Data-assimilated computational fluid dynamics modeling of convection-diffusion-reaction problems

This study focuses on the development and application of a data-assimilated multi-algorithm which combines a fourth-order finite-volume computational fluid dynamics (CFD) algorithm and the ensemble Kalman filter (EnKF) data assimilation algorithm for solving the problems involving important physics relevant to wave convection, molecular diffusion, and reaction of interest to engineering science. This data-assimilated CFD algorithm is applied to estimate an uncertain model parameter. By restricting the problems to one- and two-dimensional spatial space, this study allows us to develop a greater understanding of the integrated algorithm without the complexity or computational cost associated with three dimensions. Although scalar partial differential equations are used, fundamental issues in the algorithm development and application of EnKF to the physical processes occurring in a domain on engineering scales are sufficiently illuminated. Results of the one-dimensional convection-diffusion-reaction problem and the two-dimensional flame propagation demonstrate the validity of the data-assimilated CFD modeling system.