A study of limiter functions for high order formulations for compressible flows

Abstract

This research project aims to study, develop and improve the formulation of limiter functions used in the construction of high-order numerical schemes for the discrete solution of the gas dynamic equations. High-order schemes, that is, schemes that have third order of spatial accuracy or higher, can have many attractive properties for simulating natural phenomena that require high spatial resolution. In addition, they can be developed to have well controlled amounts of artificial dissipation, which contributes to their ability to solve flow structures of different energy scales. Currently, a strand of scientific thought that advocates the use of high-order schemes for the solution of general flow cases is also gaining momentum due to its potential to drastically reduce the number of cells that a computational mesh is required to have for a given level of accuracy. The formulation of this type of scheme, however, requires the use of limiter functions in order to avoid problems of numerical nature that appear during the process of solving the equations of interest. In this context, the present project aims to address exactly the study of limiters applied to high-order schemes, with emphasis on three different work fronts. These comprise the implementation and validation of high-order methods, the improvement of existing limiter functions, and the appropriate documentation of these formulations. The obtained results will be compared to those available in the literature in order to verify the correctness of the implementation and the effectiveness of the proposed modifications. The conclusions and main contributions from the current project will be documented and published in scientific journals. (AU)