David L. Marcum

Unstructured grid generation using iterative point insertion and local reconnection

A procedure is presented for efficient generation of high-quality two- or three-dimensional unstructured grids of triangular or tetrahedral elements. The present procedure uses an iterative point creation and insertion scheme wherein points are created using advancing-front type point placement. Initially, the connectivity for these generated points is obtained by directly subdividing the elements which contain them, without regard to quality. This connectivity is then improved by iteratively using local reconnection subject to a quality criterion. For two dimensions, a min-max criterion is used and for three dimensions, a Delaunay in-sphere criterion followed by a min-max type criterion is used. The overall procedure is applied repetitively until a complete field grid is generated with a desired point distribution. Grid quality and performance statistics are presented for a variety of two- and three-dimensional configurations. The combined quality and efficiency attributes of this procedure appear to be a substantial improvement over existing methods.

Efficient Generation of High-Quality Unstructured Surface and Volume Grids

Abstract.Procedures are presented for efficient generation of high-quality unstructured surface and volume grids. The overall procedure is based on the well proven Advancing Front/Local-Reconnection (AFLR) method. The AFLR triangular/tetrahedral grid generation procedure is a combination of automatic point creation, advancing type ideal point placement, and connectivity optimization schemes. A valid grid is maintained throughout the grid generation process. This provides a framework for implementing efficient local search operations using a simple data structure. It also provides a means for smoothly distributing the desired point spacing in the field using a point distribution function. This function is propagated through the field by interpolation from the boundary point spacing or by specified growth normal to the boundaries. Points are generated using either advancing- front type point placement for isotropic elements, advancing-point type point placement for isotropic right angle elements, or advancing-normal type point placement for high-aspect-ratio elements. The connectivity for new points is initially obtained by direct subdivision of the elements that contain them. Local-reconnection with a min-max type (minimize the maximum angle) type criterion is then used to optimize the connectivity. The overall procedure is applied repetitively until a complete field grid is obtained. An advancing-normal procedure is coupled with AFLR for anisotropic tetrahedral and pentahedral element grids. Advancing along prescribed normals from solid boundaries generates layers of anisotropic elements. The points are generated such that either pentahedral or tetrahedral elements with an implied connectivity can be directly recovered. The AFLR surface grid procedure uses an approximate physical space grid to define the surface during grid generation. The mapped space coordinates are mapped back to the actual surface at completion. Multiple surface definition patches are grouped into a single surface. A global mapping transformation is generated for the single surface using the grouped surface connectivity. The mapping coordinates are obtained by solving a coupled set of Laplacian equations. The overall procedure has been applied to a wide variety of configurations. Selected results are presented which demonstrate that high-quality unstructured grids can be efficiently and consistently generated for complex configurations.

Mixed Element Type Unstructured Grid Generation for Viscous Flow Applications

A procedure is presented for efficient generation of high-quality unstructured grids suitable for CFD simulation of high Reynolds number viscous flow fields. Layers of anisotropic elements are generated by advancing along prescribed normals from solid boundaries. The points are generated such that either pentahedral or tetrahedral elements with an implied connectivity can be be directly recovered. As points are generated they are temporarily attached to a volume triangulation of the boundary points. This triangulation allows efficient local search algorithms to be used when checking merging layers, The existing advancing-front/local-reconnection procedure is used to generate isotropic elements outside of the anisotropic region. Results are presented for a variety of applications. The results demonstrate that high-quality anisotropic unstructured grids can be efficiently and consistently generated for complex configurations.

An investigation of parallel implicit solution algorithms for incompressible flows on multielement unstructured topologies

The primary objective of this study is to develop an efficient incompressible flow solver capable of performing viscous, high Reynolds number flow simulations for complex geometries using general unstructured grids. This parallel flow solver is demonstrated for large-scale meshes with viscous sublayer resolution (p+ N 1) and approximately lo6 points or more. Primary issues addressed in this work are 1) treatment of the connectivity between subdomain interfaces, 2) proper definition of the iteration hierarchy, and 3) methods for coupling of subdomains. The present parallel unstructured viscous flow solver is based on a domain decomposition for concurrent solution within subdomains assigned to multiple processors. The solution algorithm employs iterative solution of the implicit approximation, with coupling between subdomains according to several schemes that are a primary focus of the study. MPI message passing is used for interprocessor communication. Applications include 1) a full-scale ship hull, 2) the SUBOFF model hull with stern appendages, and 3) a fully-configured high-lift transport. Introduction Implicit algorithms for flows on unstructured grids have been investigated extensively by a variety of authors [l] [2] [3] [4]. However, implicit algorithms are much more difficult to) parallelize, because of their inherent global dependencies. As such, the parallelization of unstructured Euler solvers [5] [S] [7] and Navier-Stokes solvers [S] [9] [lo] have been previously investigated. This work seeks to examine a relaxation-type algorithm *Research Assistant I, Member ASME *Research Engineer I, Member AIAA SProfessor, Member AIAA §Distinguished Professor, Member AIAA Copyright@2000 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved. in depth to provide insight concerning issues that arise in the parallelization of implicit solution algorithms on unstructured topologies. In general, the parallelization of an existing validated flow solver should satisfy several constraints. First and most important; the accuracy of the overall numerical scheme must not be compromised; i.e., the solution computed in parallel must have a oneto-one correspondence with the solution computed in serial mode. Also, the code must be efficient irrits use of computational resources. This characteristic is measured in terms of memory usage and scalability, as well as the fact that the parallel code should degenerate to the serial version if only one processor is available. Finally, the consequences of the inevitable domain decomposition should not seriously compromise the convergence rate of the iterative,algorithm. The present parallel unstructured viscous flow solver is based on a coarse-grained domain decomposition for concurrent solution within subdomains assigned to multiple processors. The solver also has the capability to map an arbitrary number of subdomains to a physical processor; thus, some flexibility is available to leverage available memory should memory resources be scarce. The present solution algorithm is related to several previous efforts. The approach is an evolution of the implicit flow solver and code of Anderson et al. [ll] [12] [13]; the solver developed in this series of works demonstrates 3D, implicit, high Reynolds number solution capability. Also, this work follows the unstructured multiblock solver of Sheng and Whitfield [14] [15] which uses the same core solver but employs a multiblock technique to reduce memory consumption by 70%. These studies are in turn related to the multiblock structured solvers originating from Taylor, Whitfield, and Sheng [16] [17] [18]. Elements of the present approach to parallel solution are related to the parallel multiblock structured grid solver of Pankajakshan and Briley [19].

Adaptive unstructured grid generation for viscous flow applications

Our objective is to develop a procedure for efficient generation of high-quality solution-adapted grids suitable for viscous flow applications. The overall approach taken in this work for solution adaptation is to generate high-aspect-ratio elements in the boundary-layer regions and to capture inviscid features and detached viscous features independently using different adaptation procedures.

Visualization of fluid flows in virtual environments

Visualization of Fluid Flows in Virtual Environments Ziegele , S. B. r r 1), Gopal, G. P. 1), Blades, E. 2), Moo head, R. J. 1), Marcum, D. L. 2) and Guan, Y. 1) 1) ERC GRI Visualization, Analysis and Imaging Laboratory, Mississippi State University, MS, U.S.A. E-mail : {sean | gopi | rjm | guanyl } @gri.msstate.edu 2) ERC SimCenter, Mississippi State University, MS, U.S.A., E-mail : { blades | marcum } @simcenter.msstate.edu

Numerical Simulation of a Spinning Missile with Dithering Canards Using Unstructured Grids

Euler and Navier-Stokes solutions were obtained using an unstructured-grid approach to predict the aerodynamic performance of a spinning missile with dithering canards. Integrated force and moment coefficients were computed, along with helicity contours to track the horseshoe vortices generated by the canards. Comparisons were made to determine the effect of grid resolution and viscous effects. The grid-resolution study was performed using three levels of refinement. Comparison of the viscous and inviscid force and moment coefficients revealed that the viscous effects were not significant for this low angle of attack. The largest viscous contribution was to the axial force, which was approximately 10% of the total axial force. Overall the viscous effects were minimal because the flow is supersonic and remains attached and there are no regions of separated flow where viscous effects are important. The vortices are due to the pressure difFerences acting on the canards and not due to viscous boundary-layer separation along the missile body. It was found that, at certain roll orientations, the canards do impinge on the tail fins. Solution comparisons were made to results from another high-resolution viscous flow solver and to experimental data and the results compared favorably to both.

A procedure for efficient generation of solution adapted unstructured grids

Abstract An efficient procedure for generation of solution adapted unstructured grids is presented. The grid generation procedure is based upon a Delaunay triangulation scheme combined with new adaptive point source techniques. With this method, high quality solution adapted grids can be generated efficiently. Techniques are presented for obtaining adaptation sources which automatically detect relevant features in the flow field. The overall procedure is coupled with a finite element flow solver. Computed solutions are presented which successfully demonstrate the overall procedure for a variety of aerospace configurations.

SOLUTION ADAPTIVE UNSTRUCTURED GRID GENERATION USING PSEUDO-PATTERN RECOGNITION TECHNIQUES

A procedure is presented for anisotropic adaptation of inviscid type flow features with CFD simulation using an unstructured grid. The basic grid generation scheme is an existing advancing-front, local-reconnection (AFLR) procedure. This procedure is modified to allow the field point spacing and alignment to vary based on a flow field solution using adaptive grid regeneration. Multiple physically based feature detectors are used to isolate regions in the field which contain physical features of interest. Using pattern recognition techniques, these regions are reduced to groups of simple geometric entities representing the physical features. Features such as expansion or stagnation regions are reduced to singular points. Shock waves and contact discontinuities are reduced to curves. In the adaptive grid regeneration procedure, singular points are treated as adaptive sources which modify the boundary and field point spacing. Curves are treated as embedded boundaries. These embedded dual-sided boundaries provide a framework for generating aligned high-aspectnratio elements. A description of the procedure is presented along with results for two-dimensional applications with multiple features. The results clearly demonstrate the capability of the overall procedure for CFD applications. And, they indicate that the method can be further developed into a robust and useful procedure.

Aerospace application of solution adaptive finite element analysis

A solution adaptive finite element procedure for calculating complex flow fields about complicated aerospace configurations is presented. The procedure includes a new adaptive grid generation method based on a Delaunay triangulation scheme combined with adaptation sources. With this method, high-quality solution adapted grids can be generated efficiently. Techniques are presented for obtaining adaptation sources which automatically detect relevant features in a flow field. Computed solutions are presented which successfully demonstrate the overall procedure for a variety of aerospace configurations.