Weak second-order splitting schemes for Lagrangian Monte Carlo particle methods for the composition PDF/FDF transport equations

详细信息    查看全文

• 作者：Haifeng Wang ; Pavel P. Popov ; Stephen B. Pope
• 关键词：Turbulent combustion ; PDF methods ; Ito stochastic differential equations ; Random differential equations ; Monte Carlo particle method ; Splitting schemes ; Weak convergence ; Method of manufactured solutions
• 刊名：Journal of Computational Physics
• 出版年：2010
• 出版时间：1 March 2010
• 年：2010
• 卷：229
• 期：5
• 页码：1852-1878
• 全文大小：1100 K

文摘

We study a class of methods for the numerical solution of the system of stochastic differential equations (SDEs) that arises in the modeling of turbulent combustion, specifically in the Monte Carlo particle method for the solution of the model equations for the composition probability density function (PDF) and the filtered density function (FDF). This system consists of an SDE for particle position and a random differential equation for particle composition. The numerical methods considered advance the solution in time with (weak) second-order accuracy with respect to the time step size. The four primary contributions of the paper are: (i) establishing that the coefficients in the particle equations can be frozen at the mid-time (while preserving second-order accuracy), (ii) examining the performance of three existing schemes for integrating the SDEs, (iii) developing and evaluating different splitting schemes (which treat particle motion, reaction and mixing on different sub-steps), and (iv) developing the method of manufactured solutions (MMS) to assess the convergence of Monte Carlo particle methods. Tests using MMS confirm the second-order accuracy of the schemes. In general, the use of frozen coefficients reduces the numerical errors. Otherwise no significant differences are observed in the performance of the different SDE schemes and splitting schemes.