Quasi-One-Dimensional Riemann Problems and Their Role in Self-Similar Two-Dimensional Problems

1998 ◽  
Vol 144 (3) ◽  
pp. 233-258 ◽  
Author(s):  
Sunčica Čanić ◽  
Barbara Lee Keyfitz
Keyword(s):  
Two Dimensional ◽  
Riemann Problems ◽  
One Dimensional ◽  
Self Similar

The bandcount increment scenario. II. Interior structures

2008 ◽  
Vol 464 (2097) ◽  
pp. 2247-2263 ◽  
Author(s):  
Viktor Avrutin ◽  
Bernd Eckstein ◽  
Michael Schanz
Keyword(s):  
Canonical Form ◽  
Parameter Space ◽  
Complex Interaction ◽  
Chaotic Attractors ◽  
Two Dimensional ◽  
Dimensional Parameter ◽  
Parameter Spaces ◽  
One Dimensional ◽  
Self Similar ◽  
Bifurcation Structures

Bifurcation structures in the two-dimensional parameter spaces formed by chaotic attractors alone are still far away from being understood completely. In a series of three papers, we investigate the chaotic domain without periodic inclusions for a map, which is considered by many authors as some kind of one-dimensional canonical form for discontinuous maps. In this second part, we investigate fine substructures nested into the basic structures reported and explained in part I. It is demonstrated that the overall structure of the chaotic domain is caused by a complex interaction of bandcount increment, bandcount adding and bandcount doubling structures, whereby some of them are nested into each other ad infinitum leading to self-similar structures in the parameter space.

Two-dimensional hydrodynamic models of laser-produced plasmas

1989 ◽  
Vol 41 (2) ◽  
pp. 263-280 ◽  
Author(s):  
G. J. Pert
Keyword(s):  
Aspect Ratio ◽  
Hybrid Model ◽  
The Self ◽  
Entire Body ◽  
Solid Target ◽  
Two Dimensional ◽  
Similar Form ◽  
Hydrodynamic Models ◽  
One Dimensional ◽  
Self Similar

Analytic modelling of laser-produced plasmas has generally been restricted to one-dimensional flow. Multi-dimensional hydrodynamic approximations are available, and are explored in this paper. Two configurations are examined. The explosive mode in which the entire body of material is uniformly heated is treated by the self-similar form, and the aspect ratio of the resulting expansion is determined. Ablative flows can be approximated by the hybrid model, and the self-regulating flow from a solid target can be calculated in this way.

The bandcount increment scenario. III. Deformed structures

2008 ◽  
Vol 465 (2101) ◽  
pp. 41-57 ◽  
Author(s):  
Viktor Avrutin ◽  
Bernd Eckstein ◽  
Michael Schanz
Keyword(s):  
Canonical Form ◽  
Chaotic Attractors ◽  
Two Dimensional ◽  
Dimensional Parameter ◽  
Parameter Spaces ◽  
One Dimensional ◽  
Practical Applications ◽  
Chaotic Region ◽  
Self Similar ◽  
Bifurcation Structures

Bifurcation structures in two-dimensional parameter spaces formed by chaotic attractors alone are still a long way from being understood completely. In a series of three papers, we investigated the chaotic domain without periodic inclusions for a map, which is considered by many authors as some kind of one-dimensional canonical form for discontinuous maps. In Part I, the basic structures in the chaotic region are explained by the bandcount increment scenario. In Part II, fine self-similar substructures nested into the bandcount increment scenario are explained by the bandcount-adding and -doubling scenarios, nested into each other ad infinitum. Hereby, we fixed in both previous parts one of the parameters to a non-generic value, and studied the remaining two-dimensional parameter subspace. In this Part III, finally we investigated the structures under variation of this third parameter. Remarkably, this step is the most important with respect to practical applications, since it cannot be expected that these operate exactly at the previously investigated specific value.

The Simulation of Mixing Layers Driven by Compound Buoyancy and Shear

1996 ◽  
Vol 118 (2) ◽  
pp. 370-376 ◽  
Author(s):  
D. M. Snider ◽  
M. J. Andrews
Keyword(s):  
Growth Rate ◽  
Flow Field ◽  
Numerical Solution ◽  
Mixing Layer ◽  
Measured Data ◽  
Mixing Layers ◽  
Two Dimensional ◽  
One Dimensional ◽  
Self Similar ◽  
Accurate Numerical Solution

Fully developed compound shear and buoyancy driven mixing layers are predicted using a k-ε turbulence model. Such mixing layers present an exchange of equilibrium in mixing flows. The k-ε buoyancy constant Cε3 = 0.91, defined in this study for buoyancy unstable mixing layers, is based on an approximate self-similar analysis and an accurate numerical solution. One-dimensional transient and two-dimensional steady calculations are presented for buoyancy driven mixing in a uniform flow field. Two-dimensional steady calculations are presented for compound shear and buoyancy driven mixing. The computed results for buoyancy alone and compound shear and buoyancy mixing compare well with measured data. Adding shear to an unstable buoyancy mixing layer does not increase the mixing growth rate compared with that from buoyancy alone. The nonmechanistic k-ε model which balances energy generation and dissipation using constants from canonical shear and buoyancy studies predicts the suppression of the compound mixing width. Experimental observations suggest that a reduction in growth rate results from unequal stream velocities that skew and stretch the normally vertical buoyancy plumes producing a reduced mixing envelope width.

A one-dimensional self-gravitating stellar gas

1966 ◽  
Vol 25 ◽  
pp. 46-48 ◽  
Author(s):  
M. Lecar
Keyword(s):  
Gravitational Field ◽  
Phase Space ◽  
Motion Picture ◽  
Space Distribution ◽  
Two Dimensional ◽  
One Dimensional ◽  
Phase Space Distribution ◽  
Dimensional Phase Space ◽  
The Mean

“Dynamical mixing”, i.e. relaxation of a stellar phase space distribution through interaction with the mean gravitational field, is numerically investigated for a one-dimensional self-gravitating stellar gas. Qualitative results are presented in the form of a motion picture of the flow of phase points (representing homogeneous slabs of stars) in two-dimensional phase space.

State-of-the-Art of Modeling Surface Water Impoundments

1982 ◽  
Vol 14 (1-2) ◽  
pp. 241-261 ◽  
Author(s):  
P A Krenkel ◽  
R H French
Keyword(s):  
Water Quality ◽  
Surface Water ◽  
State Of The Art ◽  
Rate Coefficients ◽  
Two Dimensional ◽  
One Dimensional ◽  
Integral Energy ◽  
Range Of Values ◽  
Dimensional Integral ◽  
Water Impoundment

The state-of-the-art of surface water impoundment modeling is examined from the viewpoints of both hydrodynamics and water quality. In the area of hydrodynamics current one dimensional integral energy and two dimensional models are discussed. In the area of water quality, the formulations used for various parameters are presented with a range of values for the associated rate coefficients.

The formation of gas hydrates under shock wave impact on the bubble media (two-dimensional case)

2010 ◽  
Vol 7 ◽  
pp. 90-97
Author(s):  
M.N. Galimzianov ◽  
I.A. Chiglintsev ◽  
U.O. Agisheva ◽  
V.A. Buzina
Keyword(s):  
Shock Wave ◽  
Gas Hydrates ◽  
Hydrate Formation ◽  
Dimensional Case ◽  
Two Dimensional ◽  
Wave Impact ◽  
Bubble Liquid ◽  
One Dimensional ◽  
Bubble Media ◽  
Main Factors

Formation of gas hydrates under shock wave impact on bubble media (two-dimensional case) The dynamics of plane one-dimensional shock waves applied to the available experimental data for the water–freon media is studied on the base of the theoretical model of the bubble liquid improved with taking into account possible hydrate formation. The scheme of accounting of the bubble crushing in a shock wave that is one of the main factors in the hydrate formation intensification with increasing shock wave amplitude is proposed.

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