A semi-implicit numerical scheme for reacting flow. 1: Stiff chemistry

Journal Article · Wed Jul 01 04:00:00 EDT 1998 · Journal of Computational Physics

DOI:https://doi.org/10.1006/jcph.1997.5856· OSTI ID:638434

Najim, H N; Wyckoff, P S ^[1]; Knio, O M ^[2]

---

1. Sandia National Labs., Livermore, CA (United States)
2. Johns Hopkins Univ., Baltimore, MD (United States). Dept. of Mechanical Engineering

An additive semi-implicit projection scheme for the simulation of unsteady combustion in two dimensions is constructed. The scheme relies on a zero-Mach number formulation of the compressible conservation equations with detailed chemistry. The governing equations are discretized in space using second-order differences and integrated in time using a semi-implicit approach. Time integration of the evolution equations for species mass fraction, thermodynamic pressure, and density is performed using a semi-implicit, nonsplit scheme that combines a second-order predictor-corrector treatment of convection and diffusion terms, and a still integrator for the reaction source terms. Meanwhile, the momentum equations are integrated using a second-order projection scheme. The projection scheme is based on a predictor-corrector approach that couples the evolution of the velocity and density fields in order to stabilize computations of reacting flows with large density variations. A pressure Poisson equation is inverted following both the predictor and corrector steps using a fast solver. The advantages of the stiff integration of reaction source terms are analyzed by comparing the performance of the scheme to that of a predictor-corrector scheme in which reaction and diffusion are integrated in a similar nonstiff fashion. The comparison is based on both one-dimensional (ID) unsteady tests of a premixed methane-air flame, and unsteady two-dimensional tests of the same flame interacting with a counterrotating vortex pair. In both cases, the GRImech1.2 reaction mechanism with 32 species and 177 elementary reactions is used.

• Sponsoring Organization: USDOE, Washington, DC (United States)
• OSTI ID: 638434
• Journal Information: Journal of Computational Physics, Journal Name: Journal of Computational Physics Journal Issue: 2 Vol. 143; ISSN JCTPAH; ISSN 0021-9991
• Country of Publication: United States
• Language: English

Related Subjects

40 CHEMISTRY
COMBUSTION KINETICS
COMPARATIVE EVALUATIONS
FLAMES
NUMERICAL SOLUTION
PERFORMANCE
PROJECTION OPERATORS
UNSTEADY FLOW