Solution of the Three-Dimensional Navier-Stokes Equations on a Vector Processor

Spradley, L. W.; Stalnaker, J. F.; Ratliff, A. W.

doi:10.2514/3.60064

Cited by 14 publications

(2 citation statements)

References 3 publications

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“…All but one of the elliptic methods use finite difference techniques to approximate the differential equations by an algebraic system. Spradley et al [138] use the GIM formulation which is similar to the finite volume approaches discussed earlier. The dependent variables are represented by interpolating functions over the interior of local mesh volumes, and an algebraic system is obtained from weighted integrals of the differential equation over each mesh volume.…”

Section: Methods For Steady Equationsmentioning

confidence: 98%

Review—Computational Methods for Internal Flows With Emphasis on Turbomachinery

Mcnally

Sockol

1985

Journal of Fluids Engineering

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A review is given of current computational methods for analyzing flows in turbomachinery and other related internal propulsion components. The methods are divided primarily into two classes, inviscid and viscous. The inviscid methods deal specifically with turbomachinery applications. Viscous methods, on the other hand, due to the state-of-the-art, deal with generalized duct flows as well as flows in turbomachinery passages. Inviscid methods are categorized into the potential, stream function, and Euler approaches. Viscous methods are treated in terms of parabolic, partially parabolic, and elliptic procedures.

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Section: Methods For Steady Equationsmentioning

confidence: 98%

Review—Computational Methods for Internal Flows With Emphasis on Turbomachinery

Mcnally

Sockol

1985

Journal of Fluids Engineering

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“…U " + l = U J + lim(AUh-AU') (5) in such a way that no non-physical over/undershoots are created. It is at this point that a further constraint, given by the conservation law (1) itself, must be taken into account: strict conservation on the discrete level should be maintained.…”

Section: Fct Definedmentioning

confidence: 99%

Finite elements in CFD: What lies ahead

Löhner

1987

Numerical Meth Engineering

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SUMMARYThe current state of the art of Finite Element Methods in Computational Fluid Dynamics is reviewed. The aim of this review is to point out what appear currently as the main shortcomings of Finite Element Methods, so as to concentrate the efforts to remove them. The analysis of flows using Finite Elements will only be successful if all steps involved in it are optimized. Therefore, I deem it necessary to describe explicit and implicit flow solvers, unstructured multigrid methods. adaptive refinement schemes, grid generation and graphics in 3-D, the effective use of supercomputer hardware and memory; as well as the combination of structured and unstructured grids. INTRODUCTTONComputational fluid dynamics (CFD) has always been at the forefront of the development of numerical techniques for the simulation of physical phenomena. Several reasons have contributed to this leadership among the many disciplines that can be numbered under the heading of 'Computational Mechanics'. The first is the inherently non-linear behaviour of fluids (advection, turbulence) which must bc accounted for. The second is thc mixed hyperbolic/elliptic character of the partial differential equations describing fluid motion. This mixed hyperbolie/elliptic character implies an increased algorithmic complexity. The third reason is the need of engineers designing new aeroplanes to obtain much more accurate performaiice estimates (and therefore more accurate results for the simulations) than their colleagues designing bridges. The fourth reason is the size of typical problems and follows from the first three. A problem in structural mechanics is considered large if it exceeds 5 x lo3 nodes, whereas 'large' in C F D means more than 5 x los gridpoints.For 25 years C F D grew around Finite Difference Methods, as these were simple to understand and code, easy to vectorize, and the structured grids typically associated with them described appropriately the simple geometric complexity of the fields that were solved. However, as computers became bigger and faster, attempts were made to simulate more and more complex flow domains, and it soon became clear that structured grids where not flexible enough to describe these domains. It was at this point in time that unstructured grids, and Finite Element Techniques-a natural way of discretizing operators on them-entered the scene of CFD. Since then, unstructured grids have become a driving force within CFD, and many new developments could * Invited paper presented at the First World Congress on Compulalional Mechanics, Austin, Texas, September 22-26, 1986 0029-598 1/87/09174 1-1 6$08.00 only become a reality by using them, such as domain splitting, adaptive refinement by enrichment within the same grid, directional refincmcnt and thc solution of the flowfield around a complete aircraft with engines.However impressive the entry of Finite Elements into the field of CFD may have been, many more developments are still needed in order to transform what are now still rudimentary methods into efficient pr...

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References to Chapters 1 to 7

Gentzsch¹

1984

Vectorization of Computer Programs With Applications to Computational Fluid Dynamics

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Solution of the Three-Dimensional Navier-Stokes Equations on a Vector Processor

Cited by 14 publications

References 3 publications

Review—Computational Methods for Internal Flows With Emphasis on Turbomachinery

Review—Computational Methods for Internal Flows With Emphasis on Turbomachinery

Finite elements in CFD: What lies ahead

References to Chapters 1 to 7

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