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NASA NTRS1997

Load Balancing Sequences of Unstructured Adaptive Grids

Mesh adaption is a powerful tool for efficient unstructured grid computations but causes load imbalance on multiprocessor systems. To address this problem, we have developed PLUM, an automatic portable framework for performing adaptive large-scale numerical computations in a message-passing environment. This paper makes several important additions to our previous work. First, a new remapping cost model is presented and empirically validated on an SP2. Next, our load balancing strategy is applied to sequences of dynamically adapted unstructured grids. Results indicate that our framework is effective on many processors for both steady and unsteady problems with several levels of adaption. Additionally, we demonstrate that a coarse starting mesh produces high quality load balancing, at a fraction of the cost required for a fine initial mesh. Finally, we show that the data remapping overhead can be significantly reduced by applying our heuristic processor reassignment algorithm.

Biswas, Rupak↗

NASA NTRS1993

Unstructured surface grid generation

Viewgraphs on unstructured surface grid generation are presented. Topics covered include: requirements for curves, surfaces, solids, and text; surface approximation; triangulation; advancing; projection; mapping; and parametric curves.

Jamshid Samareh-Abolhassani↗

NASA NTRS1993

A multigrid method for steady Euler equations on unstructured adaptive grids

A flux-difference splitting type algorithm is formulated for the steady Euler equations on unstructured grids. The polynomial flux-difference splitting technique is used. A vertex-centered finite volume method is employed on a triangular mesh. The multigrid method is in defect-correction form. A relaxation procedure with a first order accurate inner iteration and a second-order correction performed only on the finest grid, is used. A multi-stage Jacobi relaxation method is employed as a smoother. Since the grid is unstructured a Jacobi type is chosen. The multi-staging is necessary to provide sufficient smoothing properties. The domain is discretized using a Delaunay triangular mesh generator. Three grids with more or less uniform distribution of nodes but with different resolution are generated by successive refinement of the coarsest grid. Nodes of coarser grids appear in the finer grids. The multigrid method is started on these grids. As soon as the residual drops below a threshold value, an adaptive refinement is started. The solution on the adaptively refined grid is accelerated by a multigrid procedure. The coarser multigrid grids are generated by successive coarsening through point removement. The adaption cycle is repeated a few times. Results are given for the transonic flow over a NACA-0012 airfoil.

Riemslagh, Kris↗

NASA NTRS1994

New multigrid approach for three-dimensional unstructured, adaptive grids

A new multigrid method with adaptive unstructured grids is presented. The three-dimensional Euler equations are solved on tetrahedral grids that are adaptively refined or coarsened locally. The multigrid method is employed to propagate the fine grid corrections more rapidly by redistributing the changes-in-time of the solution from the fine grid to the coarser grids to accelerate convergence. A new approach is employed that uses the parent cells of the fine grid cells in an adapted mesh to generate successively coaser levels of multigrid. This obviates the need for the generation of a sequence of independent, nonoverlapping grids as well as the relatively complicated operations that need to be performed to interpolate the solution and the residuals between the independent grids. The solver is an explicit, vertex-based, finite volume scheme that employs edge-based data structures and operations. Spatial discretization is of central-differencing type combined with a special upwind-like smoothing operators. Application cases include adaptive solutions obtained with multigrid acceleration for supersonic and subsonic flow over a bump in a channel, as well as transonic flow around the ONERA M6 wing. Two levels of multigrid resulted in reduction in the number of iterations by a factor of 5.

Parthasarathy, Vijayan↗

NASA NTRS2010

Assessment of Hybrid RANS/LES Turbulence Models for Aeroacoustics Applications

Predicting the noise from aircraft with exposed landing gear remains a challenging problem for the aeroacoustics community. Although computational fluid dynamics (CFD) has shown promise as a technique that could produce high-fidelity flow solutions, generating grids that can resolve the pertinent physics around complex configurations can be very challenging. Structured grids are often impractical for such configurations. Unstructured grids offer a path forward for simulating complex configurations. However, few unstructured grid codes have been thoroughly tested for unsteady flow problems in the manner needed for aeroacoustic prediction. A widely used unstructured grid code, FUN3D, is examined for resolving the near field in unsteady flow problems. Although the ultimate goal is to compute the flow around complex geometries such as the landing gear, simpler problems that include some of the relevant physics, and are easily amenable to the structured grid approaches are used for testing the unstructured grid approach. The test cases chosen for this study correspond to the experimental work on single and tandem cylinders conducted in the Basic Aerodynamic Research Tunnel (BART) and the Quiet Flow Facility (QFF) at NASA Langley Research Center. These configurations offer an excellent opportunity to assess the performance of hybrid RANS/LES turbulence models that transition from RANS in unresolved regions near solid bodies to LES in the outer flow field. Several of these models have been implemented and tested in both structured and unstructured grid codes to evaluate their dependence on the solver and mesh type. Comparison of FUN3D solutions with experimental data and numerical solutions from a structured grid flow solver are found to be encouraging.

Vatsa, Veer N.↗

NASA NTRS2015

Multi-Resolution Unstructured Grid-Generation for Geophysical Applications on the Sphere

An algorithm for the generation of non-uniform unstructured grids on ellipsoidal geometries is described. This technique is designed to generate high quality triangular and polygonal meshes appropriate for general circulation modelling on the sphere, including applications to atmospheric and ocean simulation, and numerical weather predication. Using a recently developed Frontal-Delaunay-refinement technique, a method for the construction of high-quality unstructured ellipsoidal Delaunay triangulations is introduced. A dual polygonal grid, derived from the associated Voronoi diagram, is also optionally generated as a by-product. Compared to existing techniques, it is shown that the Frontal-Delaunay approach typically produces grids with near-optimal element quality and smooth grading characteristics, while imposing relatively low computational expense. Initial results are presented for a selection of uniform and non-uniform ellipsoidal grids appropriate for large-scale geophysical applications. The use of user-defined mesh-sizing functions to generate smoothly graded, non-uniform grids is discussed.

Weather↗

NASA NTRS1993

VGRIDSG: An unstructured surface grid generation program

This report contains an overview of the VGRIDSG unstructured surface grid generation program. The VGRIDSG program was created from the VGRID3D unstructured grid generation program developed by Vigyan, Inc. The purpose of this report is to document the changes from the original VGRID3D program and to describe the capabilities of the new program.

Bockelie, Michael J.↗

NASA NTRS1995

Unstructured Cartesian/prismatic grid generation for complex geometries

The generation of a hybrid grid system for discretizing complex three dimensional (3D) geometries is described. The primary grid system is an unstructured Cartesian grid automatically generated using recursive cell subdivision. This grid system is sufficient for computing Euler solutions about extremely complex 3D geometries. A secondary grid system, using triangular-prismatic elements, may be added for resolving the boundary layer region of viscous flows near surfaces of solid bodies. This paper describes the grid generation processes used to generate each grid type. Several example grids are shown, demonstrating the ability of the method to discretize complex geometries, with very little pre-processing required by the user.

Karman, Steve L., Jr.↗

NASA NTRS1996

Load Balancing Unstructured Adaptive Grids for CFD Problems

Mesh adaption is a powerful tool for efficient unstructured-grid computations but causes load imbalance among processors on a parallel machine. A dynamic load balancing method is presented that balances the workload across all processors with a global view. After each parallel tetrahedral mesh adaption, the method first determines if the new mesh is sufficiently unbalanced to warrant a repartitioning. If so, the adapted mesh is repartitioned, with new partitions assigned to processors so that the redistribution cost is minimized. The new partitions are accepted only if the remapping cost is compensated by the improved load balance. Results indicate that this strategy is effective for large-scale scientific computations on distributed-memory multiprocessors.

Biswas, Rupak↗

NASA NTRS1994

Progress in Grid Generation: From Chimera to DRAGON Grids

Hybrid grids, composed of structured and unstructured grids, combines the best features of both. The chimera method is a major stepstone toward a hybrid grid from which the present approach is evolved. The chimera grid composes a set of overlapped structured grids which are independently generated and body-fitted, yielding a high quality grid readily accessible for efficient solution schemes. The chimera method has been shown to be efficient to generate a grid about complex geometries and has been demonstrated to deliver accurate aerodynamic prediction of complex flows. While its geometrical flexibility is attractive, interpolation of data in the overlapped regions - which in today's practice in 3D is done in a nonconservative fashion, is not. In the present paper we propose a hybrid grid scheme that maximizes the advantages of the chimera scheme and adapts the strengths of the unstructured grid while at the same time keeps its weaknesses minimal. Like the chimera method, we first divide up the physical domain by a set of structured body-fitted grids which are separately generated and overlaid throughout a complex configuration. To eliminate any pure data manipulation which does not necessarily follow governing equations, we use non-structured grids only to directly replace the region of the arbitrarily overlapped grids. This new adaptation to the chimera thinking is coined the DRAGON grid. The nonstructured grid region sandwiched between the structured grids is limited in size, resulting in only a small increase in memory and computational effort. The DRAGON method has three important advantages: (1) preserving strengths of the chimera grid; (2) eliminating difficulties sometimes encountered in the chimera scheme, such as the orphan points and bad quality of interpolation stencils; and (3) making grid communication in a fully conservative and consistent manner insofar as the governing equations are concerned. To demonstrate its use, the governing equations are discretized using the newly proposed flux scheme, AUSM+, which will be briefly described herein. Numerical tests on representative 2D inviscid flows are given for demonstration. Finally, extension to 3D is underway, only paced by the availability of the 3D unstructured grid generator.

Liou, Meng-Sing↗

NASA NTRS1995

Evaluation of grid generation technologies from an applied perspective

An analysis of the grid generation process from the point of view of an applied CFD engineer is given. Issues addressed include geometric modeling, structured grid generation, unstructured grid generation, hybrid grid generation and use of virtual parts libraries in large parametric analysis projects. The analysis is geared towards comparing the effective turn around time for specific grid generation and CFD projects. The conclusion was made that a single grid generation methodology is not universally suited for all CFD applications due to both limitations in grid generation and flow solver technology. A new geometric modeling and grid generation tool, CFD-GEOM, is introduced to effectively integrate the geometric modeling process to the various grid generation methodologies including structured, unstructured, and hybrid procedures. The full integration of the geometric modeling and grid generation allows implementation of extremely efficient updating procedures, a necessary requirement for large parametric analysis projects. The concept of using virtual parts libraries in conjunction with hybrid grids for large parametric analysis projects is also introduced to improve the efficiency of the applied CFD engineer.

Hufford, Gary S.↗

NASA NTRS1993

Advancing-layers method for generation of unstructured viscous grids

A novel approach for generating highly stretched grids which is based on a modified advancing-front technique and benefits from the generality, flexibility, and grid quality of the conventional advancing-front-based Euler grid generators is presented. The method is self-sufficient for the insertion of grid points in the boundary layer and beyond. Since it is based on a totally unstructured grid strategy, the method alleviates the difficulties stemming from the structural limitations of the prismatic techniques.

Pirzadeh, Shahyar↗

NASA NTRS1996

Unstructured Adaptive Grid Computations on an Array of SMPs

Dynamic load balancing is necessary for parallel adaptive methods to solve unsteady CFD problems on unstructured grids. We have presented such a dynamic load balancing framework called JOVE, in this paper. Results on a four-POWERnode POWER CHALLENGEarray demonstrated that load balancing gives significant performance improvements over no load balancing for such adaptive computations. The parallel speedup of JOVE, implemented using MPI on the POWER CHALLENCEarray, was significant, being as high as 31 for 32 processors. An implementation of JOVE that exploits 'an array of SMPS' architecture was also studied; this hybrid JOVE outperformed flat JOVE by up to 28% on the meshes and adaption models tested. With large, realistic meshes and actual flow-solver and adaption phases incorporated into JOVE, hybrid JOVE can be expected to yield significant advantage over flat JOVE, especially as the number of processors is increased, thus demonstrating the scalability of an array of SMPs architecture.

Biswas, Rupak↗

NASA NTRS1993

Unstructured viscous grid generation by advancing-front method

A new method of generating unstructured triangular/tetrahedral grids with high-aspect-ratio cells is proposed. The method is based on new grid-marching strategy referred to as 'advancing-layers' for construction of highly stretched cells in the boundary layer and the conventional advancing-front technique for generation of regular, equilateral cells in the inviscid-flow region. Unlike the existing semi-structured viscous grid generation techniques, the new procedure relies on a totally unstructured advancing-front grid strategy resulting in a substantially enhanced grid flexibility and efficiency. The method is conceptually simple but powerful, capable of producing high quality viscous grids for complex configurations with ease. A number of two-dimensional, triangular grids are presented to demonstrate the methodology. The basic elements of the method, however, have been primarily designed with three-dimensional problems in mind, making it extendible for tetrahedral, viscous grid generation.

Pirzadeh, Shahyar↗

NASA NTRS1993

Unstructured viscous grid generation by advancing-layers method

Pirzadeh, Shahyar↗

NASA NTRS2009

Description of the F-16XL Geometry and Computational Grids Used in CAWAPI

The objective of the Cranked-Arrow Wing Aerodynamics Project International (CAWAPI) was to allow a comprehensive validation of Computational Fluid Dynamics methods against the CAWAP flight database. A major part of this work involved the generation of high-quality computational grids. Prior to the grid generation an IGES file containing the air-tight geometry of the F-16XL aircraft was generated by a cooperation of the CAWAPI partners. Based on this geometry description both structured and unstructured grids have been generated. The baseline structured (multi-block) grid (and a family of derived grids) has been generated by the National Aerospace Laboratory NLR. Although the algorithms used by NLR had become available just before CAWAPI and thus only a limited experience with their application to such a complex configuration had been gained, a grid of good quality was generated well within four weeks. This time compared favourably with that required to produce the unstructured grids in CAWAPI. The baseline all-tetrahedral and hybrid unstructured grids has been generated at NASA Langley Research Center and the USAFA, respectively. To provide more geometrical resolution, trimmed unstructured grids have been generated at EADS-MAS, the UTSimCenter, Boeing Phantom Works and KTH/FOI. All grids generated within the framework of CAWAPI will be discussed in the article. Both results obtained on the structured grids and the unstructured grids showed a significant improvement in agreement with flight test data in comparison with those obtained on the structured multi-block grid used during CAWAP.

Boelens, O. J.↗

NASA NTRS1998

Euler Technology Assessment for Preliminary Aircraft Design-Unstructured/Structured Grid NASTD Application for Aerodynamic Analysis of an Advanced Fighter/Tailless Configuration

This study supports the NASA Langley sponsored project aimed at determining the viability of using Euler technology for preliminary design use. The primary objective of this study was to assess the accuracy and efficiency of the Boeing, St. Louis unstructured grid flow field analysis system, consisting of the MACGS grid generation and NASTD flow solver codes. Euler solutions about the Aero Configuration/Weapons Fighter Technology (ACWFT) 1204 aircraft configuration were generated. Several variations of the geometry were investigated including a standard wing, cambered wing, deflected elevon, and deflected body flap. A wide range of flow conditions, most of which were in the non-linear regimes of the flight envelope, including variations in speed (subsonic, transonic, supersonic), angles of attack, and sideslip were investigated. Several flowfield non-linearities were present in these solutions including shock waves, vortical flows and the resulting interactions. The accuracy of this method was evaluated by comparing solutions with test data and Navier-Stokes solutions. The ability to accurately predict lateral-directional characteristics and control effectiveness was investigated by computing solutions with sideslip, and with deflected control surfaces. Problem set up times and computational resource requirements were documented and used to evaluate the efficiency of this approach for use in the fast paced preliminary design environment.

Michal, Todd R.↗

NASA NTRS1991

A Graphically Interactive Approach to Structured and Unstructured Surface Grid Quality Analysis

A graphically interactive approach to structured and unstructured surface grid quality analysis is described. A Surface Analysis Code SurfACe) is developed to help a user analyze surface grid quality based on surface normal vectors, first and second derivatives of these vectors, normal, Gaussian, and mean curvatures, orthogonality, aspect ratio, and cell area. The results demonstrate how this approach can be used to reduce surface grid generation errors and increase the cost effectiveness of Computational Fluid Dynamics as an aircraft design tool.

Stewart, John E.↗