An evaluation of gradient term modification methods for linearized euler equations

Simulation of sound propagation by solving linearized governing equations using time-domain methods can produce numerical instabilities in the solutions with sheared mean-flow. Several methods, including flow decomposition via source filtering, gradient term filtering, and gradient term suppression have been developed to suppress the on-set of numerical instabilities. Each method modified the governing equations differently, which may change the accuracy and physics of sound propagation. In this work, some of the existing methodologies are reviewed, and three new formulations are proposed. Several numerical tests with different background mean-flow are conducted to evaluate the modelling accuracy, and computation cost, by each method. The proposed new methods are shown offering improvement over the existing methods.