Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Directional diffusion splitting method for advection-diffusion-reaction model

R. Drebotiy, H. Shynkarenko

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.

Directional diffusion splitting method for advection-diffusion-reaction model

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.

Paper Structure

This paper contains 9 sections, 24 equations, 1 figure.

Table of Contents

  1. Introduction
  2. Advection-diffusion-reaction problem
  3. Diffusion splitting
  4. Variational formulation and semi-discretization in time
  5. Semi-discretization splitting
  6. One-dimensional reduction of semi-discretization substeps
  7. Bilinear interpolation
  8. Numerical experiment
  9. Conclusions

Figures (1)

  • Figure 7.1: Approximate solution of problem with data \ref{['Data2D']}, obtained by the proposed method.