Timothy J. Baker

Automatic mesh generation for complex three-dimensional regions using a constrained Delaunay triangulation

This paper describes a method for generating tetrahedral meshes. The algorithm, based on the Delaunay triangulation, can treat objects of essentially arbitrary complexity. In order to preserve the surface triangulation of solid objects, it is necessary to override the Delaunay property and redefine the triangulation when points are introduced that are close to solid boundaries. Details of this constrained Delaunay algorithm are presented and an efficient implementation of the triangulation method is described. Techniques for controlling the distribution of mesh points and tetrahedron quality are also discussed.

Mesh adaptation strategies for problems in fluid dynamics

Abstract Mesh adaptation procedures are reviewed and discussed with particular emphasis on methods that are based on mesh movement (r-refinement) and mesh enrichment (h-refinement). Although the need for adaptive refinement is common to many areas of scientific computation, the examples in this survey paper are drawn almost exclusively from the domain of computational fluid dynamics.

Multigrid solution of the Euler equations for aircraft configurations

A multigrid scheme for solving the Euler equations is presented. The method has been successfully applied to two-dimensional airfoil calculations on both O-type and C-type meshes. In three dimensions the scheme has proved equally effective and calclations of flows over wing/body combinations are possible with convergence achieved in less than 100 cycles.

Developments and trends in three-dimensional mesh generation

Abstract An intense research effort over the last few years has produced several competing and apparently diverse methods for generating meshes. This paper reviews recent progress and emphasizes the central themes that we can expect to form a solid foundation for future developments in mesh generation.

Mesh Movement and Metamorphosis

Abstract.Mesh coarsening and mesh enrichment are combined with a r-refinement scheme to produce a flexible approach for mesh adaptation of time evolving domains. The robustness of this method depends heavily upon maintaining mesh quality during each adaptation cycle. This in turn is inlfuenced by the ability to identify and remove badly shaped elements after the r-refinement stage. Measures of both element quality and element deformation can be defined in terms of unitarily invariant matrix norms. The construction of these element deformation and quality measures is described, and details are provided of the three stages of the adaptation cycle.

Analysis of triangle quality measures

Several of the more commonly used triangle quality measures are analyzed and compared. Proofs are provided to verify that they do exhibit the expected extremal properties. The asymptotic behavior of these measures is investigated and a number of useful results are derived. It is shown that some of the quality measures are equivalent, in the sense of displaying the same extremal and asymptotic behavior, and that it is therefore possible to achieve a concise classification of triangle quality measures.

AERODYNAMIC SHAPE OPTIMIZATION USING UNSTRUCTURED GRID METHODS

Two unstructured-grid Euler-based CFD codes, AIRPLANE and FLOWCART were coupled to a gradientbased quasi-Newton finite-difference optimization algorithm. These two optimization techniques were developed to provide detailed aerodynamic shape optimization methods for complete configurations with efficient grid generation methods. AIRPLANE utilizes a tetrahedral mesh whereas FLOWCART uses a hexahedral Cartesian mesh. Several codes were developed to facilitate aerodynamic shape optimization. These include developing surface grid perturbation methods with thickness constraint and overall surface overlap evaluations, used with both Euler codes, and adding a multigrid capability and a variety of mesh movement techniques to the AIRPLANE method. The AIRPLANE multigridding approach was proven to be accurate and effective, with typical speedup ratios of 3 to 5. The mesh movement techniques were effective in reducing the grid generation wall clock time by 70%. Detailed results of the AIRPLANE-based optimization technique are presented. The performance gains resulting from optimization are verified by computations with FLOWCART and OVERFLOW, and comparisons with experimental data on the baseline and optimized configurations. The low speed computational results of the baseline and optimized models were incorporated into an approach and landing simulation database. The controllability and handling qualities were good to excellent based on a piloted simulation in the NASA Ames Vertical Motion Simulator (VMS). FLOWCARTbased optimization was validated by comparing its gradients and design solutions with AIRPLANE’s on two separate optimization problems with identical design variables and objective functions.

Mesh generation by a sequence of transformations

Abstract A sequence of transformations is used to map a three-dimensional aerodynamic shape into a simplified configuration. Coordinate surfaces are generated in the mapped space and the transformation sequence is inverted to produce a three-dimensional mesh that conforms with solid boundaries. The method has been used to generate meshes about typical aircraft shapes consisting of a wing, body, tail and fin.

Mesh generation for the computation of flowfields over complex aerodynamic shapes

Methods are presented for generating both structured and unstructured meshes about three dimensional shapes. Results for both approaches are shown and their strengths and weaknesses are compared. For relatively simple configurations, such as wing/body combinations, a structured mesh is the preferred approach. For a complete aircraft, however, structured meshes lack the necessary flexibility, but unstructured meshes do offer the opportunity to treat completely general configurations with relative ease.

Solution of three-dimensional supersonic flowfields via adapting unstructured meshes

Abstract Solution adaptive mesh refinement in three-dimensions on unstructured Delaunay meshes was used to solve the Euler equations for two supersonic flows. One case was uniform flow past a wedge within a channel, producing a shock wave and its reflection off a wall of the channel. The other case incorporated a similar geometry but with an inviscid rotational boundary layer as an inlet condition. This flow was used to model a swept shock wave/boundary layer interaction.