Fourth order “mehrstellen”-integration for three-dimensional turbulent boundary layers

Krause, Egon; Hirschel, Ernst Heinrich; Kordulla, W.

doi:10.1016/0045-7930(76)90014-1

Cited by 32 publications

(11 citation statements)

References 4 publications

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“…Among these we mention the Mehrstellen method developped by Krause et al (1976) in which f and f are substituted in terms of f. In this way f becomes solution of a x~ .…”

Section: Other Hermitian Methodsmentioning

confidence: 99%

Optimisation of Hermitian methods for Navier-Stokes equations in the vorticity and stream-function formulation

Roux¹,

Bontoux²,

Loc

et al. 1980

Lecture Notes in Mathematics

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The aim of this paper is to show the efficiency of a "combined" method proposed to solve the 2D incompressible Navier-Stokes equations in the vorticity and stream-function formulation. A compact hermitian scheme is used for the stream function equation while a classical second order accurate scheme is taken for the vorticity equation. Comparisons have been made with purely hermitian or purely second order accurate methods. Numerical experiments have been carried out for a large variety of steady and unsteady, internal or external flows. For these problems, comparisons have been made with available experimental or computed datal

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“…Among these we mention the Mehrstellen method developped by Krause et al (1976) in which f and f are substituted in terms of f. In this way f becomes solution of a x~ .…”

Section: Other Hermitian Methodsmentioning

confidence: 99%

Optimisation of Hermitian methods for Navier-Stokes equations in the vorticity and stream-function formulation

Roux¹,

Bontoux²,

Loc

et al. 1980

Lecture Notes in Mathematics

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“…The same method of solution has also been applied to the analysis of turbulent boundary layers for three-dimensional flows. By reliance on higher-order accuracy the validity of extensions of simple models for the Reynolds stresses to three-dimensional flows could clearly be disproven for adverse-pressure gradient flows' 73 '. The need for numerically accurate solutions is perhaps best demonstrated for the simulation of atmospheric circulation.…”

Section: Finite-difference-approximationmentioning

confidence: 99%

“…Effect of step size on accuracy of numerical solution'73 ' of the boundary-layer equations for turbulent flow.…”

mentioning

confidence: 99%

Application of numerical techniques in fluid mechanics

Krause

1974

Aeronaut. j.

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More than sixty years ago Theodore von Kármán showed in a paper entitled Über die Turbulenzreibung verschiedener Flüssigkeiten (On turbulent friction of various fluids) how the pressure drop of various fluid flows through pipes could be correlated in a single curve. The correlation parameter he used is now known as Reynolds number. It had been named after Osborne Reynolds only three years earlier in 1908 by A. Sommerfeld, shordy after he had left Aachen, in a note at the Internationaler Mathematiker Kongress in Rome. Sommerfeld had recognised the importance of Reynolds' similarity law and was deeply persuaded by his experimental and theoretical work.

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“…Other approximation methods exist, and they include finite elements, finite volumes, and spectral methods. While there are a number of problems, for example, elliptic systems, which can be solved with low-order approximation methods (second or lower) with reasonable accuracies, there is also a large class of problems, including those of acoustics [1,2,3], and of fluid dynamics [5,6,7,9,13,14], the solutions of which typically require higher order approximation solution schemes for higher levels of accuracy.…”

Section: Introductionmentioning

confidence: 99%

“…These compact schemes generally fall into two classes. The first class consists of those solution methods which are best suited for uniform grids, and they include the Kreiss and Oliger's approximating scheme [18,4], and the Mehrstellen's scheme [1]. The second class consists of methods that allow for variable grids.…”

Section: Introductionmentioning

confidence: 99%

On a High-Order Compact Scheme and Its Utilization in Parallel Solution of a Time-Dependent System on a Distributed Memory Processor

Akpan

2007

Lecture Notes in Computer Science

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Abstract. The study resulting in this paper applied a parallel algorithm based on a fourth-order compact scheme and suitable for parallel implementation of scientific/engineering systems. The particular system used for demonstration in the study was a time-dependendent system solved in parallel on a 2-head-node, 224-compute-node Apple Xserve G5 multiprocessor. The use of the approximation scheme, which necessitated discretizing in both space and time with hx space width and ht time step, produced a linear tridiagonal, almost-Toeplitz system. The solution used p processors with p ranging from 3 to 63. The speedups, sp, approached the limiting value of p only when p was small but yieldd poor computations errors which became progressively better as p increases. The parallel solution is very accurate having good speedups and accuracies but only when p is within reasonable range of values.

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Fourth order “mehrstellen”-integration for three-dimensional turbulent boundary layers

Cited by 32 publications

References 4 publications

Optimisation of Hermitian methods for Navier-Stokes equations in the vorticity and stream-function formulation

Optimisation of Hermitian methods for Navier-Stokes equations in the vorticity and stream-function formulation

Application of numerical techniques in fluid mechanics

On a High-Order Compact Scheme and Its Utilization in Parallel Solution of a Time-Dependent System on a Distributed Memory Processor

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