An efficient solver for the algebraic equations resulting from discretization of the governing equations for fluid flow and heat transfer

An efficient solver for the algebraic equations resulting from the discretization of governing equations of fluid flow and heat transfer problems is proposed. This method is based on the concept of the Gauss-Seidel point iteration method, but modifications are made in that not only the dependent variable itself but also the coefficients and the source term of the algebraic equations are updated in timely manner in the iterative solution process. Comparisons are conducted with the conventional alternating-direction implicit+tridiagonal matrix algorithm (ADI+TDMA) solution method, and numerical results show that the proposed solution method is very effective, with an average saving of computational time of about 50%.