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NASA NTRS1992

Unstructured grid solutions to a wing/pylon/store configuration using VGRID3D/USM3D

The purpose of this paper is to validate an inviscid flow solution package based on a new unstructured grid methodology using experimental data on a wing/pylon/store configuration. The solution package consists of an advancing front unstructured grid generator, VGRID3D, and an efficient Euler equation solver, USM3D. Comparisons of computed data versus experimental data are made for two free-stream Mach numbers at five store locations relative to the wing. Both rigid body aerodynamics and mutual interference effects are explored. A very good agreement is observed between computed and wind tunnel data.

Parikh, Paresh↗

NASA NTRS1992

PARTI primitives for unstructured and block structured problems

Described here is a set of primitives (PARTI) developed to efficiently execute unstructured and block structured problems on distributed memory parallel machines. We present experimental data from a 3-D unstructured Euler solver run on the Intel Touchstone Delta to demonstrate the usefulness of our methods.

Sussman, A.↗

NASA NTRS1993

A hybrid structured-unstructured grid method for unsteady turbomachinery flow computations

A hybrid grid technique for the solution of 2D, unsteady flows is developed. This technique is capable of handling complex, multiple component geometries in relative motion, such as those encountered in turbomachinery. The numerical approach utilizes a mixed structured-unstructured zonal grid topology along with modeling equations and solution methods that are most appropriate in the individual domains, therefore combining the advantages of both structured and unstructured grid techniques.

Mathur, Sanjay R.↗

NASA NTRS1993

Application of an unstructured grid flow solver to planes, trains and automobiles

Rampant, an unstructured flow solver developed at Fluent Inc., is used to compute three-dimensional, viscous, turbulent, compressible flow fields within complex solution domains. Rampant is an explicit, finite-volume flow solver capable of computing flow fields using either triangular (2d) or tetrahedral (3d) unstructured grids. Local time stepping, implicit residual smoothing, and multigrid techniques are used to accelerate the convergence of the explicit scheme. The paper describes the Rampant flow solver and presents flow field solutions about a plane, train, and automobile.

Spragle, Gregory S.↗

NASA NTRS1992

A finite-volume Euler solver for computing rotary-wing aerodynamics on unstructured meshes

An unstructured-grid solver for the unsteady Euler equations has been developed for predicting the aerodynamics of helicopter rotor blades. This flow solver is a finite-volume scheme that computes flow quantities at the vertices of the mesh. Special treatments are used for the flux differencing and boundary conditions in order to compute rotary-wing flowfields, and these are detailed in the paper. The unstructured-grid solver permits adaptive grid refinement in order to improve the resolution of flow features such as shocks, rotor wakes and acoustic waves. These capabilities are demonstrated in the paper. Example calculations are presented for two hovering rotors. In both cases, adaptive-grid refinement is used to resolve high gradients near the rotor surface and also to capture the vortical regions in the rotor wake. The computed results show good agreement with experimental results for surface airloads and wake geometry.

Strawn, Roger C.↗

NASA NTRS1993

Unstructured viscous grid generation by advancing-layers 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 NTRS1992

Multigrid solution of internal flows using unstructured solution adaptive meshes

This is the final report of the NASA Lewis SBIR Phase 2 Contract Number NAS3-25785, Multigrid Solution of Internal Flows Using Unstructured Solution Adaptive Meshes. The objective of this project, as described in the Statement of Work, is to develop and deliver to NASA a general three-dimensional Navier-Stokes code using unstructured solution-adaptive meshes for accuracy and multigrid techniques for convergence acceleration. The code will primarily be applied, but not necessarily limited, to high speed internal flows in turbomachinery.

Smith, Wayne A.↗

NASA NTRS1993

Time-domain analysis of planar microstrip devices using a generalized Yee-algorithm based on unstructured grids

The generalized Yee-algorithm is presented for the temporal full-wave analysis of planar microstrip devices. This algorithm has the significant advantage over the traditional Yee-algorithm in that it is based on unstructured and irregular grids. The robustness of the generalized Yee-algorithm is that structures that contain curved conductors or complex three-dimensional geometries can be more accurately, and much more conveniently modeled using standard automatic grid generation techniques. This generalized Yee-algorithm is based on the the time-marching solution of the discrete form of Maxwell's equations in their integral form. To this end, the electric and magnetic fields are discretized over a dual, irregular, and unstructured grid. The primary grid is assumed to be composed of general fitted polyhedra distributed throughout the volume. The secondary grid (or dual grid) is built up of the closed polyhedra whose edges connect the centroid's of adjacent primary cells, penetrating shared faces. Faraday's law and Ampere's law are used to update the fields normal to the primary and secondary grid faces, respectively. Subsequently, a correction scheme is introduced to project the normal fields onto the grid edges. It is shown that this scheme is stable, maintains second-order accuracy, and preserves the divergenceless nature of the flux densities. Finally, for computational efficiency the algorithm is structured as a series of sparse matrix-vector multiplications. Based on this scheme, the generalized Yee-algorithm has been implemented on vector and parallel high performance computers in a highly efficient manner.

Gedney, Stephen D.↗

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 NTRS1993

Unstructured multigrid through agglomeration

In this work the compressible Euler equations are solved using finite volume techniques on unstructured grids. The spatial discretization employs a central difference approximation augmented by dissipative terms. Temporal discretization is done using a multistage Runge-Kutta scheme. A multigrid technique is used to accelerate convergence to steady state. The coarse grids are derived directly from the given fine grid through agglomeration of the control volumes. This agglomeration is accomplished by using a greedy-type algorithm and is done in such a way that the load, which is proportional to the number of edges, goes down by nearly a factor of 4 when moving from a fine to a coarse grid. The agglomeration algorithm has been implemented and the grids have been tested in a multigrid code. An area-weighted restriction is applied when moving from fine to coarse grids while a trivial injection is used for prolongation. Across a range of geometries and flows, it is shown that the agglomeration multigrid scheme compares very favorably with an unstructured multigrid algorithm that makes use of independent coarse meshes, both in terms of convergence and elapsed times.

Venkatakrishnan, V.↗

NASA NTRS1993

Three-dimensional unstructured grid method applied to turbomachinery

This work has three objectives: to develop a three-dimensional flow solver based on unstructured tetrahedral meshes for turbomachinery flows; to validate the solver through comparisons with experimental data; and to apply the solver for better understanding of the flow through turbomachinery geometries and design improvement. The work followed three different approaches: an existing external flow solver/grid generator (USM3D/VGRID) was extensively modified for internal flows; a three-dimensional, finite-volume solver based on Roe's flux-difference splitting and explicit Runge-Kutta time stepping; and three-dimensional unstructured tetrahedral mesh generation using an advancing-front technique. A discussion of these topics is presented in viewgraph form.

Oh Joon Kwon↗

NASA NTRS1993

Unstructured grid large eddy simulation of wall bounded turbulent flows

Historically, large eddy simulations (LES) have been restricted to simple geometries where spectral or finite difference methods have dominated due to their efficient use of structured grids. Structured grids, however, not only have difficulty representing complex domains and adapting to complicated flow features, but also are rather inefficient for simulating flows at high Reynolds numbers. The lack of efficiency stems from the need to resolve the viscous sub layer which requires very fine resolution in all three directions near the wall. Structured grids make use of a stretching to reduce the normal grid spacing but must carry the fine resolution in the streamwise and spanwise directions throughout the domain. The unnecessarily fine grid for much of the domain leads to disturbingly high grid estimates. Chapman (1979), and later Moin & Jimenez (1993), pointed out that, in order to advance the technology to airfoils at flight Reynolds numbers, structured grids must be abandoned in lieu of what are known as nested or unstructured grids. We illustrate the ability of an unstructured mesh to refine only the near wall region. Note the large number of points near the wall (where the fine vortical features need better resolution) and the coarseness in all directions away from the wall (where the scales are much larger). The important difference between this approach and the usual structured grid stretching is that the number of elements used to discretize the spanwise and streamwise features of the flow is reduced in each successive layer coming off the wall. This is due to the fact that the elements not only grow in the normal direction, but in the other directions as well. This greatly reduces the total number of points or elements required for a given Reynolds number flow.

Jansen, Kenneth↗

NASA NTRS1994

An implementation of a chemical and thermal nonequilibrium flow solver on unstructured meshes and application to blunt bodies

This paper presents a nonequilibrium flow solver, implementation of the algorithm on unstructured meshes, and application to hypersonic flow past blunt bodies. Air is modeled as a mixture of five chemical species, namely O2, N2, O, NO, and N, having two temperatures namely translational and vibrational. The solution algorithm is a cell centered, point implicit upwind scheme that employs Roe's flux difference splitting technique. Implementation of this algorithm on unstructured meshes is described. The computer code is applied to solve Mach 15 flow with and without a Type IV shock interference on a cylindrical body of 2.5mm radius representing a cowl lip. Adaptively generated meshes are employed, and the meshes are refined several times until the solution exhibits detailed flow features and surface pressure and heat flux distributions. Effects of a catalytic wall on surface heat flux distribution are studied. For the Mach 15 Type IV shock interference flow, present results showed a peak heat flux of 544 MW/m2 for a fully catalytic wall and 431 MW/m(exp 2) for a noncatalytic wall. Some of the results are compared with available computational data.

Prabhu, Ramadas K.↗

NASA NTRS1994

Laminar and turbulent flow computations of Type 4 shock-shock interference aerothermal loads using unstructured grids

This report presents computations for the Type 4 shock-shock interference flow under laminar and turbulent conditions using unstructured grids. Mesh adaptation was accomplished by remeshing, refinement, and mesh movement. Two two-equation turbulence models were used to analyze turbulent flows. The mean flow governing equations and the turbulence governing equations are solved in a coupled manner. The solution algorithm and the details pertaining to its implementation on unstructured grids are described. Computations were performed at two different freestream Reynolds numbers at a freestream Mach number of 11. Effects of the variation in the impinging shock location are studied. The comparison of the results in terms of wall heat flux and wall pressure distributions is presented.

Vemaganti, Gururaja R.↗

NASA NTRS1994

Unstructured grids on SIMD torus machines

Unstructured grids lead to unstructured communication on distributed memory parallel computers, a problem that has been considered difficult. Here, we consider adaptive, offline communication routing for a SIMD processor grid. Our approach is empirical. We use large data sets drawn from supercomputing applications instead of an analytic model of communication load. The chief contribution of this paper is an experimental demonstration of the effectiveness of certain routing heuristics. Our routing algorithm is adaptive, nonminimal, and is generally designed to exploit locality. We have a parallel implementation of the router, and we report on its performance.

Bjorstad, Petter E.↗

NASA NTRS1995

Unstructured mesh generation and adaptivity

An overview of current unstructured mesh generation and adaptivity techniques is given. Basic building blocks taken from the field of computational geometry are first described. Various practical mesh generation techniques based on these algorithms are then constructed and illustrated with examples. Issues of adaptive meshing and stretched mesh generation for anisotropic problems are treated in subsequent sections. The presentation is organized in an education manner, for readers familiar with computational fluid dynamics, wishing to learn more about current unstructured mesh techniques.

Mavriplis, D. J.↗

NASA NTRS1992

A MIMD implementation of a parallel Euler solver for unstructured grids

A mesh-vertex finite volume scheme for solving the Euler equations on triangular unstructured meshes is implemented on a MIMD (multiple instruction/multiple data stream) parallel computer. Three partitioning strategies for distributing the work load onto the processors are discussed. Issues pertaining to the communication costs are also addressed. We find that the spectral bisection strategy yields the best performance. The performance of this unstructured computation on the Intel iPSC/860 compares very favorably with that on a one-processor CRAY Y-MP/1 and an earlier implementation on the Connection Machine.

Venkatakrishnan, V.↗

NASA NTRS1995

Parallel volume ray-casting for unstructured-grid data on distributed-memory architectures

As computing technology continues to advance, computational modeling of scientific and engineering problems produces data of increasing complexity: large in size and unstructured in shape. Volume visualization of such data is a challenging problem. This paper proposes a distributed parallel solution that makes ray-casting volume rendering of unstructured-grid data practical. Both the data and the rendering process are distributed among processors. At each processor, ray-casting of local data is performed independent of the other processors. The global image composing processes, which require inter-processor communication, are overlapped with the local ray-casting processes to achieve maximum parallel efficiency. This algorithm differs from previous ones in four ways: it is completely distributed, less view-dependent, reasonably scalable, and flexible. Without using dynamic load balancing, test results on the Intel Paragon using from two to 128 processors show, on average, about 60% parallel efficiency.

Ma, Kwan-Liu↗