# A consistent hybrid finite-volume/particle method for the PDF equations of turbulent reactive flows

## Abstract

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 the Reynolds stresses, the scalar fluxes, and the 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 the stochastic ideal flow equations. Numerical results are obtained for 1D 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 themore »

- Authors:

- Publication Date:

- Research Org.:
- Cornell Univ., Ithaca, NY (US)

- Sponsoring Org.:
- USDOE

- OSTI Identifier:
- 20000633

- DOE Contract Number:
- FG02-90ER14128

- Resource Type:
- Journal Article

- Journal Name:
- Journal of Computational Physics

- Additional Journal Information:
- Journal Volume: 154; Journal Issue: 2; Other Information: PBD: 20 Sep 1999; Journal ID: ISSN 0021-9991

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 42 ENGINEERING; 99 MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE; CONVERGENCE; NUMERICAL SOLUTION; TURBULENT FLOW; CONSERVATION LAWS; STOCHASTIC PROCESSES; IDEAL FLOW; ONE-DIMENSIONAL CALCULATIONS

### Citation Formats

```
Muradoglu, M., Jenny, P., Pope, S.B., and Caughey, D.A.
```*A consistent hybrid finite-volume/particle method for the PDF equations of turbulent reactive flows*. United States: N. p., 1999.
Web. doi:10.1006/jcph.1999.6316.

```
Muradoglu, M., Jenny, P., Pope, S.B., & Caughey, D.A.
```*A consistent hybrid finite-volume/particle method for the PDF equations of turbulent reactive flows*. United States. doi:10.1006/jcph.1999.6316.

```
Muradoglu, M., Jenny, P., Pope, S.B., and Caughey, D.A. Mon .
"A consistent hybrid finite-volume/particle method for the PDF equations of turbulent reactive flows". United States. doi:10.1006/jcph.1999.6316.
```

```
@article{osti_20000633,
```

title = {A consistent hybrid finite-volume/particle method for the PDF equations of turbulent reactive flows},

author = {Muradoglu, M. and Jenny, P. and Pope, S.B. and Caughey, D.A.},

abstractNote = {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 the Reynolds stresses, the scalar fluxes, and the 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 the stochastic ideal flow equations. Numerical results are obtained for 1D 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.},

doi = {10.1006/jcph.1999.6316},

journal = {Journal of Computational Physics},

issn = {0021-9991},

number = 2,

volume = 154,

place = {United States},

year = {1999},

month = {9}

}