Augmented proper orthogonal decomposition for problems with moving discontinuities

A method is proposed to augment the proper orthogonal decomposition basis functions with discontinuity modes to better capture moving discontinuities in reduced-order models. Moving discontinuities can be shocks in unsteady gas flows or bubbles in multiphase flow. The method is shown to work for a simple test problem using the first-order wave equation. A method for detecting discontinuities numerically is developed using mathematical morphology. This method is shown to properly identify the edges of bubbles in multiphase flow.