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**A consistent hybrid finite-volume/particle method for the PDF equations of turbulent reactive flows.**
*(English)*
Zbl 0953.76062

Summary: The paper describes a new hybrid finite-volume (FV)/particle method developed for the solution of the PDF equations for statistically stationary turbulent reactive flows. In this approach, the conservation equations for mean mass, momentum, and energy conservation are solved by a FV method, while a particle algorithm is employed to solve the fluctuating velocity-turbulence frequency-compositions joint PDF transport equation. The mean velocity and pressure are supplied to the particle code by the FV code, which in turn obtains all Reynolds stresses, scalar fluxes, and reaction terms needed in the FV code. An important feature of the method is the complete consistency between the set of equations solved by the FV and particle methods.

The algorithmic and numerical issues arising in the development of the hybrid method are studied in the simple setting of stochastic ideal flow equations. Numerical results are obtained for one-dimensional reactive stochastic ideal flow to demonstrate numerical properties of the method. The total numerical error is identified as statistical error, bias, spatial truncation error, and temporal truncation error. In contrast to the self-contained particle method, the bias is found to be negligibly small. It is shown that all the numerical errors converge at the expected rates. Finally, the global convergence of the hybrid method is demonstrated and the optimal strategy for time-averaging that gives the best global convergence rate is investigated.

The algorithmic and numerical issues arising in the development of the hybrid method are studied in the simple setting of stochastic ideal flow equations. Numerical results are obtained for one-dimensional reactive stochastic ideal flow to demonstrate numerical properties of the method. The total numerical error is identified as statistical error, bias, spatial truncation error, and temporal truncation error. In contrast to the self-contained particle method, the bias is found to be negligibly small. It is shown that all the numerical errors converge at the expected rates. Finally, the global convergence of the hybrid method is demonstrated and the optimal strategy for time-averaging that gives the best global convergence rate is investigated.

### MSC:

76M12 | Finite volume methods applied to problems in fluid mechanics |

76M28 | Particle methods and lattice-gas methods |

76V05 | Reaction effects in flows |

76F25 | Turbulent transport, mixing |

### Keywords:

hybrid finite-volume/particle method; numerical convergence; statistically stationary turbulent reactive flows; conservation equations; particle algorithm; stochastic ideal flow equations; numerical error; global convergence### Software:

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\textit{M. Muradoglu} et al., J. Comput. Phys. 154, No. 2, 342--371 (1999; Zbl 0953.76062)

### References:

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