Approximate Lie Group Analysis of a Model Advection Equation on an Unstructured Grid

Abstract

A technique of ``approximate group analysis'' recently developed by Baikov, Gazizov and Ibragimov is applied to a differential approximation (otherwise referred to as an equivalent differential equation) corresponding to the finite difference approximation of a nonlinear advection equation on unstructured grid. We determine which groups from the infinite variety of groups admitted by a nonlinear advection equation ``survive'' the discretization. The situations arising for different choices of an arbitrary function (local speed of propagation) are also studied.