An explicit time integration method for Boussinesq approximation

Abstract This paper presents a novel approach to the discretization of the Boussinesq equation using finite elements, coupled with an explicit pressure correction scheme. The entire numerical scheme is formulated exclusively in terms of matrix‐vector products, enabling a highly efficient numerical solution. The key advantage of this approach lies in its suitability for fast computations and seamless parallelization on graphics processing units (GPUs). We present the numerical scheme and discuss different computational examples.