ALGEBRAIC SCHUR COMPLEMENT APPROACH FOR A NON LINEAR 2D ADVECTION DIFFUSION EQUATION

Abstract

This work deals with a domain decomposition approach for non stationary non linear advection diffusion equation. The domain of calculation is decomposed into q≥2 non-overlapping sub-domains. On each sub-domain the linear part of the equation is descretized using implicit finite volumes scheme and the non linear advection term is integrated explicitly into the scheme. As nonoverlapping domain decomposition, we propose the Schur Complement (SC) Method. The proposed approach is applied for solving the local boundary sub-problems. The numerical experiments applied to Burgers equation show the interest of the method compared to the global calculation. The proposed algorithm has both the properties of stability and efficiency. It can be applied to more general non linear PDEs and can be adapted to different FV schemes.