National Aeronautics and Space Administration


Date of this Version



Center for Turbulence Research Annual Research Briefs 2008


U.S. government work


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.