A three-dimensional modified strongly implicit procedure for heat conduction
Mohamed Magdy Zedan, Gerry E. Schneider · AIAA Journal · 1983
The application of discretizatio n techniques frequently leads to a system of algebraic equations having a welldefined coefficient structure. A modified strongly implicit procedure for solving the system resulting from the modeling of heat conduction in three dimensions is presented in this work. The method is derived for a 19 point scheme with the more common 7 point scheme emerging as a special case of the procedure. In this way, the asymmetric influence of the additional terms in the LU matrix product is weakened. As a consequence, the method is less sensitive to the iteration parameter and mesh aspect ratio and, in addition, provides considerably more rapid convergence than does the strongly implicit procedure. The increased convergence is exhibited by a significant reduction in the computational cost. The characteristics of the method are examined through application to several model problems and application is made to a more complex three-dimensional problem. Comparisons with the SIP (strongly implicit) and ADI (alternating direction implicit) methods are provided.