Numerical simulation of the wave (shock profile) propagation of the Kuramoto-Sivanshinky equation using an adaptive mesh method

Abstract

In this dissertation we solve the Kuramoto-Sivanshinsky equation numerically using an adaptive mesh method. Discretization in time is done using Crank- Nicolson with septic Hermite collocation method applied in space on an adaptive mesh. The adaptive mesh is a solution of moving mesh partial differential equations derived from the principle of equidistribution. A rezoning approach which works with a decoupled solution procedure is then used to develop a matlab code to produce the numerical results. The method is evaluated for effectiveness and computational efficiency with the most current best method available in the literature.