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
It’s your single place to instantly
discover and read the research
that matters to you.
Enjoy affordable access to
over 18 million articles from more than
15,000 peer-reviewed journals.
All for just $49/month
Query the DeepDyve database, plus search all of PubMed and Google Scholar seamlessly
Save any article or search result from DeepDyve, PubMed, and Google Scholar... all in one place.
Get unlimited, online access to over 18 million full-text articles from more than 15,000 scientific journals.
Read from thousands of the leading scholarly journals from SpringerNature, Wiley-Blackwell, Oxford University Press and more.
All the latest content is available, no embargo periods.
“Hi guys, I cannot tell you how much I love this resource. Incredible. I really believe you've hit the nail on the head with this site in regards to solving the research-purchase issue.”Daniel C.
“Whoa! It’s like Spotify but for academic articles.”@Phil_Robichaud
“I must say, @deepdyve is a fabulous solution to the independent researcher's problem of #access to #information.”@deepthiw
“My last article couldn't be possible without the platform @deepdyve that makes journal papers cheaper.”@JoseServera