ERENA: A fast and robust Jacobian-free integration method for ordinary differential equations of chemical kinetics

Morii, Youhi; Terashima, Hiroshi; Koshi, Mitsuo; Shimizu, Taro; Shima, Eiji

doi:10.1016/j.jcp.2016.06.022

Cited by 30 publications

(21 citation statements)

References 20 publications

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“…Free propagation of the two-dimensional premix hydrogen-air flame was simulated with the Navier-Stokes equations on a rectangular domain with a fixed length of −L/2 ≤ x ≤ L/2 and a fixed height of 0 ≤ y ≤ h, where L = 10.0 cm and h = 0.4 cm. Detailed descriptions on the computational method with relevant references [13][14][15][16][17][18][19][20] are given in the supplemental material. The premixed hydrogen-air mixtures at equivalence ratios of φ = 0.5 and 1.0 entered the domain from the left (x < 0) boundary at a uniform unburned gas temperature (T u = 300 K), pressure (p = 1 atm), and velocity (laminar flame velocity, S L ).…”

Section: Methodsmentioning

confidence: 99%

Diffusive-thermal effect on local chemical structures in premixed hydrogen–air flames

Matsugi

Terashima

2017

Combustion and Flame

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The diffusive-thermal effect plays an important role in the intrinsic instability of premixed flames. A two-dimensional direct numerical simulation of the propagation of premixed hydrogen-air flames was performed using a detailed chemical kinetics model. The cellular behavior of a lean hydrogen-air flame was analyzed on the basis of its chemical structure.The primary consequence of the diffusive-thermal effect was found to be a change in the buildup process of reactive intermediates by the chain reaction mechanism at the preheat zone. The resultant chemical structure at the main reaction zone can be explained by the local composition change of the gas flowing into the reaction zone from the preheat zone.

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Section: Methodsmentioning

confidence: 99%

Diffusive-thermal effect on local chemical structures in premixed hydrogen–air flames

Matsugi

Terashima

2017

Combustion and Flame

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“…There have also been significant advances in methods for computing solvation effects 36,37 . There have also been continuing improvements in methods for estimating rate and thermochemistry parameters (including solvation and pressure‐dependence of rate coefficients) 38‐44 and in algorithms for solving kinetic simulations 45‐53 . We suggest an efficient workflow combining all these software components to build predictive models in Figure 1.…”

Section: Technical Issuesmentioning

confidence: 99%

Moving from postdictive to predictive kinetics in reaction engineering

Green

2020

AIChE Journal

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“…Consequently, the method is promising for both stiff and nonstiff problems in under-resolved and resolved conditions. On the other hand, different from the famous ODEs solvers such as the implicit solver VODE [9], explicit CHEMEQ2 [36], scale-separated MTS/HMTS [19] and the recent quasi-steady-state approximation based ERENA [35], the present random ODEs solver basically takes the advantages of the Split Single Reaction Integrator (SSRI) [38] for chemical kinetics in both mass conservation and preserving the positivity of mass fractions. Using analytical solutions in SSRI or the approximate exact solution in our development, almost unconditional stability can be a promise for the present ODEs solver.…”

Section: Introductionmentioning

confidence: 99%

A split random time-stepping method for stiff and nonstiff detonation capturing

Wang

Pan

et al. 2019

Combustion and Flame

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In this paper, a new fractional step method is proposed for simulating stiff and nonstiff chemically reacting flows. In stiff cases, a well-known spurious numerical phenomenon, i.e. the incorrect propagation speed of discontinuities, may be produced by general fractional step methods due to the under-resolved discretization in both space and time. The previous random projection method has been successfully applied for stiff detonation capturing in under-resolved conditions. Not to randomly project the intermediate state into two presumed equilibrium states (completely burnt or unburnt) as in the random projection method, the present study is to randomly choose the time-dependent advance or stop of a reaction process. Each one-way reaction has been decoupled from the multi-reaction kinetics using operator splitting and the local smeared temperature due to numerical dissipation of shock-capturing schemes is compared with a random one within two limited temperatures corresponding to the advance and its inverse states, respectively, to control the random reaction. The random activation or deactivation in the reaction step is thus promising to correct the deterministic accumulative error of the propagation of discontinuities. Extensive numerical experiments, including model problems and realistic reacting flows in one and two dimensions, demonstrate this expectation as well as the effectiveness and robustness of the method. Meanwhile, for nonstiff problems when spatial and temporal resolutions are fine, the proposed random method recovers the results as general fractional step methods, owing to the increasing possibility of activation with diminishing randomness by adding a shift term.

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ERENA: A fast and robust Jacobian-free integration method for ordinary differential equations of chemical kinetics

Cited by 30 publications

References 20 publications

Diffusive-thermal effect on local chemical structures in premixed hydrogen–air flames

Diffusive-thermal effect on local chemical structures in premixed hydrogen–air flames

Moving from postdictive to predictive kinetics in reaction engineering

A split random time-stepping method for stiff and nonstiff detonation capturing

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