On postshock oscillations due to shock capturing schemes in unsteady flows (Q675177)

The issue of postshock oscillations generated by shock-capturing schemes is investigated. Although these oscillations are frequently small enough to be ignored, there are contexts such as shock-noise interaction where they might prove very intrusive. Numerical experiments on simple nonlinear \(2\times 2\) systems of conservation laws are found to refute some earlier conjectures on their behavior. The trajectories in phase space of a computed state passing through a captured shock suggest the underlying mechanism that creates these oscillations.