Research Directions in Computational Mechanics (1991) / Chapter Skim
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11 Numerical Modeling of Turbulence
11 Numerical Modeling of Turbulence
Pages 108-114
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From page 108... ...
A related turbulence feature, which is indeed the fundamental characteristic that makes it so theoretically and computationally difficult, is that it exhibits far more small-scale structure than its nonturbulent counterparts. This small-scale structure is responsible for the enhanced turbulent transport phenomena and is itself evidence of enhanced transport in the sense that small scales develop from the degradation of large-scale excitations that are maintained by energy transport from one scale to another.
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From page 109... ...
One of the main results of turbulence theory is that the range of significantly excited scales of motion in both space and time is of the order R3/4 Therefore, to calculate a high Reynolds number flow in three space dimensions plus time, it is necessary to perform order (R 54= R3 computational work. This means that calculating a flow at Reynolds number 2R requires roughly 10 times more work than calculating at Reynolds number R!
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From page 110... ...
It is expected that this trend will continue and may, indeed, accelerate over the next decade, especially with the advent of new cost-effective parallel computers. In the following paragraphs, we review the progress on certain specific key problems in turbulence -- theory and application -- and note the current unsolved issues that numerical simulations have raised.
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From page 111... ...
Generally, the CRAY-1 brought a range of threedimensional turbulence problems within the realm of numerical scrutiny, and it permitted the rudiments of inertial ranges to be defined for simple geometries. For two-dimensional turbulence, considerable progress was made in understanding detailed inertial range effects.
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From page 112... ...
In the past decade, calculations using improved resolution (up to 10242) have profoundly affected our understanding of these flows; for example, an initial state of random vortices tends, in time, to become a system of isolated vortices whose dynamics are controlled by their distant interactions with an occasional collisional interaction.
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From page 113... ...
In reality this method is the only hope we have to detail flow models of real-world engineering complexity, and it has wide applications ranging from calculating detailed flows over aircraft wings to global models of the planetary boundary layer. The current state of the art here is 1283 calculations in relatively simple geometries.
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From page 114... ...
, , ~ ~ , ~ In summary, John von Neumann's 1949 prediction that computers would prove particularly useful to the study of turbulent flows has come true. Because of still limited theoretical understanding of nonlinear phenomena, engineers, atmospheric scientists, astrophysicists, fluid dynamicists, and others are in great need of computer simulations.
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