Introducing Hugonions: Particle-like shocks that travel, interact, and annihilate

Abstract

This talk presents a novel computational method for 1-D wave processes in fluids, the applicability of which extends to strongly-nonlinear waves of arbitrary strength. A common approach to modeling waves of arbitrary strength in fluid dynamics is the Riemann solver of the Euler equations, requiring enormous computation time and resources. In this study, we expand upon our previous work [Lee et al., AIP Conf. Proc. 1685, 070011 (2015)], in which the propagation of a strongly-nonlinear wave is described by a collection of forward-traveling, particle-like shocks, dubbed “Hugonions” for their adherence to the Rankine-Hugoniot relations. To extend the applicability of Hugonions to compound waves, the Riemann solution of an arbitrary discontinuity is augmented to the defining characteristics of Hugonions. This way, Hugonions behave like particles, which travel, interact with each other, and annihilate if certain conditions are met. Because a computational mesh is not necessary (i.e., the method simply keeps track of Hugonions), and most importantly Hugonions will reduce in numbers following successive interactions, our computational method leads to a few orders-of-magnitude reduction in computation time compared to the existing Riemann solver-based schemes. Verification of the method against the Riemann solver is performed for a number of well-known benchmark problems.