An adaptive mesh refinement method for solution of the transported PDF equation.

*(English)*Zbl 1176.80089Summary: This paper presents the results of an investigation into a possible alternative to Monte Carlo methods for solving the transported probability density function (PDF) equation for scalars (compositions). The method uses a finite-volume approach combined with adaptive mesh refinement (AMR) in a multi-dimensional compositional space. Comparisons are made between the new method and Monte Carlo solutions for analytical test cases involving the reaction of two or three chemical species. These tests demonstrate the potential of the new method in terms of both accuracy and run time. Additional test cases involving various models for molecular mixing were also conducted with similar conclusions.

##### MSC:

80M12 | Finite volume methods applied to problems in thermodynamics and heat transfer |

80M31 | Monte Carlo methods applied to problems in thermodynamics and heat transfer |

80A32 | Chemically reacting flows |

##### Keywords:

transported PDF; adaptive mesh refinement; finite-volume method; Eulerian Monte Carlo; molecular mixing
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\textit{D. A. Olivieri} et al., Int. J. Numer. Methods Eng. 79, No. 12, 1536--1556 (2009; Zbl 1176.80089)

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