Approaching a solution for richards-2D equation by finite volumes method with the aid of Picard-Krylov algorithms

Abstract

This research evaluates the Richards equation through the method of finite volumes in two dimensions making use of the Picard’s method with the most computational efficiency. To do so it were used iterative resolution techniques of linear systems based in the space of Krylov with preconditioners matrices, together with the help of the numerical library Portable, Extensible Toolkit for Scientific Computation (PETSc). The results show that when solving the Richards equation making use of the method PICARD-KRYLOV, it does not matter the model of soil in evaluation, the best combination to the resolution of the linear systems are KSPBCGS PCSOR. However, when making use of the equations of van Genuchten (1980) we choose the combination KSPCG PCSOR. Lastly, the study makes contributions to the field of mathematics, specifically to the methods of applied numbers in the resolution of flow problems in the unsaturated porous media. In particular the proposed modeling might also help in the understanding of the recharge of groundwater aquifers.

Keywords

• Fluidodinâmica computacional. Equação de Richards. Método dos volumes finitos. Picard-Krylov. Meios porosos não saturados