A comparative study of the performance of high resolution advection schemes in the context of data assimilation
S. Akella, I.Michael Navon
High resolution advection schemes have been developed and studied to model propagation of flows involving sharp fronts and shocks. So far the impact of these schemes in the framework of inverse problem solution has been studied only in the context of linear models. A detailed study of the impact of various slope limiters and the piecewise parabolic method (PPM) on data assimilation is the subject of this work, using the nonlinear viscous Burgers equation as the mathematical model paradigm. The monotonicity preserving limiter of van Leer is shown to be the most efficient in terms of both faster minimization convergence and ability to recover the initial conditions. The results obtained in this work may point out to suitability of these advection schemes for data assimilation in more complex higher dimensional models.