A Second Order Projection-based Time-splitting Scheme for Computing Chemically Reacting Flows

The computation of velocity eld, pressure, temperature distribution and mass fraction functions that are coupled in a nonlinear PDE describing chemically reacting ows is a challenging task since computational resources are limited. Implicit solution ansatzes of the coupled quantities require a vast amount of storage capacities that is lacking on normal workstations to resolve complex ow structures. The present paper proposes and analyzes a 2nd order time-splitting scheme that leads to a signiicant reduction of computational work and is appropriate to parallelization strategies in solving approximates in each iteration step. Optimal convergence results justify the accuracy of the splitting approach. 1 Introduction. The study of chemically reacting uid ows is the subject of many engineering sciences: the observation and prediction of future ow phenomena is basic for people working in these areas to optimize involved reaction processes. For example, complex ow structures arising in chemical vapor deposition (CVD) reactors need to be understood to design an optimized apparatus that ensures an improved manufacturing of semiconductors. In typical construction processes, there can be more than thirty important chemical species undergoing more than fty reactions, see 1, 6, 9, 14]. Computer modeling of these complex ows can greatly aid in the understanding, design and optimization of engineering procedures. Moreover, it is particularly attractive for applications where involved chemicals are expensive and/or toxic, like e.g. Arsine. However, the numerical modeling of ongoing relevant processes is a challenging task for existing computer resources, since standard discretization strategies lead to very large (algebraic) nonlinear problems that can only be solved on huge parallel machines, see 14]. This motivates to develop new, less expensive algorithms that can be implemented even on workstations, and give reasonably accurate solutions. A rst step in this direction has been made in 13], where a rst order time-splitting scheme has been proposed and analyzed. This scheme is based on the projection method of Chorin, see 2, 3], to reduce the computational eeort. In particular, this scheme is appropriate for parallelization strategies, since the computation of iterates will be accomplished in a decoupled manner. | In the present work, we focus on a higher order projection-based time-splitting scheme that inherits the advantages of the rst order projection-based time-splitting scheme of 13]. We start with the presentation of the system of equations that describes the dynamics of the chemically reacting ow. They are derived from the the conservation principles for impulse, mass and …