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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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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↗
NASA NTRS1995

Three-dimensional unstructured method for flows past bodies in 6-DOF relative motion

A three dimensional, unstructured-mesh methodology was developed to simulate unsteady flows past bodies in relative motion, where the trajectory was determined from the instantaneous aerodynamics. The method coupled the equations of fluid flow and those of rigid-body dynamics, and captured the time-dependent interference between stationary and moving boundaries. The unsteady, compressible Euler equations were solved on dynamic, unstructured meshes by an explicit, finite-volume, upwind method. The grid adaptation was performed within a window placed around the moving body. The Euler equations of dynamics were solved by a Runge-Kutta integration scheme. The flow solver and the adaptation scheme were validated by simulating the transonic, unsteady flow around a wing undergoing a forced, periodic pitching motion, then comparing the results with the experimental data. To validate the trajectory code, the six-degrees-of-freedom (DOF) motion of a store separating from a wing was computed using the experimentally determined force and moment fields, then comparing with an independently generated trajectory. Finally, the overall methodology was demonstrated by simulating the unsteady flowfield and the trajectory of a store dropped from a wing. The methodology, its computational cost notwithstanding, has proven to be accurate, automated, easy for dynamic gridding, and relatively efficient for the required man-hours.

Singh, K. P.↗
NASA NTRS1996

High Performance Parallel Multigrid Algorithms for Unstructured Grids

We describe a high performance parallel multigrid algorithm for a rather general class of unstructured grid problems in two and three dimensions. The algorithm PUMG, for parallel unstructured multigrid, is related in structure to the parallel multigrid algorithm PSMG introduced by McBryan and Frederickson, for they both obtain a higher convergence rate through the use of multiple coarse grids. Another reason for the high convergence rate of PUMG is its smoother, an approximate inverse developed by Baumgardner and Frederickson.

Frederickson, Paul O.↗
NASA NTRS1996

Large-Eddy Simulation of Flow Around a NACA 4412 Airfoil Using Unstructured Grids

Large-eddy simulation (LES) has matured to the point where application to complex flows is described. The extension to higher Reynolds numbers leads to an impractical number of grid points with existing structured-grid methods. Furthermore, most real world flows are rather difficult to represent geometrically with structured grids. Unstructured-grid methods offer a release from both of these constraints. However, just as it took many years for structured-grid methods to be well understood and reliable tools for LES, unstructured-grid methods must be carefully studied before we can expect them to attain their full potential.

Jansen, Kenneth↗
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 NTRS1998

PLUM: Parallel Load Balancing for Unstructured Adaptive Meshes

Dynamic mesh adaption on unstructured grids is a powerful tool for computing large-scale problems that require grid modifications to efficiently resolve solution features. By locally refining and coarsening the mesh to capture physical phenomena of interest, such procedures make standard computational methods more cost effective. Unfortunately, an efficient parallel implementation of these adaptive methods is rather difficult to achieve, primarily due to the load imbalance created by the dynamically-changing nonuniform grid. This requires significant communication at runtime, leading to idle processors and adversely affecting the total execution time. Nonetheless, it is generally thought that unstructured adaptive- grid techniques will constitute a significant fraction of future high-performance supercomputing. Various dynamic load balancing methods have been reported to date; however, most of them either lack a global view of loads across processors or do not apply their techniques to realistic large-scale applications.

Oliker, Leonid↗
NASA NTRS1998

Multigrid Strategies for Viscous Flow Solvers on Anisotropic Unstructured Meshes

Unstructured multigrid techniques for relieving the stiffness associated with high-Reynolds number viscous flow simulations on extremely stretched grids are investigated. One approach consists of employing a semi-coarsening or directional-coarsening technique, based on the directions of strong coupling within the mesh, in order to construct more optimal coarse grid levels. An alternate approach is developed which employs directional implicit smoothing with regular fully coarsened multigrid levels. The directional implicit smoothing is obtained by constructing implicit lines in the unstructured mesh based on the directions of strong coupling. Both approaches yield large increases in convergence rates over the traditional explicit full-coarsening multigrid algorithm. However, maximum benefits are achieved by combining the two approaches in a coupled manner into a single algorithm. An order of magnitude increase in convergence rate over the traditional explicit full-coarsening algorithm is demonstrated, and convergence rates for high-Reynolds number viscous flows which are independent of the grid aspect ratio are obtained. Further acceleration is provided by incorporating low-Mach-number preconditioning techniques, and a Newton-GMRES strategy which employs the multigrid scheme as a preconditioner. The compounding effects of these various techniques on speed of convergence is documented through several example test cases.

Movriplis, Dimitri J.↗
NASA NTRS1998

PLUM: Parallel Load Balancing for Unstructured Adaptive Meshes

Dynamic mesh adaption on unstructured grids is a powerful tool for computing large-scale problems that require grid modifications to efficiently resolve solution features. Unfortunately, an efficient parallel implementation is difficult to achieve, primarily due to the load imbalance created by the dynamically-changing nonuniform grid. To address this problem, we have developed PLUM, an automatic portable framework for performing adaptive large-scale numerical computations in a message-passing environment. First, we present an efficient parallel implementation of a tetrahedral mesh adaption scheme. Extremely promising parallel performance is achieved for various refinement and coarsening strategies on a realistic-sized domain. Next we describe PLUM, a novel method for dynamically balancing the processor workloads in adaptive grid computations. This research includes interfacing the parallel mesh adaption procedure based on actual flow solutions to a data remapping module, and incorporating an efficient parallel mesh repartitioner. A significant runtime improvement is achieved by observing that data movement for a refinement step should be performed after the edge-marking phase but before the actual subdivision. We also present optimal and heuristic remapping cost metrics that can accurately predict the total overhead for data redistribution. Several experiments are performed to verify the effectiveness of PLUM on sequences of dynamically adapted unstructured grids. Portability is demonstrated by presenting results on the two vastly different architectures of the SP2 and the Origin2OOO. Additionally, we evaluate the performance of five state-of-the-art partitioning algorithms that can be used within PLUM. It is shown that for certain classes of unsteady adaption, globally repartitioning the computational mesh produces higher quality results than diffusive repartitioning schemes. We also demonstrate that a coarse starting mesh produces high quality load balancing, at a fraction of the cost required a fine initial mesh. Results indicate that our parallel load balancing strategy will remain viable on large numbers of processors.

Oliker, Leonid↗
NASA NTRS1998

On Convergence Acceleration Techniques for Unstructured Meshes

A discussion of convergence acceleration techniques as they relate to computational fluid dynamics problems on unstructured meshes is given. Rather than providing a detailed description of particular methods, the various different building blocks of current solution techniques are discussed and examples of solution strategies using one or several of these ideas are given. Issues relating to unstructured grid CFD problems are given additional consideration, including suitability of algorithms to current hardware trends, memory and cpu tradeoffs, treatment of non-linearities, and the development of efficient strategies for handling anisotropy-induced stiffness. The outlook for future potential improvements is also discussed.

Mavriplis, Dimitri J.↗
NASA NTRS1999

A Robust and Scalable Software Library for Parallel Adaptive Refinement on Unstructured Meshes

The design and implementation of Pyramid, a software library for performing parallel adaptive mesh refinement (PAMR) on unstructured meshes, is described. This software library can be easily used in a variety of unstructured parallel computational applications, including parallel finite element, parallel finite volume, and parallel visualization applications using triangular or tetrahedral meshes. The library contains a suite of well-designed and efficiently implemented modules that perform operations in a typical PAMR process. Among these are mesh quality control during successive parallel adaptive refinement (typically guided by a local-error estimator), parallel load-balancing, and parallel mesh partitioning using the ParMeTiS partitioner. The Pyramid library is implemented in Fortran 90 with an interface to the Message-Passing Interface (MPI) library, supporting code efficiency, modularity, and portability. An EM waveguide filter application, adaptively refined using the Pyramid library, is illustrated.

Lou, John Z.↗