Time Advancement Schemes and Numerical Convective and Absolute Instabilities :

While a very large amount of attention has been paid to increase the accuracy of spatial discretization schemes, in comparison very little work has been reported for time-advancement techniques. In actual computations, standard time-advancement strategies are used. For example, apart from first order accurate Euler time-integration strategy, multi-time level strategies like Leap-frog, Adams-Bashforth time-integration schemes are used with increasing frequency. Additionally, multi-stage Runge-Kutta methods are also used. We have used our analysis methods for stability, DRP properties of various schemes in the following work. What emerged out of this can be startling for not only beginners, but also for well-experienced researchers! For example, it has been shown clearly that Adams-Bashforth scheme that has been and continues to be used for many DNS work actually produces spurious results and SHOULD NEVER BE USED. It is equally true for computational acoustics also (Go to the link on Jets, Acoustics and Instabilities). In the following paper, this is graphically demonstrated.

The work on numerical convective and absolute instabilities are in progress and will be announced very soon!