Performance of Iterative Methods in Steady-State Diffusion Problems with Discontinuous Properties

Abstract

The development of numerical methods for the simulation of multiphase flows is a topic of intense research due to its numerous industrial and environmental applications. This work studies the effect of the presence of discontinuities in steady-state diffusion problems, particularly in the numerical resolution of algebraic systems resulting from the discretization of the Laplacian operator. Two-dimensional cases are considered, involving different combinations of boundary conditions and spatial distributions of diffusivity, including abrupt jumps between regions of the domain. The study focuses on analyzing the numerical stability and convergence of iterative methods based on Krylov subspaces, evaluating their performance in the presence of discontinuities in the diffusion coefficients. The results make it possible to identify the advantages and limitations of each approach, offering both theoretical and practical tools to improve the simulation of flows with discontinuous physical properties.