Residual Monte Carlo for the One-Dimensional Particle Transport Equation

2016 ◽  
Vol 38 (6) ◽  
pp. B941-B961 ◽  
Author(s):  
J. R. Peterson ◽  
J. E. Morel ◽  
J. C. Ragusa
Keyword(s):  
Monte Carlo ◽  
Transport Equation ◽  
Particle Transport ◽  
One Dimensional ◽  
The One

scholarly journals A fractional generalization of the dirichlet distribution and related distributions

2021 ◽  
Vol 24 (1) ◽  
pp. 112-136
Author(s):  
Elvira Di Nardo ◽  
Federico Polito ◽  
Enrico Scalas
Keyword(s):  
Monte Carlo ◽  
Probability Density Function ◽  
Monte Carlo Simulations ◽  
Probability Density ◽  
Dirichlet Distribution ◽  
One Dimensional ◽  
Reasonable Approximation ◽  
Generalized Dirichlet Distribution ◽  
The One ◽  
Generalized Dirichlet

Abstract This paper is devoted to a fractional generalization of the Dirichlet distribution. The form of the multivariate distribution is derived assuming that the n partitions of the interval [0, Wn ] are independent and identically distributed random variables following the generalized Mittag-Leffler distribution. The expected value and variance of the one-dimensional marginal are derived as well as the form of its probability density function. A related generalized Dirichlet distribution is studied that provides a reasonable approximation for some values of the parameters. The relation between this distribution and other generalizations of the Dirichlet distribution is discussed. Monte Carlo simulations of the one-dimensional marginals for both distributions are presented.

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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