triangulation. In all cases considered, the approach provided reliable estimates of the output functional on computationally affordable meshes.

A comparative evaluation of genetic and gradient-based algorithms applied to aerodynamic optimization

A genetic algorithm is compared with a gradient-based (adjoint) algorithm in the context of several aerodynamic shape optimization problems. The examples include singlepoint and multipoint optimization problems, as well as the computation of a Pareto front. The results demonstrate that both algorithms converge reliably to the same optimum. Depending on the nature of the problem, the number of design variables, and the degree of convergence, the genetic algorithm requires from 5 to 200 times as many function evaluations as the gradientbased algorithm.

Adjoint-Based Adaptive Mesh Refinement for Sonic Boom Prediction

Output-driven mesh adaptation is used in conjunction with an embedded-boundary Cartesian meshing scheme for sonic-boom simulations. The approach automatically refines the volume mesh in order to minimize discretization errors in pressure signals located several body-lengths away from the surface geometry. Techniques and strategies used to improve accuracy of the propagated signal while decreasing total number of cells are described. Investigations include examination of cell aspect ratio and comparisons with manual mesh adaptation. The effectiveness of this approach is demonstrated in three dimensions using axisymmetric bodies, a lifting wing-body configuration, and both the F-5E and Shaped Sonic Boom Demonstration flight-test aircraft. Results are validated with available experimental data for a variety of signal forms. These comparisons show that accurate pressure signatures can be produced for three-dimensional geometry in just over an hour using a conventional desktop PC.

Inviscid Analysis of Extended-Formation Flight

Flying airplanes in extended formations, with separation distances of tens of wingspans, significantly improves safety while maintaining most of the fuel savings achieved in close formations. The p...

Adjoint Formulation for an Embedded-Boundary Cartesian Method

A discrete-adjoint formulation is presented for the three-dimensional Euler equations discretized on a Cartesian mesh with embedded boundaries. The solution algorithm for the adjoint and flow-sensitivity equations leverages the Runge‐Kutta time-marching scheme in conjunction with the parallel multigrid method of the flow solver. The matrix-vector products associated with the linearization of the flow equations are computed on-the-fly, thereby minimizing the memory requirements of the algorithm at a computational cost roughly equivalent to a flow solution. Three-dimensional test cases, including a wing-body geometry at transonic flow conditions and an entry vehicle at supersonic flow conditions, are presented. These cases verify the accuracy of the linearization and demonstrate the eciency and robustness of the adjoint algorithm for complex-geometry problems.

CAD-Based Aerodynamic Design of Complex Configurations using a Cartesian Method

1 Abstract A modular framework for aerodynamic optimization of complex geometries is developed. By working directly with a parametric CAD system, complex-geometry models are modified and tessellated in an automatic fashion. The use of a component-based Cartesian method significantly reduces the demands on the CAD system, and also provides for robust and efficient flowfield analysis. The optimization is controlled using either a genetic or quasi‐Newton algorithm. Parallel efficiency of the framework is maintained even when subject to limited CAD resources by dynamically re-allocating the processors of the flow solver. Overall, the resulting framework can explore designs incorporating large shape modifications and changes in topology.

Parallel Adjoint Framework for Aerodynamic Shape Optimization of Component-Based Geometry

We present a parallel adjoint framework for aerodynamic shape optimization problems using an embedded-boundary Cartesian mesh method. The design goals for the framework focus on an efficient and systematic integration of the underlying software modules. By linearizing the geometric constructors used in intersecting triangulated components, we develop a robust approach for computing surface shape sensitivities of complex configurations. The framework uses multilevel parallelism in sensitivity computations. Serial and parallel codes are executed concurrently to speedup gradient computations. A variety of optimizers are supported, and geometric modelers can be either CAD-based or CAD-free. We present design examples involving sonic-boom mitigation and nacelle integration for transport aircraft involving over 160 design variables and using up to 256 processors. This is an important step in our research toward making aerodynamic shape optimization tools available to the broader aerodynamics community instead of CFD specialists only.