scholarly journals A comparison of particle and fluid models for positive streamer discharges in air

2021 ◽  
Author(s):  
Zhen Wang ◽  
Anbang Sun ◽  
Jannis Teunissen
Keyword(s):  
Fluid Model ◽  
Field Approximation ◽  
Diffusion Reaction ◽  
Particle Model ◽  
Mean Deviation ◽  
Fluid Models ◽  
Streamer Velocity ◽  
Background Fields ◽  
Good Agreement ◽  
Streamer Discharges

Abstract Both fluid and particle models are commonly used to simulate streamer discharges. In this paper, we quantitatively study the agreement between these approaches for axisymmetric and 3D simulations of positive streamers in air. We use a drift-diffusion-reaction fluid model with the local field approximation and a PIC-MCC (particle-in-cell, Monte Carlo collision) particle model. The simulations are performed at 300 K and 1 bar in a 10 mm plate-plate gap with a 2 mm needle electrode. Applied voltages between 11.7 and 15.6 kV are used, which correspond to background fields of about 15 to 20 kV/cm. Streamer properties like maximal electric field, head position and velocity are compared as a function of time or space. Our results show good agreement between the particle and fluid simulations, in contrast to some earlier comparisons that were carried out in 1D or for negative streamers. To quantify discrepancies between the models, we mainly look at streamer velocities as a function of streamer length. For the test cases considered here, the mean deviation in streamer velocity between the particle and fluid simulations is less than 4\%. We study the effect of different types of transport data for the fluid model, and find that flux coefficients lead to good agreement whereas bulk coefficients do not. Furthermore, we find that with a two-term Boltzmann solver, data should be computed using a temporal growth model for the best agreement. The numerical convergence of the particle and fluid models is also studied. In fluid simulations the streamer velocity increases somewhat using finer grids, whereas the particle simulations are less sensitive to the grid. Photoionization is the dominant source of stochastic fluctuations in our simulations. When the same stochastic photoionization model is used, particle and fluid simulations exhibit similar fluctuations.

scholarly journals Virtual FFR Quantified with a Generalized Flow Model Using Windkessel Boundary Conditions

2020 ◽  
Vol 2020 ◽  
pp. 1-14
Author(s):  
Keltoum Chahour ◽  
Rajae Aboulaich ◽  
Abderrahmane Habbal ◽  
Nejib Zemzemi ◽  
Chérif Abdelkhirane
Keyword(s):  
Boundary Conditions ◽  
Flow Model ◽  
Fluid Model ◽  
Invasive Procedure ◽  
Navier Stokes ◽  
Fractional Flow ◽  
Flow Reserve ◽  
Arbitrary Position ◽  
Model Versus ◽  
Good Agreement

Fractional flow reserve (FFR) has proved its efficiency in improving patient diagnosis. In this paper, we consider a 2D reconstructed left coronary tree with two artificial lesions of different degrees. We use a generalized fluid model with a Carreau law and use a coupled multidomain method to implement Windkessel boundary conditions at the outlets. We introduce our methodology to quantify the virtual FFR and conduct several numerical experiments. We compare FFR results from the Navier–Stokes model versus generalized flow model and for Windkessel versus traction-free outlet boundary conditions or mixed outlet boundary conditions. We also investigate some sources of uncertainty that the FFR index might encounter during the invasive procedure, in particular, the arbitrary position of the distal sensor. The computational FFR results show that the degree of stenosis is not enough to classify a lesion, while there is a good agreement between the Navier–Stokes model and the non-Newtonian flow model adopted in classifying coronary lesions. Furthermore, we highlight that the lack of standardization while making FFR measurement might be misleading regarding the significance of stenosis.

scholarly journals Numerical Study of Shear Banding in Flows of Fluids Governed by the Rolie-Poly Two-Fluid Model via Stabilized Finite Volume Methods

Processes ◽  
2020 ◽  
Vol 8 (7) ◽  
pp. 810
Author(s):  
Jade Gesare Abuga ◽  
Tiri Chinyoka
Keyword(s):  
Finite Volume ◽  
Numerical Algorithm ◽  
Numerical Study ◽  
Fluid Model ◽  
Shear Banding ◽  
Numerical Algorithms ◽  
Viscoelastic Fluids ◽  
Two Fluid Model ◽  
Two Fluid ◽  
Good Agreement

The flow of viscoelastic fluids may, under certain conditions, exhibit shear-banding characteristics that result from their susceptibility to unusual flow instabilities. In this work, we explore both the existing shear banding mechanisms in the literature, namely; constitutive instabilities and flow-induced inhomogeneities. Shear banding due to constitutive instabilities is modelled via either the Johnson–Segalman or the Giesekus constitutive models. Shear banding due to flow-induced inhomogeneities is modelled via the Rolie–Poly constitutive model. The Rolie–Poly constitutive equation is especially chosen because it expresses, precisely, the shear rheometry of polymer solutions for a large number of strain rates. For the Rolie–Poly approach, we use the two-fluid model wherein the stress dynamics are coupled with concentration equations. We follow a computational analysis approach via an efficient and versatile numerical algorithm. The numerical algorithm is based on the Finite Volume Method (FVM) and it is implemented in the open-source software package, OpenFOAM. The efficiency of our numerical algorithms is enhanced via two possible stabilization techniques, namely; the Log-Conformation Reformulation (LCR) and the Discrete Elastic Viscous Stress Splitting (DEVSS) methodologies. We demonstrate that our stabilized numerical algorithms accurately simulate these complex (shear banded) flows of complex (viscoelastic) fluids. Verification of the shear-banding results via both the Giesekus and Johnson-Segalman models show good agreement with existing literature using the DEVSS technique. A comparison of the Rolie–Poly two-fluid model results with existing literature for the concentration and velocity profiles is also in good agreement.

SECOND ORDER BOUNDARY CONDITIONS FOR THE DRIFT-DIFFUSION EQUATIONS OF SEMICONDUCTORS

1995 ◽  
Vol 05 (04) ◽  
pp. 429-455 ◽  
Author(s):  
A. YAMNAHAKKI
Keyword(s):  
Boundary Conditions ◽  
Test Problem ◽  
Fluid Model ◽  
Diffusion Equations ◽  
Robin Boundary Conditions ◽  
Fluid Models ◽  
Drift Diffusion ◽  
Dirichlet Conditions ◽  
Robin Boundary ◽  
Two Fluid

By an asymptotic analysis of the Boltzmann equation of semiconductors, we prove that Robin boundary conditions for drift-diffusion equations provide a more accurate fluid model than Dirichlet conditions. The Robin conditions involve the concept of the extrapolation length which we compute numerically. We compare the two-fluid models for a test problem. The numerical results show that the current density is correctly computed with Robin conditions. This is not the case with Dirichlet conditions.

scholarly journals Effect of Magnetic Field on Dilepton Production Rate in Relativistic Heavy Ion Collisions

2020 ◽  
Vol 12 (2) ◽  
pp. 215-221
Author(s):  
P. K. Sethy ◽  
Y. Kumar ◽  
S. S. Singh
Keyword(s):  
Magnetic Field ◽  
Heavy Ion ◽  
Relativistic Heavy Ion Collisions ◽  
Particle Model ◽  
Heavy Ion Collision ◽  
Dilepton Production ◽  
Quasi Particle ◽  
Ion Collisions ◽  
Ion Collision ◽  
Good Agreement

It is believed that a transient strong magnetic field is generated in heavy-ion collision. The strength of this field perpendicular to the reaction plane and is estimated to be around eB=0.03GeV2 at RHIC and eB=0.3GeV2 at LHC. We study the effect of this magnetic field on dilepton yield using a modified quasi particle model. The results show a clear enhancement in dilepton yield and our result is in good agreement with the recently reported results.

scholarly journals The Variational Reduction for Low-Dimensional Fermi Gases and Bose–Fermi Mixtures: A Brief Review

2019 ◽  
Vol 4 (1) ◽  
pp. 22
Author(s):  
Pablo Díaz ◽  
David Laroze ◽  
Boris Malomed
Keyword(s):  
Equations Of Motion ◽  
Mean Field ◽  
Three Dimensional ◽  
Field Approximation ◽  
Matter Wave ◽  
Mean Field Approximation ◽  
Degenerate Gases ◽  
Dynamical Regimes ◽  
Low Dimensional ◽  
Good Agreement

We present a summary of some recent theoretical results for matter-wave patterns in Fermi and Bose–Fermi degenerate gases, obtained in the framework of the quasi-mean-field approximation. We perform a dimensional reduction from the three-dimensional (3D) equations of motion to 2D and 1D effective equations. In both cases, comparison of the low-dimensional reductions to the full model is performed, showing very good agreement for ground-state solutions. Some complex dynamical regimes are reported too for the corresponding 1D systems.

scholarly journals An introductory guide to fluid models with anisotropic temperatures. Part 1. CGL description and collisionless fluid hierarchy

2019 ◽  
Vol 85 (6) ◽  
Author(s):  
P. Hunana ◽  
A. Tenerani ◽  
G. P. Zank ◽  
E. Khomenko ◽  
M. L. Goldstein ◽  
...  
Keyword(s):  
Heat Flux ◽  
Evolution Equations ◽  
Fluid Model ◽  
Maximum Growth ◽  
Maximum Growth Rate ◽  
Normal Closure ◽  
Larmor Radius ◽  
Order Moment ◽  
Fourth Moment ◽  
Fluid Models

We present a detailed guide to advanced collisionless fluid models that incorporate kinetic effects into the fluid framework, and that are much closer to the collisionless kinetic description than traditional magnetohydrodynamics. Such fluid models are directly applicable to modelling the turbulent evolution of a vast array of astrophysical plasmas, such as the solar corona and the solar wind, the interstellar medium, as well as accretion disks and galaxy clusters. The text can be viewed as a detailed guide to Landau fluid models and it is divided into two parts. Part 1 is dedicated to fluid models that are obtained by closing the fluid hierarchy with simple (non-Landau fluid) closures. Part 2 is dedicated to Landau fluid closures. Here in Part 1, we discuss the fluid model of Chew–Goldberger–Low (CGL) in great detail, together with fluid models that contain dispersive effects introduced by the Hall term and by the finite Larmor radius corrections to the pressure tensor. We consider dispersive effects introduced by the non-gyrotropic heat flux vectors. We investigate the parallel and oblique firehose instability, and show that the non-gyrotropic heat flux strongly influences the maximum growth rate of these instabilities. Furthermore, we discuss fluid models that contain evolution equations for the gyrotropic heat flux fluctuations and that are closed at the fourth-moment level by prescribing a specific form for the distribution function. For the bi-Maxwellian distribution, such a closure is known as the ‘normal’ closure. We also discuss a fluid closure for the bi-kappa distribution. Finally, by considering one-dimensional Maxwellian fluid closures at higher-order moments, we show that such fluid models are always unstable. The last possible non Landau fluid closure is therefore the ‘normal’ closure, and beyond the fourth-order moment, Landau fluid closures are required.

Harmonie Force Fields and Bond Orders for Naphthalene, Anthracene, Biphenylene and Perylene with Mean Amplitudes for Perylene

1978 ◽  
Vol 33 (1) ◽  
pp. 45-54 ◽  
Author(s):  
J. C. Whitmer ◽  
S. J. Cyvin ◽  
B. N. Cyvin
Keyword(s):  
Force Field ◽  
Force Fields ◽  
Field Approximation ◽  
Force Constants ◽  
Bond Orders ◽  
Mean Amplitudes Of Vibration ◽  
Complete Set ◽  
First Time ◽  
The Relationship ◽  
Good Agreement

Complete normal coordinate analyses were performed for naphthalene, anthracene, biphenylene and perylene, starting from a simple force field with seven adjustable force constants. A relationship between bond orders and carbon-carbon stretching force constants was deduced from: (a) bond distances as a function of bond orders, (b) a version of Badger's rule relating stretching force constants to the bond distances. The relationship was used to modify the initial seven-parameter force field, and the vibrational frequencies calculated from both the initial and modified force fields are discussed. In general the simple force field approximation produces sets of frequencies in remarkably good agreement with experimental assignments. The force field approximation failed badly when applied to benzene. No obvious explanation was found for this unexpected feature, which makes it worth while to continue the investigations. The mean amplitudes of vibration were calculated. For perylene an account of the complete set of mean amplitudes is given for the first time.

Study on the Flow Behavior in Thin Cavity during Water-Assisted Injection Molding

2011 ◽  
Vol 467-469 ◽  
pp. 80-83
Author(s):  
Tang Qing Kuang ◽  
Kun Han
Keyword(s):  
Injection Molding ◽  
Control Volume ◽  
Fluid Model ◽  
Flow Behavior ◽  
Experimental Result ◽  
Bulk Temperature ◽  
Injection Molding Process ◽  
Molding Process ◽  
Injection Location ◽  
Good Agreement

A numerical simulation model for the flow behavior of fluids in thin cavity during water assisted injection molding process is built up by adopting general Newtonian fluid model for the filling stage and non-Newtonian and compressible fluid model for the packing stage separately. Finite element/finite difference/control volume methods are adopted for the simulation of melt front, pressure variation at injection location, water thickness fraction and bulk temperature about a plate with trapezoidal cross-section. The simulated melt front location and shape have good agreement with experimental result. In comparison with the simulation results of conventional injection molding, it turns out that water assisted injection molding can obtain parts with low pressure requirement, perfect surface quality and rapid cooling.

THE SINGLE-SITE APPROXIMATION TO THE HUBBARD MODEL

1993 ◽  
Vol 07 (14) ◽  
pp. 2667-2684
Author(s):  
MASSIMO CORRIAS
Keyword(s):  
Hubbard Model ◽  
Fermi Liquid ◽  
Particle Density ◽  
Fluid Model ◽  
Interaction Strength ◽  
Electron System ◽  
Field Approximation ◽  
Single Site ◽  
Mean Field Approximation ◽  
Half Filling

The diagrammatic formulation of the single-site approximation to the Hubbard model immediately yields the exact solution to the Falikov-Kimball model in infinite dimensions. By an extension of the alloy analogy, we then derive a two-fluid model, dividing self-consistently the electron system among itinerating and relatively localized particles. Our theory coincides with the CPA only the at half-filling and u=∞. We start by studying the mean field approximation to our theory and identify a phase boundary in the particle density-interaction strength (n−u) plane at which the Fermi liquid model breaks down. Then the effect of fluctuations in the Fermi liquid regime is considered and, finally, we construct, at half-filling, a model which interpolates between the Fermi liquid and the Mott insulating phases.

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