A high-order spectral deferred correction strategy for low Mach number flow with complex chemistry
Abstract
This article presents a fourth-order finite-volume algorithm in space and time for low Mach number reacting flow with detailed kinetics and transport. Our temporal integration scheme is based on a Multi-Implicit Spectral Deferred Correction (MISDC) strategy that iteratively couples advection, diffusion, and reactions evolving subject to a constraint. Our new approach overcomes a stability limitation of our previous second-order method encountered when trying to incorporate higher-order polynomial representations of the solution in time to increase accuracy. We have developed a new iterative scheme that naturally fits within our MISDC framework and allows us to conserve mass and energy while simultaneously satisfying the equation of state. We analyse the conditions for which the iterative schemes are guaranteed to converge to the fixed point solution. Finally, we present numerical examples illustrating the performance of the new method on premixed hydrogen, methane, and dimethyl ether flames.
- Authors:
-
- Brown Univ., Providence, RI (United States)
- Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)
- Publication Date:
- Research Org.:
- Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA (United States)
- Sponsoring Org.:
- USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR)
- OSTI Identifier:
- 1379326
- Grant/Contract Number:
- AC02-05CH11231
- Resource Type:
- Journal Article: Accepted Manuscript
- Journal Name:
- Combustion Theory and Modelling
- Additional Journal Information:
- Journal Volume: 20; Journal Issue: 3; Journal ID: ISSN 1364-7830
- Publisher:
- Taylor & Francis
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CHEMISTRY; low Mach number combustion; spectral deferred corrections; fourth-order spatiotemporal discretisations; flame simulations; detailed chemistry and kinetics
Citation Formats
Pazner, Will E., Nonaka, Andrew, Bell, John B., Day, Marcus S., and Minion, Michael L. A high-order spectral deferred correction strategy for low Mach number flow with complex chemistry. United States: N. p., 2016.
Web. doi:10.1080/13647830.2016.1150519.
Pazner, Will E., Nonaka, Andrew, Bell, John B., Day, Marcus S., & Minion, Michael L. A high-order spectral deferred correction strategy for low Mach number flow with complex chemistry. United States. https://doi.org/10.1080/13647830.2016.1150519
Pazner, Will E., Nonaka, Andrew, Bell, John B., Day, Marcus S., and Minion, Michael L. 2016.
"A high-order spectral deferred correction strategy for low Mach number flow with complex chemistry". United States. https://doi.org/10.1080/13647830.2016.1150519. https://www.osti.gov/servlets/purl/1379326.
@article{osti_1379326,
title = {A high-order spectral deferred correction strategy for low Mach number flow with complex chemistry},
author = {Pazner, Will E. and Nonaka, Andrew and Bell, John B. and Day, Marcus S. and Minion, Michael L.},
abstractNote = {This article presents a fourth-order finite-volume algorithm in space and time for low Mach number reacting flow with detailed kinetics and transport. Our temporal integration scheme is based on a Multi-Implicit Spectral Deferred Correction (MISDC) strategy that iteratively couples advection, diffusion, and reactions evolving subject to a constraint. Our new approach overcomes a stability limitation of our previous second-order method encountered when trying to incorporate higher-order polynomial representations of the solution in time to increase accuracy. We have developed a new iterative scheme that naturally fits within our MISDC framework and allows us to conserve mass and energy while simultaneously satisfying the equation of state. We analyse the conditions for which the iterative schemes are guaranteed to converge to the fixed point solution. Finally, we present numerical examples illustrating the performance of the new method on premixed hydrogen, methane, and dimethyl ether flames.},
doi = {10.1080/13647830.2016.1150519},
url = {https://www.osti.gov/biblio/1379326},
journal = {Combustion Theory and Modelling},
issn = {1364-7830},
number = 3,
volume = 20,
place = {United States},
year = {Wed Mar 30 00:00:00 EDT 2016},
month = {Wed Mar 30 00:00:00 EDT 2016}
}
Works referenced in this record:
Implications of the Choice of Quadrature Nodes for Picard Integral Deferred Corrections Methods for Ordinary Differential Equations
journal, June 2005
- Layton, Anita T.; Minion, Michael L.
- BIT Numerical Mathematics, Vol. 45, Issue 2
A fourth-order auxiliary variable projection method for zero-Mach number gas dynamics
journal, January 2008
- Kadioglu, Samet Y.; Klein, Rupert; Minion, Michael L.
- Journal of Computational Physics, Vol. 227, Issue 3
On the Use of Higher-Order Projection Methods for Incompressible Turbulent Flow
journal, January 2013
- Almgren, A. S.; Aspden, A. J.; Bell, J. B.
- SIAM Journal on Scientific Computing, Vol. 35, Issue 1
A deferred correction coupling strategy for low Mach number flow with complex chemistry
journal, December 2012
- Nonaka, A.; Bell, J. B.; Day, M. S.
- Combustion Theory and Modelling, Vol. 16, Issue 6
A Semi-implicit Numerical Scheme for Reacting Flow
journal, September 1999
- Knio, Omar M.; Najm, Habib N.; Wyckoff, Peter S.
- Journal of Computational Physics, Vol. 154, Issue 2
Conservative multi-implicit spectral deferred correction methods for reacting gas dynamics
journal, March 2004
- Layton, Anita T.; Minion, Michael L.
- Journal of Computational Physics, Vol. 194, Issue 2
An Analytical Jacobian Approach to Sparse Reaction Kinetics for Computationally Efficient Combustion Modeling with Large Reaction Mechanisms
journal, July 2012
- Perini, Federico; Galligani, Emanuele; Reitz, Rolf D.
- Energy & Fuels, Vol. 26, Issue 8
Maestro: an Adaptive low mach Number Hydrodynamics Algorithm for Stellar Flows
journal, May 2010
- Nonaka, A.; Almgren, A. S.; Bell, J. B.
- The Astrophysical Journal Supplement Series, Vol. 188, Issue 2
A high-order finite-volume method for conservation laws on locally refined grids
journal, January 2011
- McCorquodale, Peter; Colella, Phillip
- Communications in Applied Mathematics and Computational Science, Vol. 6, Issue 1
High-order multi-implicit spectral deferred correction methods for problems of reactive flow
journal, August 2003
- Bourlioux, Anne; Layton, Anita T.; Minion, Michael L.
- Journal of Computational Physics, Vol. 189, Issue 2
The Derivation and Numerical Solution of the Equations for Zero Mach Number Combustion
journal, January 1985
- Majda, Andfrew; Sethian, James
- Combustion Science and Technology, Vol. 42, Issue 3-4
Numerical Methods in Laminar Flame Propagation
book, January 1982
- Peters, Norbert; Warnatz, Jürgen
- Vieweg+Teubner Verlag Wiesbaden
An Adaptive Projection Method for Unsteady, Low-Mach Number Combustion
journal, December 1998
- Pember, R. B.; Howell, L. H.; Bell, J. B.
- Combustion Science and Technology, Vol. 140, Issue 1-6
A Fourth-Order Accurate Finite-Volume Method with Structured Adaptive Mesh Refinement for Solving the Advection-Diffusion Equation
journal, January 2012
- Zhang, Qinghai; Johansen, Hans; Colella, Phillip
- SIAM Journal on Scientific Computing, Vol. 34, Issue 2
Numerical simulation of laminar reacting flows with complex chemistry
journal, December 2000
- Day, M. S.; Bell, J. B.
- Combustion Theory and Modelling, Vol. 4, Issue 4
Semi-implicit spectral deferred correction methods for ordinary differential equations
journal, January 2003
- Minion, Michael L.
- Communications in Mathematical Sciences, Vol. 1, Issue 3
Direct numerical simulations of autoignition in stratified dimethyl-ether (DME)/air turbulent mixtures
journal, March 2015
- Bansal, Gaurav; Mascarenhas, Ajith; Chen, Jacqueline H.
- Combustion and Flame, Vol. 162, Issue 3
A Semi-implicit Numerical Scheme for Reacting Flow
journal, July 1998
- Najm, Habib N.; Wyckoff, Peter S.; Knio, Omar M.
- Journal of Computational Physics, Vol. 143, Issue 2
A multi-level spectral deferred correction method
journal, August 2014
- Speck, Robert; Ruprecht, Daniel; Emmett, Matthew
- BIT Numerical Mathematics, Vol. 55, Issue 3
Spectral Deferred Correction Methods for Ordinary Differential Equations
journal, June 2000
- Dutt, Alok; Greengard, Leslie; Rokhlin, Vladimir
- Bit Numerical Mathematics, Vol. 40, Issue 2, p. 241-266
Efficient Variable-Coefficient Finite-Volume Stokes Solvers
journal, November 2014
- Cai, Mingchao; Nonaka, Andy; Bell, John B.
- Communications in Computational Physics, Vol. 16, Issue 5
A Low Mach Number Model for Moist Atmospheric Flows
journal, April 2015
- Duarte, Max; Almgren, Ann S.; Bell, John B.
- Journal of the Atmospheric Sciences, Vol. 72, Issue 4
The equations of motion for thermally driven, buoyant flows
journal, May 1978
- Rehm, R. G.; Baum, H. R.
- Journal of Research of the National Bureau of Standards, Vol. 83, Issue 3
An Analytical Jacobian Approach to Sparse Reaction Kinetics for Computationally Efficient Combustion Modeling with Large Reaction Mechanisms
journal, July 2012
- Perini, Federico; Galligani, Emanuele; Reitz, Rolf D.
- Energy & Fuels, Vol. 26, Issue 8
Maestro: an Adaptive low mach Number Hydrodynamics Algorithm for Stellar Flows
journal, May 2010
- Nonaka, A.; Almgren, A. S.; Bell, J. B.
- The Astrophysical Journal Supplement Series, Vol. 188, Issue 2
Implications of the Choice of Quadrature Nodes for Picard Integral Deferred Corrections Methods for Ordinary Differential Equations
journal, January 2005
- Anita, Layton,; Michael, Minion,
- BIT - Numerical Mathematics, Vol. 45, Issue 2
A multi-level spectral deferred correction method
text, January 2013
- Speck, Robert; Ruprecht, Daniel; Emmett, Matthew
- arXiv
A Low Mach Number Model for Moist Atmospheric Flows
text, January 2014
- Duarte, Max; Almgren, Ann; Bell, John
- arXiv
The equations of motion for thermally driven, buoyant flows
journal, May 1978
- Rehm, R. G.; Baum, H. R.
- Journal of Research of the National Bureau of Standards, Vol. 83, Issue 3