12. Numerical experiments on “stability” of 2‐D quasi‐linear advection equation

Abstract

While still arguing whether a quasi‐linear equation has a “stability” problem in integration, comparative analyses are made by numerical experimentations using conservation with smoothing and non‐conservation schemes as well as a time‐moving treatment scheme proposed by the first author respectively. The results show that the solution seeking method of the quasi‐linear model should not be considered as a “stability” problem. The traditional well‐posed computational model needs to be improved. The Lorenz’s “butterfly effect” should be in nature a Richardson’s explosive increase in time evolution of moving fluid.

Citation

OuYang, S. and Lin, Y. (1998), "12. Numerical experiments on “stability” of 2‐D quasi‐linear advection equation", Kybernetes, Vol. 27 No. 6/7, pp. 742-763. https://doi.org/10.1108/03684929810223148