The Interaction of Solid or Liquid Particles and Turbulent Fluid Flow Fields—A Numerical Simulation

1979 ◽  
Vol 101 (2) ◽  
pp. 265-269 ◽  
Author(s):  
D. J. Brown ◽  
P. Hutchinson
Keyword(s):  
Numerical Simulation ◽  
Diffusion Coefficient ◽  
The Other ◽  
Dispersion Process ◽  
Turbulent Fluid Flow ◽  
One Dimensional ◽  
Constant Diffusion Coefficient ◽  
Constant Diffusion ◽  
Bounded System

Using a simple model of turbulence a simulation is made of the interaction of an ensemble of discrete solid or liquid particles and a fluid continuum. Two notional one - dimensional systems are considered: one of which is unbounded and the other bounded by perfectly absorbing walls. The results for the unbounded system indicate that at sufficiently long times discrete particles may disperse more rapidly than the elements of the fluid continuum. The study on the bounded system, however, shows that in practice the ratio of particle relaxation time to particle mean residence time may be such that this rapid dispersion will not be achieved and, moreover, that characterization of the dispersion process by a constant diffusion coefficient leads to significant errors.

The computer simulation of the boost diffusion oxidation process for the deep-case hardening of titanium alloys

2004 ◽  
Vol 120 ◽  
pp. 259-268
Author(s):  
J. Luo ◽  
Z. Zhang ◽  
H. Dong ◽  
T. Bell
Keyword(s):  
Diffusion Coefficient ◽  
Titanium Alloys ◽  
Concentration Dependence ◽  
Oxygen Diffusion ◽  
Oxidation Process ◽  
Case Hardening ◽  
One Dimensional ◽  
Constant Diffusion Coefficient ◽  
Constant Diffusion ◽  
Simulation Results

A one dimensional finite difference diffusion model for simulating the Boost Diffusion Oxidation (BDO) process of titanium alloys is developed and implemented as a window-based program. The program can simulate the BDO process for both constant diffusion coefficient and concentration dependent diffusion coefficient. It is found that to accurately simulate the BDO process, the concentration dependence of oxygen diffusion has to be taken into account. If the concentration dependence is taken as the Shamblen and Redden’s equation, the simulation results agree well with the experimental results.

scholarly journals Fractional stochastic heat equation with piecewise constant coefficients

2020 ◽  
Vol 21 (01) ◽  
pp. 2150002
Author(s):  
Yuliya Mishura ◽  
Kostiantyn Ralchenko ◽  
Mounir Zili ◽  
Eya Zougar
Keyword(s):  
Diffusion Coefficient ◽  
Heat Equation ◽  
Divergence Form ◽  
Stochastic Heat Equation ◽  
Piecewise Constant ◽  
Constant Diffusion Coefficient ◽  
Infinite Dimensional ◽  
Order Elliptic Operator ◽  
Constant Diffusion ◽  
Constant Coefficients

We introduce a fractional stochastic heat equation with second-order elliptic operator in divergence form, having a piecewise constant diffusion coefficient, and driven by an infinite-dimensional fractional Brownian motion. We characterize the fundamental solution of its deterministic part, and prove the existence and the uniqueness of its solution.

Multi-layered diffusive convection. Part 2. Dynamics of layer evolution

2010 ◽  
Vol 651 ◽  
pp. 465-481 ◽  
Author(s):  
TAKASHI NOGUCHI ◽  
HIROSHI NIINO
Keyword(s):  
Numerical Simulation ◽  
Numerical Model ◽  
Direct Numerical Simulation ◽  
Analytical Model ◽  
The Other ◽  
One Dimensional ◽  
Turbulent Entrainment ◽  
Diffusive Convection ◽  
Two Component

Evolution of layers in an unbounded diffusively stratified two-component fluid and its dynamics are studied by means of a direct numerical simulation (DNS) and an analytical model. The numerical simulation shows that the layers grow by repeating mergings with the neighbouring layers. By analysing the results of the numerical simulation, the mechanism of the merging is examined in detail. Two modes of merging are found to exist: one is the layer vanishing mode and the other is the interface vanishing mode. The vanishings of layers and interfaces are caused by turbulent entrainment at the interfaces. Based on the analysis of the numerical model, a one-dimensional asymmetric entrainment model is proposed. In the model, each layer is assumed to interact with its neighbouring layers through simplified convective entrainment laws. The model is applied to two simple configurations of layers and is proved to reproduce the layer evolutions found in the DNS successfully.

scholarly journals Time-Dependent Simulation of Cosmic-Ray Shocks, Including Alfvén Transport

1994 ◽  
Vol 142 ◽  
pp. 969-973
Author(s):  
T. W. Jones
Keyword(s):  
Diffusion Coefficient ◽  
Cosmic Rays ◽  
Wave Energy ◽  
Cosmic Ray ◽  
Alfven Waves ◽  
Alfven Wave ◽  
Alfvén Waves ◽  
Constant Diffusion Coefficient ◽  
Constant Diffusion ◽  
Transport Effects

AbstractTime evolution of plane, cosmic-ray modified shocks has been simulated numerically for the case with parallel magnetic fields. Computations were done in a “three-fluid” dynamical model incorporating cosmic-ray and Alfvén-wave energy transport equations. Nonlinear feedback from the cosmic rays and Alfvén waves is included in the equation of motion for the underlying plasma, as is the finite propagation speed and energy dissipation of the Alfvén waves. Exploratory results confirm earlier, steady state analyses that found these Alfvén transport effects to be potentially important when the upstream Alfvén speed and gas sound speeds are comparable. As noted earlier, Alfvén transport effects tend to reduce the transfer of energy through a shock from gas to energetic particles. These studies show as well that the timescale for modification of the shock is altered in nonlinear ways. It is clear, however, that the consequences of Alfvén transport are strongly model dependent and that both advection of cosmic rays by the waves and dissipation of wave energy in the plasma will be important to model correctly when quantitative results are needed. Comparison is made between simulations based on a constant diffusion coefficient and more realistic diffusion models allowing the diffusion coefficient to vary in response to changes in Alfvén wave intensity. No really substantive differences were found between them.Subject headings: cosmic rays — MHD — shock waves

scholarly journals On Solving the Poisson Equation with Discontinuities on Irregular Interfaces: GFM and VIM

2018 ◽  
Vol 2018 ◽  
pp. 1-8
Author(s):  
Ásdís Helgadóttir ◽  
Arthur Guittet ◽  
Frédéric Gibou
Keyword(s):  
Diffusion Coefficient ◽  
Poisson Equation ◽  
Real Life ◽  
Ghost Fluid Method ◽  
Constant Diffusion Coefficient ◽  
The Poisson Equation ◽  
Constant Diffusion ◽  
Physical Phenomena ◽  
Irregular Interface ◽  
Better Than

We analyze the accuracy of two numerical methods for the variable coefficient Poisson equation with discontinuities at an irregular interface. Solving the Poisson equation with discontinuities at an irregular interface is an essential part of solving many physical phenomena such as multiphase flows with and without phase change, in heat transfer, in electrokinetics, and in the modeling of biomolecules’ electrostatics. The first method, considered for the problem, is the widely known Ghost-Fluid Method (GFM) and the second method is the recently introduced Voronoi Interface Method (VIM). The VIM method uses Voronoi partitions near the interface to construct local configurations that enable the use of the Ghost-Fluid philosophy in one dimension. Both methods lead to symmetric positive definite linear systems. The Ghost-Fluid Method is generally first-order accurate, except in the case of both a constant discontinuity in the solution and a constant diffusion coefficient, while the Voronoi Interface Method is second-order accurate in the L∞-norm. Therefore, the Voronoi Interface Method generally outweighs the Ghost-Fluid Method except in special case of both a constant discontinuity in the solution and a constant diffusion coefficient, where the Ghost-Fluid Method performs better than the Voronoi Interface Method. The paper includes numerical examples displaying this fact clearly and its findings can be used to determine which approach to choose based on the properties of the real life problem in hand.

Certain Problems with the Application of Stochastic Diffusion Processes for the Description of Chemical Engineering Phenomena. Numerical Simulation of One-Dimensional Diffusion Process

1996 ◽  
Vol 61 (4) ◽  
pp. 512-535 ◽  
Author(s):  
Pavel Hasal ◽  
Vladimír Kudrna
Keyword(s):  
Numerical Simulation ◽  
Diffusion Coefficient ◽  
Differential Equations ◽  
Stochastic Differential Equations ◽  
Chemical Engineering ◽  
Diffusion Processes ◽  
Stochastic Integral ◽  
Random Motion ◽  
One Dimensional ◽  
Dimensional Diffusion

Some problems are analyzed arising when a numerical simulation of a random motion of a large ensemble of diffusing particles is used to approximate the solution of a one-dimensional diffusion equation. The particle motion is described by means of a stochastic differential equation. The problems emerging especially when the diffusion coefficient is a function of spatial coordinate are discussed. The possibility of simulation of various kinds of stochastic integral is demonstrated. It is shown that the application of standard numerical procedures commonly adopted for ordinary differential equations may lead to erroneous results when used for solution of stochastic differential equations. General conclusions are verified by numerical solution of three stochastic differential equations with different forms of the diffusion coefficient.

Numerical Simulation of AlxGa1-XN/GaN Hetero Junction Quantum Well by AMPS-1D

2011 ◽  
Vol 282-283 ◽  
pp. 518-521
Author(s):  
Kai Ju Zhang ◽  
B. Wan
Keyword(s):  
Numerical Simulation ◽  
Quantum Well ◽  
The Other ◽  
Simulation Program ◽  
One Dimensional ◽  
Photonic Structures ◽  
Other Hand ◽  
Dimensional Simulation ◽  
The One

In this work, the one dimensional simulation program called analysis of microelectronic and photonic structures (AMPS-1D) is used to study the performances of depth of AlxGa1-xN/GaN heterojunction quantum well. The calculated results of AMPS-1D software show that the effect of different Al composition on the depth of AlxGa1-xN/GaN heterojunction quantum well is slight. On the other hand, the effect of different doped concentration in AlxGa1-xN is obvious.

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