| The purpose of this study is to explore some of the possibilities for improving upon numerical methods used for the computation of inviscid, compressible flows with finite-rate chemistry. This work is divided into two parts: The first one is the derivation of a well designed eigensystem for the Euler equations for flows in chemical nonequilibrium. This eigensystem does not contain possible indefinite mass species source terms and can be used in developing high-order, spatially accurate, flux-difference schemes. The second part compares fully-implicit and semi-implicit time-integration methods in order to determine the most efficient procedure for solving chemically reacting flows. The semi-implicit method treats the chemistry source terms, which are responsible for stiffness in the system, implicitly, while all other terms are treated explicitly. This method allows for the evolution of chemistry phenomena and flow dynamics to proceed at comparable time scales and does not require the inversion of large block matrices, as in the case of the fully-implicit algorithm.;A timing study was conducted in order to quantify the computational efficiency of the schemes for a set of test cases. The fully-implicit method proved to be substantially faster for low temperature flows. The two schemes were competitive for higher temperature flows, where chemistry tends to dominate the flow, and the implicit treatment of the chemistry source terms becomes the most important factor for convergence.;A computational time saving procedure was implemented by updating the values of the flux Jacobian matrices only every ten iterations for the fully-implicit method. Computational time saves was observed without the loss of accuracy. A freezing of chemical Jacobians was also investigated. While the chemical Jacobians needed to be calculated every two iterations, the decrease in computational time was significant.;Overall, the modified two-pass method provided the best computational method for solving finite-rate chemically reacting flows. The scheme is very efficient for perfect gas and low temperature flows, and with the addition of flux reuse and chemical Jacobian reuse significant time savings can be obtained over the entire temperature regime studied. |
