Analysis of a new time filter algorithm for the convection problem of superposition of incompressible flow and porous media flow

Abstract

In this paper, an efficient numerical algorithm is proposed to solve the convection problem in the superposition of incompressible flow and porous media flow. The displayed numerical method is a first-order $\gamma$-scheme of linear multi-step methods plus time filter algorithm(LMTF), and can effectively increase the convergence order from the first order to the second order with almost no increasing in computation, and easy to implement in program. The stability and error estimation of the decoupled LMTF algorithm are analyzed theoretically. Meanwhile, three numerical experiments are given to illustrate the theoretical results and to show that the second-order convergence, high efficiency and effectiveness of the algorithm. The results demonstrate that the algorithm effectively simulates the geothermal system.