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D. Haworth, S. Pope (1986)
A second-order Monte Carlo method for the solution of the Ito stochastic differential equationStochastic Analysis and Applications, 4
P. Kloeden, E. Platen (1977)
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Arkady Tsinober (1998)
Statistical fluid mechanicsEuropean Journal of Mechanics B-fluids, 17
H. Haken (1989)
Synergetics: an overviewReports on Progress in Physics, 52
(1998)
Probability density function modelling of dispersed twophase turbulent °ows
S. Pope (1995)
Particle method for turbulent flows: integration of stochastic model equationsJournal of Computational Physics, 117
J. Minier, E. Peirano (2001)
The pdf approach to turbulent polydispersed two-phase flowsPhysics Reports, 352
(1988)
Computer simulations using particles
Jinchao Xu, S. Pope (1999)
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A. Monin, A. Yaglom, T. Lundgren (1976)
Statistical Fluid Mechanics, Vol. IIJournal of Applied Mechanics, 43
(1995)
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L. Arnold (1992)
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J. Minier (2001)
Probabilistic approach to turbulent two-phase flows modelling and simulation: theoretical and numerical issues, 7
J. Minier, R. Cao, S. Pope (2003)
Comment on the article "An effective particle tracing scheme on structured/unstructured grids in hybrid finite volume/PDF Monte Carlo methods" by Li and ModestJournal of Computational Physics, 186
D. Talay (1995)
Simulation of stochastic differential systems
E. Peirano, J. Minier (2002)
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S. Pope (1994)
Lagrangian PDF Methods for Turbulent FlowsAnnual Review of Fluid Mechanics, 26
Weak first- and second-order numerical schemes are developed to integrate the stochastic differential equations that arise in mean-field - pdf methods (Lagrangian stochastic approach) for modeling polydispersed turbulent two-phase flows. These equations present several challenges, the foremost being that the problem is characterized by the presence of different time scales that can lead to stiff equations, when the smallest time-scale is significantly less than the time-step of the simulation. The numerical issues have been detailed by Minier Monte Carlo Meth. and Appl. 7 295-310, (2000) and the present paper proposes numerical schemes that satisfy these constraints. This point is really crucial for physical and engineering applications, where various limit cases can be present at the same time in different parts of the domain or at different times. In order to build up the algorithm, the analytical solutions to the equations are first carried out when the coefficients are constant. By freezing the coefficients in the analytical solutions, first and second order unconditionally stable weak schemes are developed. A prediction/ correction method, which is shown to be consistent for the present stochastic model, is used to devise the second-order scheme. A complete numerical investigation is carried out to validate the schemes, having included also a comprehensive study of the different error sources. The final method is demonstrated to have the required stability, accuracy and efficiency.
Monte Carlo Methods and Applications – de Gruyter
Published: Apr 1, 2003
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