Lie subgroups of symmetry groups of fluid dynamics and magnetohydro-dynamics equations

1995 ◽  
Vol 73 (7-8) ◽  
pp. 463-477 ◽  
Author(s):  
A. M. Grundland ◽  
L. Lalague
Keyword(s):  
Fluid Dynamics ◽  
Symmetry Algebra ◽  
Symmetry Groups ◽  
Systems Of Equations ◽  
Magnetohydrodynamics Equations ◽  
Infinite Dimensional ◽  
Isentropic Flow ◽  
Fluid Dynamics Equations ◽  
Symmetry Algebras

We classify the subalgebras of the symmetry algebras of fluid dynamics and magnetohydrodynamics equations into conjugacy classes under their respective groups. Both systems of equations are invariant under a Galilean-similitude algebra. In the case of the fluid dynamics equations, when the adiabatic exponent γ = 5/3, the symmetry algebra widens to a Galilean-projective algebra. We extend our previous classification of the symmetry algebra in the case of a nonstationary and isentropic flow to the general case of fluid dynamics and magnetohydrodynamics equations in (3 + 1) dimensions. The representatives of these algebras are given in normalized lists and presented in tables. Examples of invariant and partially invariant solutions, for both systems, are computed from representatives of these classifications. The final part of this work contains an analysis of this classification in connection with a further classification of the symmetry algebras in the case of the equations describing the flow of perfect gases. An explicit solution, in terms of Riemann invariants, is constructed from infinite-dimensional subalgebras of the symmetry algebra of the magnetohydrodynamics equations in the (1 + 2)-dimensional case.

Noether symmetries of vacuum classes of pp-waves and the wave equation

2016 ◽  
Vol 13 (09) ◽  
pp. 1650109 ◽  
Author(s):  
Sameerah Jamal ◽  
Ghulam Shabbir
Keyword(s):  
Wave Equation ◽  
Gravitational Waves ◽  
Wave Equations ◽  
Noether Symmetry ◽  
Symmetry Groups ◽  
Noether Symmetries ◽  
Noether’S Theorem ◽  
Metric Functions ◽  
Symmetry Algebras

The Noether symmetry algebras admitted by wave equations on plane-fronted gravitational waves with parallel rays are determined. We apply the classification of different metric functions to determine generators for the wave equation, and also adopt Noether's theorem to derive conserved forms. For the possible cases considered, there exist symmetry groups with dimensions two, three, five, six and eight. These symmetry groups contain the homothetic symmetries of the spacetime.

Harish-Chandra Modules of the Intermediate Series over the Topological N = 2 Superconformal Algebra

2020 ◽  
Vol 27 (02) ◽  
pp. 343-360 ◽  
Author(s):  
Hengyun Yang ◽  
Ying Xu ◽  
Jiancai Sun
Keyword(s):  
Topological Strings ◽  
Symmetry Algebra ◽  
Lie Superalgebra ◽  
Superconformal Algebra ◽  
Infinite Dimensional ◽  
Graded Modules ◽  
Intermediate Series

The topological N = 2 superconformal algebra was introduced by Dijkgraaf, Verlinde and Verlinde as the symmetry algebra of topological strings at d < 1. We give a classification of irreducible 𝕫 × 𝕫-graded modules of the intermediate series over this infinite-dimensional Lie superalgebra.

Modeling of Coal-Biomass Fluidization Using Computational Fluid Dynamics

2013 ◽  
Author(s):  
Bahareh Estejab ◽  
Francine Battaglia
Keyword(s):  
Fluid Dynamics ◽  
Computational Fluid Dynamics ◽  
Hybrid Poplar ◽  
Particle Interactions ◽  
Particle Mixing ◽  
Bed Height ◽  
Wood Particles ◽  
Computational Fluid Dynamics Cfd ◽  
Computational Platform

In an effort to assess the fluidization characteristics of coal-biomass mixtures, computational fluid dynamics (CFD) was used and validated. The gas and solids phases were modeled using an Eulerian-Eulerian approach to efficiently simulate the physics. The computational platform Multiphase Flow with Interphase eXchanges (MFIX) was employed to simulate the particle-particle interactions of coal-biomass mixtures and compare the predictions with experimental data. The coal-biomass mixtures included sub-bituminous coal and hybrid poplar wood. Particles properties of both materials fall within the Geldart A classification. Of particular interest to this study was predicting particle mixing in fluidized beds and biomass hydrodynamics. Both materials and two mass ratio mixtures were studied and pressure drop across the bed for various gas inlet velocities and bed height were analyzed and compared to the experiments.

Column Separation Accompanying Liquid Transients in Pipes

1967 ◽  
Vol 89 (4) ◽  
pp. 837-846 ◽  
Author(s):  
R. A. Baltzer
Keyword(s):  
Fluid Dynamics ◽  
Method Of Characteristics ◽  
Time Pressure ◽  
Experimental Information ◽  
Free Surface Flows ◽  
Energy Losses ◽  
Nonlinear Friction ◽  
Systems Of Equations ◽  
Surface Flows ◽  
Column Separation

Column separation is described and investigated in terms of the governing fluid dynamics. The partial differential equations of continuity and momentum, including nonlinear friction losses, are used to mathematically represent the transient movement of liquids in pipes under conditions of both full-pipe and free-surface flows. The complete systems of equations are programmed for numerical simulation of the column-separation phenomenon using a digital computer and the method of characteristics. Theoretical time-pressure information derived from mathematical simulation is compared with the corresponding experimental information obtained from laboratory investigation. Despite higher-than-anticipated energy losses in the prototype flow, the general comparison of the two sets of information is favorable.

scholarly journals Recurrent flows: the clockwork behind turbulence

2013 ◽  
Vol 726 ◽  
pp. 1-4 ◽  
Author(s):  
Predrag Cvitanović
Keyword(s):  
Fluid Dynamics ◽  
Reynolds Number ◽  
Chaotic Dynamics ◽  
High Dimensional ◽  
Governing Equations ◽  
Infinite Dimensional ◽  
Long Run ◽  
Moderate Reynolds Number ◽  
Dimensional State Space ◽  
Exhaustive Study

AbstractThe understanding of chaotic dynamics in high-dimensional systems that has emerged in the last decade offers a promising dynamical framework to study turbulence. Here turbulence is viewed as a walk through a forest of exact solutions in the infinite-dimensional state space of the governing equations. Recently, Chandler & Kerswell (J. Fluid Mech., vol. 722, 2013, pp. 554–595) carry out the most exhaustive study of this programme undertaken so far in fluid dynamics, a feat that requires every tool in the dynamicist’s toolbox: numerical searches for recurrent flows, computation of their stability, their symmetry classification, and estimating from these solutions statistical averages over the turbulent flow. In the long run this research promises to develop a quantitative, predictive description of moderate-Reynolds-number turbulence, and to use this description to control flows and explain their statistics.

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