TY - JOUR
T1 - ERENA
T2 - A fast and robust Jacobian-free integration method for ordinary differential equations of chemical kinetics
AU - Morii, Youhi
AU - Terashima, Hiroshi
AU - Koshi, Mitsuo
AU - Shimizu, Taro
AU - Shima, Eiji
N1 - Funding Information:
We are grateful to Dr. Tetsu R. Satoh (NHN Japan Corp.) for advice and discussions on the integrators with conservation laws. This work was partially supported by JSPS KAKENHI Grant Numbers 26390128 and 15H05510.
Publisher Copyright:
© 2016 Elsevier Inc.
PY - 2016/10/1
Y1 - 2016/10/1
N2 - We herein propose a fast and robust Jacobian-free time integration method named as the extended robustness-enhanced numerical algorithm (ERENA) to treat the stiff ordinary differential equations (ODEs) of chemical kinetics. The formulation of ERENA is based on an exact solution of a quasi-steady-state approximation that is optimized to preserve the mass conservation law through use of a Lagrange multiplier method. ERENA exhibits higher accuracy and faster performance in homogeneous ignition simulations compared to existing popular explicit and implicit methods for stiff ODEs such as VODE, MTS, and CHEMEQ2. We investigate the effects of user-specified threshold values in ERENA, to provide trade-off information between the accuracy and the computational cost.
AB - We herein propose a fast and robust Jacobian-free time integration method named as the extended robustness-enhanced numerical algorithm (ERENA) to treat the stiff ordinary differential equations (ODEs) of chemical kinetics. The formulation of ERENA is based on an exact solution of a quasi-steady-state approximation that is optimized to preserve the mass conservation law through use of a Lagrange multiplier method. ERENA exhibits higher accuracy and faster performance in homogeneous ignition simulations compared to existing popular explicit and implicit methods for stiff ODEs such as VODE, MTS, and CHEMEQ2. We investigate the effects of user-specified threshold values in ERENA, to provide trade-off information between the accuracy and the computational cost.
KW - Chemical reaction equations
KW - Computational fluid dynamics
KW - Jacobian-free integration method
KW - Ordinary differential equations
KW - Stiffness
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U2 - 10.1016/j.jcp.2016.06.022
DO - 10.1016/j.jcp.2016.06.022
M3 - Article
AN - SCOPUS:84979887606
SN - 0021-9991
VL - 322
SP - 547
EP - 558
JO - Journal of Computational Physics
JF - Journal of Computational Physics
ER -