An operations research approach to solve complex and unstructured problems illustrated for the case of cost-plus-award fee contracts.
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A two-step explicit finite element based solution procedure for the compressible Euler equations is described. Convergence to steady state can be accelerated by using a multigrid technique. The geometric flexibility of the finite element method is retained by using a sequence of unnested grids. The viability of this approach is demonstrated for elliptic problems and initial experiences with the technique applied to the Euler equations are reported.
The use of the multigrid procedure with a sequence of unnested coarser grids is discussed. Validity of the procedure is assessed by considering the solution of a single linear elliptic equation. It is demonstrated how a scheme with the optimum order of operations can be constructed. Application to the solution of the Euler equations is considered.
The incorporation of algebraic turbulence models in a solver for the 2-D compressible Navier-Stokes equations using triangular grids is described. A practical way to use the Cebeci Smith model, and to modify it in separated regions is proposed. The ability of the model to predict high speed, perfect gas boundary layers is investigated from a numerical point of view.
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The incorporation of algebraic turbulence models in a solver for the 2-D compressible Navier-Stokes equations using triangular grids is described. A practial way to use the Cebeci Smith model, and to modify it in separated regions is proposed. The ability of the model to predict high speed, perfect gas boundary layers is investigated from a numerical point of view.
Grid generation and adaptive refinement techniques suitable for the simulation of strongly unsteady flows past geometrically complex bodies in 3-D are described. The grids are generated using the advancing front technique. Emphasis is placed not to generate elements that are too small, as this would severely increase the cost of simulations with explicit flow solvers. The grids are adapted to an evolving flowfield using simple h-refinement. A grid change is performed every 5 to 10 timesteps, and only one level of refinement/coarsening is allowed per mesh change.
Mesh generation methods for Computational Fluid Dynamics (CFD) are outlined. Geometric modeling is discussed. An advancing front method is described. Flow past a two engine Falcon aeroplane is studied. An algorithm and associated data structure called the alternating digital tree, which efficiently solves the geometric searching problem is described. The computation of an initial approximation to the steady state solution of a given poblem is described. Mesh generation for transient flows is described.
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High order accurate finite-volume schemes for solving the Euler equations of gasdynamics are developed. Central to the development of these methods are the construction of a k-exact reconstruction operator given cell-averaged quantities and the use of high order flux quadrature formulas. General polygonal control volumes (with curved boundary edges) are considered. The formulations presented make no explicit assumption as to complexity or convexity of control volumes. Numerical examples are presented for Ringleb flow to validate the methodology.
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The advancing front technique is being used to develop a code to generate grids around complex 3-D configurations for use in computing the invisid flow solutions by the Euler equations. By the advancing front technique points are introduced concurrently with the connectivity information so that a separate library is not required. The generation of a 3-D grid is accomplished in several steps. First the boundaries of the domain to be gridded must be described by two-, three- or four-sided surface patches. Next, a background mesh is required to control the grid spacing and stretching throughout the domain. This coarse tetrahedral grid is not required to conform to any of the boundaries. Next, each of the patches is mapped to 2-D, triangulated by the advancing front technique and mapped back to 3-D. These triangles form the initial front for the generation of the final tetrahedral mesh.
A wavefront mesh generator for two dimensional triangular meshes as well as a brief description of the solution method used with these meshes are presented. The interest is in creating meshes for solving the equations of fluid mechanics in complex turbomachinery problems, although the mesh generator and flow solver may be used for a larger variety of applications. The focus is on the flexibility and power of the mesh generation method for triangulating extremely complex geometries and in changing the geometry to create a new mesh. Two turbomachinery applications are presented which take advantage of this method: the analysis of pylon/strut and pylon/OGV interaction in the bypass of a turbofan.
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This paper describes an algorithm for reconstructing a surface from a randomly digitized object. Scan data (treated as a cloud of points) is first tesselated out to its convex hull using Delaunay triangulation. The line-of-sight between each surface point and the scanning device is traversed, and any tetrahedra which are pierced by it are removed. The remaining tetrahedra form an approximate solid model of the scanned object. Due to the inherently limited resolution of any scan, this algorithm requires two additional procedures to produce a smooth, polyhedral surface: one process removes long, narrow tetrahedra which span indentations in the surface between digitized points; the other smooths sharp edges. The results for a moderately resolved sample body and a highly resolved aircraft are displayed.