Date of this Version
Center for Turbulence Research Annual Research Briefs 2008
In the modeling of unsteady reactive problems, the interaction of turbulence with finiterate chemistry introduces a wide range of space and time scales, leading to additional numerical difficulties. A main difficulty stems from the fact that most numerical algorithms used in reacting flows were originally designed to solve non-reacting fluids. As a result, spatial stiffness due to reacting source terms and turbulence/chemistry interaction are major stumbling blocks to numerical algorithm development. One of the important numerical issues is the proper numerical treatment of a system of highly coupled stiff non-linear source terms, which will result in possible spurious steady state numerical solutions (see Lafon & Yee 1996). It was shown in LeVeque (1998) that a well-balanced scheme, which can preserve the steady state solution exactly, may solve this spurious numerical behavior. The goal of this work is to consider a simple 1-D model with one temperature and three species as studied by Gnoffo, Gupta & Shinn (1989) and to study the well-balanced property of various popular linear and non-linear numerical schemes in the literature. The different behaviors of those numerical schemes in preserving steady states and in resolving small perturbations of such states will be shown.