Diffusion Source Term Research Articles

Monotonicity-preserving splitting schemes for solving balance laws

In this paper, some monotonicity-preserving (MP) and positivity-preserving (PP) splitting methods for solving the balance laws of the reaction and diffusion source terms are investigated. To capture the solution with high accuracy and resolution, the original equation with reaction source termis separated through the splitting method into two sub-problems including the homogeneous conservation law and a simple ordinary differential equation (ODE). The resulting splitting methods preserve monotonicity and positivity property for a normal CFL condition. A trenchant numerical analysis made it clear that the computing time of the proposed methods decreases when the so-called MP process for the homogeneous conservation law is imposed. Moreover, the proposed methods are successful in recapturing the solution of the problem with high-resolution in the case of both smooth and non-smooth initial profiles. To show the efficiency of proposed methods and to verify the order of convergence and capability of these methods, several numerical experiments are performed through some prototype examples.

Identification of premixed flame propagation modes using chemical explosive mode analysis

A criterion based on chemical explosive mode analysis (CEMA) is proposed to identify different local combustion modes, such as auto-ignition, diffusion-assisted ignition, and local extinction in laminar and turbulent premixed flames. The criterion is employed to distinguish between two different propagation modes of one-dimensional (1-D) freely propagating premixed flames, that is the canonical deflagration wave controlled by heat and species back-diffusion, which features a unique flame speed, and the auto-ignition controlled reaction front propagation, which may feature an arbitrary propagation speed. In the CEMA based diagnostic, the local chemistry and diffusion source terms are projected to the chemical explosive mode (CEM), such that the roles of diffusion and chemistry in the CEM can be quantified and compared for identification of the flame propagation mode. The new criterion is further applied to analyze two-dimensional (2-D) DNS datasets of homogeneous charge compression ignition (HCCI) combustion of n-heptane/air with different levels of thermal stratification. Both flame propagation modes are observed and contribute significantly to the overall flame burning in the case with a high level of thermal stratification, while the flame propagation is found dominated by the auto-ignition mode in the case with a low level of thermal stratification, which agrees with the finding in previous studies.