Half boundary method for two-dimensional steady-state nonlinear convection-diffusion equations

Abstract

In this research, half-boundary method (HBM) is developed for nonlinear convection-diffusion equations (CDEs) which play an important role in applied mathematics and physics. The HBM is based on the variable relationship between the nodes inside the domain and the nodes on half of the boundaries, making it ideal for reducing the maximum order of matrix and calculation memory storage. Besides, the HBM can solve discontinuous problems directly without adding continuity conditions due to the use of the mixed variables. The effectiveness and accuracy of the proposed algorithm are investigated mainly for the two-dimensional(2D) steady-state Burgers’ equation, the material nonlinear 2D CDEs and the system of 2D Burgers’ equations. The results show the excellent performance of the HBM in simulating flow and heat transfer, especially for convection domination.