Numerical solving of parabolic Cauchy problems by reduction on bounded domain and application to solute water pollution
Slavi G. Georgiev, Lubin G. Vulkov · AIP conference proceedings · 2022
Many problems of contaminant transport in porous media are described by parabolic equations on unbounded domains and must be solved numerically. For computation of such kind of problems, it is necessary to reduce them to a bounded domain and the question of appropriate boundary conditions arises. In this paper, using the Green function method (often called method of fundamental solutions), we propose a procedure for construction of efficient boundary conditions on arbitrary bounded domains for 1D and 2D parabolic Cauchy problems. The method is tested on a model of solute water pollution.