Directional diffusion splitting method for advection-diffusion-reaction model

2024/11/17 by Drebotiy, R., Shynkarenko, H.
#FOS: Mathematics #Numerical Analysis (math.NA)

paper · doi:10.48550/arxiv.2411.11041

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.

Related

• Convergence of the directional diffusion splitting method
• A domain splitting strategy for solving PDEs
• A second order directional split exponential integrator for systems of advection–diffusion–reaction equations
• A second order directional split exponential integrator for systems of advection--diffusion--reaction equations
• An initial-corrected splitting approach for convection-diffusion-reaction problems