Directional diffusion splitting method for advection-diffusion-reaction model

TL;DR

This paper introduces a splitting method for advection-diffusion-reaction equations that reduces 2D problems to 1D problems, enabling parallel computation and flexible discretization approaches.

Contribution

The paper presents a novel splitting and interpolation scheme for efficiently solving 2D advection-diffusion-reaction problems by reducing them to 1D problems, enhancing parallelization.

Findings

Method allows large parallelization potential.

Compatible with finite element, finite volume, and finite difference methods.

Effective for both stationary and non-stationary problems.

Abstract

We propose certain approach of solving two-dimensional non-stationary and stationary advection-diffusion-reaction boundary value problems through their reduction to the set of corresponding one-dimensional problems. This method leverages special splitting and interpolation schemes, providing iterative algorithm with a large degree of parallelization possibilities. We combine that algorithm with the finite element method to solve obtained one-dimensional problems, but in fact, it can be combined also with other discretization methods, like finite volume or finite difference methods.