Numerical solution of a parabolic system in air pollution

TL;DR

This paper develops a numerical method for solving a nonlinear parabolic PDE system modeling air pollution, including domain transformation, analysis of well-posedness, and finite volume discretization, with computational results demonstrating effectiveness.

Contribution

It introduces a new approach combining domain transformation and weighted Sobolev space analysis for a degenerated parabolic system in air pollution modeling.

Findings

The scheme is stable and convergent.

Computational results validate the method.

The approach ensures positivity of solutions.

Abstract

An air pollution model is generally described by a system of PDEs on unbounded domain. Transformation of the independent variable is used to convert the problem for nonlinear air pollution on finite computational domain. We investigate the new, degenerated parabolic problem in Sobolev spaces with weights for well-posedness and positivity of the solution. Then we construct a fitted finite volume difference scheme. Some results from computations are presented.