scholarly journals A special form of solution to half-wave equations

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Hyungjin Huh
Keyword(s):  
Transport Equation ◽  
Hilbert Transform ◽  
Special Form ◽  
Wave Equations ◽  
Nonlinear Transport ◽  
One Dimensional ◽  
Nonlinear Transport Equation ◽  
Half Wave ◽  
The One ◽  
Nonlocal Nonlinear

<p style='text-indent:20px;'>We investigate a special form of solution to the one-dimensional half-wave equations with particular forms of nonlinearities. Using the special form of solution involving Hilbert transform, the half-wave equations reduce to nonlocal nonlinear transport equation which can be solved explicitly.</p>

scholarly journals Triangular Gross-Pitaevskii breathers and Damski-Chandrasekhar shock waves

2021 ◽  
Vol 10 (5) ◽  
Author(s):  
Maxim Olshanii ◽  
Dumesle Deshommes ◽  
Jordi Torrents ◽  
Marina Gonchenko ◽  
Vanja Dunjko ◽  
...  
Keyword(s):  
Shock Wave ◽  
Shock Waves ◽  
Initial Conditions ◽  
Broad Class ◽  
Hydrodynamic Equations ◽  
Nonlinear Transport ◽  
One Dimensional ◽  
Nonlinear Transport Equation ◽  
Bosonic Case ◽  
The One

The recently proposed map [5] between the hydrodynamic equations governing the two-dimensional triangular cold-bosonic breathers [1] and the high-density zero-temperature triangular free-fermionic clouds, both trapped harmonically, perfectly explains the former phenomenon but leaves uninterpreted the nature of the initial (t=0) singularity. This singularity is a density discontinuity that leads, in the bosonic case, to an infinite force at the cloud edge. The map itself becomes invalid at times t<0t<0. A similar singularity appears at t = T/4t=T/4, where T is the period of the harmonic trap, with the Fermi-Bose map becoming invalid at t > T/4t>T/4. Here, we first map—using the scale invariance of the problem—the trapped motion to an untrapped one. Then we show that in the new representation, the solution [5] becomes, along a ray in the direction normal to one of the three edges of the initial cloud, a freely propagating one-dimensional shock wave of a class proposed by Damski in [7]. There, for a broad class of initial conditions, the one-dimensional hydrodynamic equations can be mapped to the inviscid Burgers’ equation, which is equivalent to a nonlinear transport equation. More specifically, under the Damski map, the t=0 singularity of the original problem becomes, verbatim, the initial condition for the wave catastrophe solution found by Chandrasekhar in 1943 [9]. At t=T/8t=T/8, our interpretation ceases to exist: at this instance, all three effectively one-dimensional shock waves emanating from each of the three sides of the initial triangle collide at the origin, and the 2D-1D correspondence between the solution of [5] and the Damski-Chandrasekhar shock wave becomes invalid.

Two-Fluid CFD Model of Adiabatic Air-Water Upward Bubbly Flow Through a Vertical Pipe With a One-Group Interfacial Area Transport Equation

2009 ◽  
Author(s):  
Deoras Prabhudharwadkar ◽  
Chris Bailey ◽  
Martin Lopez de Bertodano ◽  
John R. Buchanan
Keyword(s):  
Experimental Data ◽  
Transport Equation ◽  
Bubbly Flow ◽  
Interfacial Area ◽  
Correct Prediction ◽  
Interfacial Area Transport ◽  
One Dimensional ◽  
Interfacial Area Transport Equation ◽  
The One ◽  
Two Fluid

This paper describes in detail the assessment of the CFD code CFX to predict adiabatic liquid-gas two-phase bubbly flow. This study has been divided into two parts. In the first exercise, the effect of Lift Force, Wall Force and the Turbulent Diffusion Force have been assessed using experimental data from the literature for air-water upward bubbly flows through a pipe. The data used here had a characteristic near wall void peaking which was largely influenced by the joint action of the three forces mentioned above. The simulations were performed with constant bubble diameter assuming no bubble interactions. This exercise resulted in selection of the most appropriate closure form and closure coefficients for the above mentioned forces for the range of flow conditions chosen. In the second exercise, the One-Group Interfacial Area Transport equation was introduced in the two-fluid model of CFX. The interfacial area density plays important role in the correct prediction of interfacial mass, momentum and energy transfer and is affected by bubble breakup and coalescence processes in adiabatic flows. The One-Group Interfacial Area Transport Equation (IATE) has been developed and implemented for one-dimensional models and validated using cross-sectional area averaged experimental data over the last decade by various researchers. The original one-dimensional model has been extended to multidimensional flow predictions in this study and the results are presented in this paper. The paper also discusses constraints posed by the commercial CFD code CFX and the solutions worked out to obtain the most accurate implementation of the model.

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