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Title: A high-order numerical algorithm for DNS of low-Mach-number reactive flows with detailed chemistry and quasi-spectral accuracy

Abstract

A novel and efficient algorithm is presented in this paper to deal with DNS of turbulent reacting flows under the low-Mach-number assumption, with detailed chemistry and a quasi-spectral accuracy. The temporal integration of the equations relies on an operating-split strategy, where chemical reactions are solved implicitly with a stiff solver and the convection-diffusion operators are solved with a Runge-Kutta-Chebyshev method. The spatial discretisation is performed with high-order compact schemes, and a FFT based constant-coefficient spectral solver is employed to solve a variable-coefficient Poisson equation. The numerical implementation takes advantage of the 2DECOMP&FFT libraries developed by, which are based on a pencil decomposition method of the domain and are proven to be computationally very efficient. An enhanced pressure-correction method is proposed to speed up the achievement of machine precision accuracy. It is demonstrated that a second-order accuracy is reached in time, while the spatial accuracy ranges from fourth-order to sixth-order depending on the set of imposed boundary conditions. In conclusion, the software developed to implement the present algorithm is called HOLOMAC, and its numerical efficiency opens the way to deal with DNS of reacting flows to understand complex turbulent and chemical phenomena in flames.

Authors:
ORCiD logo [1];  [2]
  1. Univ. of Adelaide, SA (Australia). School of Mechanical Engineering
  2. Univ. of Adelaide, SA (Australia). School of Mechanical Engineering; Purdue Univ., West Lafayette, IN (United States). School of Mechanical Engineering
Publication Date:
Research Org.:
Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)
Sponsoring Org.:
USDOE Office of Science (SC)
OSTI Identifier:
1525148
Grant/Contract Number:  
AC02-05CH11231
Resource Type:
Journal Article: Accepted Manuscript
Journal Name:
Journal of Computational Physics
Additional Journal Information:
Journal Volume: 313; Journal Issue: C; Journal ID: ISSN 0021-9991
Publisher:
Elsevier
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICS AND COMPUTING; 37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CHEMISTRY; DNS; Low-Mach-number; Detailed chemistry; Turbulent reacting flow; High-order methods; Spectral accuracy; Operator splitting

Citation Formats

Motheau, E., and Abraham, J. A high-order numerical algorithm for DNS of low-Mach-number reactive flows with detailed chemistry and quasi-spectral accuracy. United States: N. p., 2016. Web. doi:10.1016/j.jcp.2016.02.059.
Motheau, E., & Abraham, J. A high-order numerical algorithm for DNS of low-Mach-number reactive flows with detailed chemistry and quasi-spectral accuracy. United States. https://doi.org/10.1016/j.jcp.2016.02.059
Motheau, E., and Abraham, J. Sat . "A high-order numerical algorithm for DNS of low-Mach-number reactive flows with detailed chemistry and quasi-spectral accuracy". United States. https://doi.org/10.1016/j.jcp.2016.02.059. https://www.osti.gov/servlets/purl/1525148.
@article{osti_1525148,
title = {A high-order numerical algorithm for DNS of low-Mach-number reactive flows with detailed chemistry and quasi-spectral accuracy},
author = {Motheau, E. and Abraham, J.},
abstractNote = {A novel and efficient algorithm is presented in this paper to deal with DNS of turbulent reacting flows under the low-Mach-number assumption, with detailed chemistry and a quasi-spectral accuracy. The temporal integration of the equations relies on an operating-split strategy, where chemical reactions are solved implicitly with a stiff solver and the convection-diffusion operators are solved with a Runge-Kutta-Chebyshev method. The spatial discretisation is performed with high-order compact schemes, and a FFT based constant-coefficient spectral solver is employed to solve a variable-coefficient Poisson equation. The numerical implementation takes advantage of the 2DECOMP&FFT libraries developed by, which are based on a pencil decomposition method of the domain and are proven to be computationally very efficient. An enhanced pressure-correction method is proposed to speed up the achievement of machine precision accuracy. It is demonstrated that a second-order accuracy is reached in time, while the spatial accuracy ranges from fourth-order to sixth-order depending on the set of imposed boundary conditions. In conclusion, the software developed to implement the present algorithm is called HOLOMAC, and its numerical efficiency opens the way to deal with DNS of reacting flows to understand complex turbulent and chemical phenomena in flames.},
doi = {10.1016/j.jcp.2016.02.059},
url = {https://www.osti.gov/biblio/1525148}, journal = {Journal of Computational Physics},
issn = {0021-9991},
number = C,
volume = 313,
place = {United States},
year = {2016},
month = {2}
}

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Works referencing / citing this record:

A fourth-order adaptive mesh refinement algorithm for the multicomponent, reacting compressible Navier–Stokes equations
journal, January 2019