A full discretization of a time-dependent closed-loop geothermal system by a two-grid scheme

Abstract

In this paper, a two-grid scheme for a time-dependent closed-loop geothermal system is proposed. The scheme solves a coupled partial differential equation model for this system on a coarse mesh with a mesh size of H and a decoupled problem on a fine mesh with a mesh size of h. In theoretical analysis, the stability and convergence of the two-grid scheme are proven. It is shown that when the coarse and fine mesh sizes satisfy h=H2, the accuracy of this scheme is almost the same as that of solving the nonlinear system directly on the fine mesh. At the same time, it saves a lot of calculation time and improves the efficiency of solving the coupled system. The effectiveness of the presented scheme is verified by numerical experiments.