Concurrent implicit spectral deferred correction scheme for low-Mach number combustion with detailed chemistry

Hamon, François P.; Day, Marcus S.; Minion, Michael L.

doi:10.1080/13647830.2018.1524156

Title: Concurrent implicit spectral deferred correction scheme for low-Mach number combustion with detailed chemistry

Abstract

We present a parallel multi-implicit time integration scheme for the advection-diffusion-reaction systems arising from the equations governing low-Mach number combustion with complex chemistry. Here, our strategy employs parallelisation across the method to accelerate the serial Multi-Implicit Spectral Deferred Correction (MISDC) scheme used to couple the advection, diffusion, and reaction processes. In our approach, the diffusion solves and the reaction solves are performed concurrently by different processors. Our analysis shows that the proposed parallel scheme is stable for stiff problems and that the sweeps converge to the fixed-point solution at a faster rate than with serial MISDC. We present numerical examples to demonstrate that the new algorithm is high-order accurate in time, and achieves a parallel speedup compared to serial MISDC.

Authors:

Hamon, François P. ^[1]; Day, Marcus S. ^[1]; Minion, Michael L. ^[1]

Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States). Center for Computational Sciences and Engineering

Publication Date:: Fri Sep 28 00:00:00 EDT 2018

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:: 1525276

Grant/Contract Number:: AC02-05CH11231

Resource Type:: Accepted Manuscript

Journal Name:: Combustion Theory and Modelling

Additional Journal Information:: Journal Volume: 23; Journal Issue: 2; Journal ID: ISSN 1364-7830

Publisher:: Taylor & Francis

Country of Publication:: United States

Language:: English

Subject:: 97 MATHEMATICS AND COMPUTING; low-Mach number combustion; complex chemistry; time integration; multi-implicit spectral deferred corrections; parallelization across the method

Citation Formats


                    Hamon, François P., Day, Marcus S., and Minion, Michael L. Concurrent implicit spectral deferred correction scheme for low-Mach number combustion with detailed chemistry.  United States: N. p., 2018. 
Web.  doi:10.1080/13647830.2018.1524156.

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                    Hamon, François P., Day, Marcus S., & Minion, Michael L. Concurrent implicit spectral deferred correction scheme for low-Mach number combustion with detailed chemistry.  United States.  https://doi.org/10.1080/13647830.2018.1524156

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                    Hamon, François P., Day, Marcus S., and Minion, Michael L. Fri .  
"Concurrent implicit spectral deferred correction scheme for low-Mach number combustion with detailed chemistry".  United States.  https://doi.org/10.1080/13647830.2018.1524156.  https://www.osti.gov/servlets/purl/1525276.

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@article{osti_1525276,

  title        = {Concurrent implicit spectral deferred correction scheme for low-Mach number combustion with detailed chemistry},

  author       = {Hamon, François P. and Day, Marcus S. and Minion, Michael L.},

  abstractNote = {We present a parallel multi-implicit time integration scheme for the advection-diffusion-reaction systems arising from the equations governing low-Mach number combustion with complex chemistry. Here, our strategy employs parallelisation across the method to accelerate the serial Multi-Implicit Spectral Deferred Correction (MISDC) scheme used to couple the advection, diffusion, and reaction processes. In our approach, the diffusion solves and the reaction solves are performed concurrently by different processors. Our analysis shows that the proposed parallel scheme is stable for stiff problems and that the sweeps converge to the fixed-point solution at a faster rate than with serial MISDC. We present numerical examples to demonstrate that the new algorithm is high-order accurate in time, and achieves a parallel speedup compared to serial MISDC.},

  doi          = {10.1080/13647830.2018.1524156},

  journal      = {Combustion Theory and Modelling},

  number       = 2,

  volume       = 23,

  place        = {United States},

  year         = {Fri Sep 28 00:00:00 EDT 2018},

  month        = {Fri Sep 28 00:00:00 EDT 2018}

}

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Works referenced in this record:

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Works referencing / citing this record:

Multi-Level Spectral Deferred Corrections Scheme for the Shallow Water Equations on the Rotating Sphere
text, January 2018

Hamon, Francois; Schreiber, Martin; Minion, Michael
arXiv
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Title: Concurrent implicit spectral deferred correction scheme for low-Mach number combustion with detailed chemistry

Abstract

Citation Formats

A high-order spectral deferred correction strategy for low Mach number flow with complex chemistry journal, March 2016

A Semi-implicit Numerical Scheme for Reacting Flow journal, September 1999

Conservative multi-implicit spectral deferred correction methods for reacting gas dynamics journal, March 2004

Comments on high-order integrators embedded within integral deferred correction methods journal, January 2009

Parallelizing spectral deferred corrections across the method journal, July 2018

On the Theory of Parallel Runge—Kutta Methods journal, January 1990

An Adaptive Projection Method for Unsteady, Low-Mach Number Combustion journal, December 1998

Parallel High-Order Integrators journal, January 2010

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Direct numerical simulations of autoignition in stratified dimethyl-ether (DME)/air turbulent mixtures journal, March 2015

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Spectral Deferred Correction Methods for Ordinary Differential Equations journal, June 2000

The equations of motion for thermally driven, buoyant flows journal, May 1978

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A waveform relaxation algorithm with overlapping splitting for reaction diffusion equations journal, March 1999

A deferred correction coupling strategy for low Mach number flow with complex chemistry journal, December 2012

Efficient time discretization for local discontinuous Galerkin methods journal, July 2007

Time–space adaptive numerical methods for the simulation of combustion fronts journal, June 2013

An Analytical Jacobian Approach to Sparse Reaction Kinetics for Computationally Efficient Combustion Modeling with Large Reaction Mechanisms journal, July 2012

A high-order finite-volume method for conservation laws on locally refined grids journal, January 2011

High-order multi-implicit spectral deferred correction methods for problems of reactive flow journal, August 2003

The Derivation and Numerical Solution of the Equations for Zero Mach Number Combustion journal, January 1985

A high-order low-Mach number AMR construction for chemically reacting flows journal, December 2010

Parallel Time Integration with Multigrid journal, January 2014

A Fourth-Order Accurate Finite-Volume Method with Structured Adaptive Mesh Refinement for Solving the Advection-Diffusion Equation journal, January 2012

Numerical simulation of laminar reacting flows with complex chemistry journal, December 2000

Toward an efficient parallel in time method for partial differential equations journal, January 2012

A Parallel Space-Time Algorithm journal, January 2012

Modeling low mach number reacting flow with detailed chemistry and transport journal, November 2005

A high-order numerical algorithm for DNS of low-Mach-number reactive flows with detailed chemistry and quasi-spectral accuracy journal, May 2016

On the spectral deferred correction of splitting methods for initial value problems journal, January 2006

A Semi-implicit Numerical Scheme for Reacting Flow journal, July 1998

A multi-level spectral deferred correction method journal, August 2014

An Analytical Jacobian Approach to Sparse Reaction Kinetics for Computationally Efficient Combustion Modeling with Large Reaction Mechanisms journal, July 2012

The Waveform Relaxation Method for Time-Domain Analysis of Large Scale Integrated Circuits journal, July 1982

Parallel methods for integrating ordinary differential equations journal, December 1964

A high-order finite-volume method for conservation laws on locally refined grids journal, January 2011

A multi-level spectral deferred correction method text, January 2013

Multi-Level Spectral Deferred Corrections Scheme for the Shallow Water Equations on the Rotating Sphere text, January 2018

A high-order spectral deferred correction strategy for low Mach number flow with complex chemistry
journal, March 2016

A Semi-implicit Numerical Scheme for Reacting Flow
journal, September 1999

Conservative multi-implicit spectral deferred correction methods for reacting gas dynamics
journal, March 2004

Comments on high-order integrators embedded within integral deferred correction methods
journal, January 2009

Parallelizing spectral deferred corrections across the method
journal, July 2018

On the Theory of Parallel Runge—Kutta Methods
journal, January 1990

An Adaptive Projection Method for Unsteady, Low-Mach Number Combustion
journal, December 1998

Parallel High-Order Integrators
journal, January 2010

Parallel methods for integrating ordinary differential equations
journal, December 1964

Semi-implicit spectral deferred correction methods for ordinary differential equations
journal, January 2003

Parallel methods for the numerical integration of ordinary differential equations
journal, September 1967

Direct numerical simulations of autoignition in stratified dimethyl-ether (DME)/air turbulent mixtures
journal, March 2015

Faster SDC convergence on non-equidistant grids by DIRK sweeps
journal, December 2014

Spectral Deferred Correction Methods for Ordinary Differential Equations
journal, June 2000

The equations of motion for thermally driven, buoyant flows
journal, May 1978

Influence of Transport Models and Boundary Conditions on Flame Structure
book, January 1982

A waveform relaxation algorithm with overlapping splitting for reaction diffusion equations
journal, March 1999

A deferred correction coupling strategy for low Mach number flow with complex chemistry
journal, December 2012

Efficient time discretization for local discontinuous Galerkin methods
journal, July 2007

Time–space adaptive numerical methods for the simulation of combustion fronts
journal, June 2013

An Analytical Jacobian Approach to Sparse Reaction Kinetics for Computationally Efficient Combustion Modeling with Large Reaction Mechanisms
journal, July 2012

A high-order finite-volume method for conservation laws on locally refined grids
journal, January 2011

High-order multi-implicit spectral deferred correction methods for problems of reactive flow
journal, August 2003

The Derivation and Numerical Solution of the Equations for Zero Mach Number Combustion
journal, January 1985

A high-order low-Mach number AMR construction for chemically reacting flows
journal, December 2010

Parallel Time Integration with Multigrid
journal, January 2014

A Fourth-Order Accurate Finite-Volume Method with Structured Adaptive Mesh Refinement for Solving the Advection-Diffusion Equation
journal, January 2012

Numerical simulation of laminar reacting flows with complex chemistry
journal, December 2000

Toward an efficient parallel in time method for partial differential equations
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Modeling low mach number reacting flow with detailed chemistry and transport
journal, November 2005

A high-order numerical algorithm for DNS of low-Mach-number reactive flows with detailed chemistry and quasi-spectral accuracy
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On the spectral deferred correction of splitting methods for initial value problems
journal, January 2006

A Semi-implicit Numerical Scheme for Reacting Flow
journal, July 1998

A multi-level spectral deferred correction method
journal, August 2014

An Analytical Jacobian Approach to Sparse Reaction Kinetics for Computationally Efficient Combustion Modeling with Large Reaction Mechanisms
journal, July 2012

The Waveform Relaxation Method for Time-Domain Analysis of Large Scale Integrated Circuits
journal, July 1982

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journal, December 1964

A high-order finite-volume method for conservation laws on locally refined grids
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