Moving mesh methods for Boussinesq equation

Abstract

The Boussinesq equation is a challenging problem both analytically and numerically. Owing to the complex dynamic development of small scales and the rapid loss of solution regularity, the Boussinesq equation pushes any numerical strategy to the limit. With uniform meshes, the amount of computational time is too large to enable us to obtain useful numerical approximations. Therefore, developing effective and robust moving mesh methods for these problems becomes necessary. In this work, we develop an efficient moving mesh algorithm for solving the two-dimensional Boussinesq equation. Our moving mesh algorithm is an extension