A methodology for the integration of stiff chemical kinetics on GPUs
File(s)
Accepted version
Author(s)
Sewerin, F
Rigopoulos, S
Type
Journal Article
Abstract
Numerical schemes for reacting flows typically invoke the method of fractional steps in order to isolate the chemical kinetics model from diffusion/convection phenomena. Here, the reaction fractional step requires the solution of a collection of independent ODE systems which may be severely stiff. Recently, researchers have begun to explore the highly parallel structure of graphics processing units (GPUs) in order to accelerate integration schemes for these ODE systems. However, much of the existing work concentrates on explicit integration algorithms which may fall short in the presence of stiffness.
In this light, we have carefully reimplemented in OpenCL C the Fortran 77 program of the 3-stage/5th order implicit Runge–Kutta method Radau5 by Hairer and Wanner (1991) and tested it extensively in the context of a transient equilibrium scheme for the flamelet model. Our implementation can easily be integrated with any existing reactive flow software in order to solve the reaction fractional step on an OpenCL-enabled GPU. Moreover, it is suited for any Chemkin-format reaction mechanism with ≲200≲200 species without incurring a loss in occupancy and it reaches its limit speedup (which is largely independent of the mechanism size) at a small problem size (≈500 ODE systems). In view of memory constraints, we include an optimized scheme for splitting the ODE systems across several kernel invocations and overlapping the kernel execution with data transfers. An in-depth evaluation is based upon runtime measurements of the CPU and the GPU implementation on a user level and a high-end CPU/GPU for an increasing number of ODE systems, reduced and detailed reaction mechanisms and a range of time step sizes.
In this light, we have carefully reimplemented in OpenCL C the Fortran 77 program of the 3-stage/5th order implicit Runge–Kutta method Radau5 by Hairer and Wanner (1991) and tested it extensively in the context of a transient equilibrium scheme for the flamelet model. Our implementation can easily be integrated with any existing reactive flow software in order to solve the reaction fractional step on an OpenCL-enabled GPU. Moreover, it is suited for any Chemkin-format reaction mechanism with ≲200≲200 species without incurring a loss in occupancy and it reaches its limit speedup (which is largely independent of the mechanism size) at a small problem size (≈500 ODE systems). In view of memory constraints, we include an optimized scheme for splitting the ODE systems across several kernel invocations and overlapping the kernel execution with data transfers. An in-depth evaluation is based upon runtime measurements of the CPU and the GPU implementation on a user level and a high-end CPU/GPU for an increasing number of ODE systems, reduced and detailed reaction mechanisms and a range of time step sizes.
Date Issued
2015-04-01
Date Acceptance
2014-11-03
Citation
Combustion and Flame, 2015, 162 (4), pp.1375-1394
ISSN
0010-2180
Publisher
Elsevier
Start Page
1375
End Page
1394
Journal / Book Title
Combustion and Flame
Volume
162
Issue
4
Copyright Statement
© 2014 The Combustion Institute.Copyright. NOTICE: this is the author’s version of a work that was accepted for publication in Combustion and Flame. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Combustion and Flame, 2 December 2014 DOI 10.1016/j.combustflame.2014.11.003
Identifier
https://www.sciencedirect.com/science/article/pii/S0010218014003459?via%3Dihub
Subjects
Science & Technology
Physical Sciences
Technology
Thermodynamics
Energy & Fuels
Engineering, Multidisciplinary
Engineering, Chemical
Engineering, Mechanical
Engineering
GPU
Chemical kinetics
Implicit Runge-Kutta methods
ATMOSPHERIC CHEMISTRY PROBLEMS
ODE SOLVERS
Energy
0902 Automotive Engineering
0904 Chemical Engineering
0913 Mechanical Engineering
Publication Status
Published
Date Publish Online
2014-12-02