caa a22 4500 378876503 CHVBK 20180305123421.0 cr unu---uuuuu 161128e20030401xx s 000 0 eng 10.1515/156939603322663312 doi (NATIONALLICENCE)gruyter-10.1515/156939603322663312 Weak first- and second-order numerical schemes for stochastic differential equations appearing in Lagrangian two-phase flow modeling [Elektronische Daten] [Jean-Pierre Minier, Eric Peirano, Sergio Chibbaro] 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. Copyright 2003, Walter de Gruyter Minier Jean-Pierre Electricité de France, MFTT, 6 Quati Watier 78400 France. aut Peirano Eric ADEME-Der, 500 Route des Lucioles 06560 Valbonne France. aut Chibbaro Sergio Dipartimento di fisica and INFN, Università di Cagliari, Cittadella Universitaria Monserrato CA, Italy. aut Monte Carlo Methods and Applications Walter de Gruyter 9/2(2003-04-01), 93-133 0929-9629 9:2<93 2003 9 mcma https://doi.org/10.1515/156939603322663312 text/html Onlinezugriff via DOI 1 research article jats NATIONALLICENCE 856 40 https://doi.org/10.1515/156939603322663312 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Minier Jean-Pierre Electricité de France, MFTT, 6 Quati Watier 78400 France aut NATIONALLICENCE 700 1- Peirano Eric ADEME-Der, 500 Route des Lucioles 06560 Valbonne France aut NATIONALLICENCE 700 1- Chibbaro Sergio Dipartimento di fisica and INFN, Università di Cagliari, Cittadella Universitaria Monserrato CA, Italy aut NATIONALLICENCE 773 0- Monte Carlo Methods and Applications Walter de Gruyter 9/2(2003-04-01), 93-133 0929-9629 9:2<93 2003 9 mcma CC0 http://creativecommons.org/publicdomain/zero/1.0 nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-gruyter