Time-Dependent Solutions to the 2D Kuramoto-Sivashinsky Equation via Pseudospectral Method on a Rectangular Domain
Abstract
This report provides an investigation into solving the Kuramoto-Sivashinsky equation in two spatial dimensions (2DKS) using a pseudo-spectral method on various rectangular periodic domains. The Kuramoto-Sivashinsky equation is a fluid dynamics model that exhibits dynamical features that are highly dependent on the length of the periodic domain. The goals of this report are to describe the mathematical problem; explain the details of the chosen numerical method; inspect solutions and dynamical features for varying grid sizes, step sizes, and domains; and summarize the findings.
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