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Integration Strategies for Efficient Multizone Chemical Kinetics
Matthew J. McNenly, Mark A. Havstad, Salvador M. Aceves and William J. Pitz
Lawrence Livermore National Laboratory
Copyright 2010 SAE International
Three integration strategies are developed and tested for the stiff, ordinary differential equation (ODE)
integrators used to solve the fully coupled multizone chemical kinetics model. Two of the strategies tested are
found to provide more than an order of magnitude of improvement over the original, basic level of usage for the
stiff ODE solver. One of the faster strategies uses a decoupled, or segregated, multizone model to generate an
approximate Jacobian. This approach yields a 35-fold reduction in the computational cost for a 20 zone model.
Using the same approximate Jacobian as a preconditioner for an iterative Krylov-type linear system solver, the
second improved strategy achieves a 75-fold reduction in the computational cost for a 20 zone model. The
faster strategies achieve their cost savings with no significant loss of accuracy. The pressure, temperature and
major species mass fractions agree with the solution from the original integration approach to within six
significant digits; and the radical mass fractions agree with the original solution to within four significant digits.
The faster strategies effectively change the cost scaling of the multizone model from cubic to quadratic, with
respect to the number of zones. As a consequence of the improved scaling, the 40 zone model offers more than
a 250-fold cost savings over the basic calculation.
Predicting the performance of an internal combustion engine solely through simulation is one of the most
challenging goals of computational science. The large span of length and time scales is simply too great at this
time to completely resolve the physical phenomena in the multi-dimensional, turbulent, chemically reacting
flow present in-cylinder. Ambitious efforts are underway to resolve the smallest turbulent length scales and
chemical time scales in a laboratory-scale flame using direct numerical simulation (DNS) and detailed chemical
kinetics methods on petascale computing architecture . Without significant algorithmic improvements , the
necessary computational resources for simulating this level of detail will not appear in the desktop computer of
an engine designer in industry for at least another two decades given current trends in hardware development.
In the interim, the practice of simplifying the physical models for complex in-cylinder flows to the level of
available computational resources will continue. Such practices commonly depend on one or more of the
following: reduced dimensionality and geometric detail, reduced chemical kinetic mechanisms, simplified
turbulent transport models, and simplified bulk fluid dynamics. The multizone model is an example of the last
type of simplification.
The multizone model approximates the in-cylinder flow as a series of coupled, well-mixed reactors. The model
does not consider the fluid velocity in the cylinder; only the conservation laws for mass, energy and species are
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Chen, Bin; Lin, Jung-Fu; Chen, Jiuhua; Zhang, Hengzhong & Zeng, Qiaoshi. Synchrotron-based high-pressure research in materials science, article, June 1, 2016; (digital.library.unt.edu/ark:/67531/metadc929483/m1/3/: accessed January 23, 2019), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.