Nultitridiagonal-Natrix Algorithm for Coupled Heat Transfer in Porous Media: Stability Analysis and Computational Performance

摘要

Many phenomena present in nature are complex to study because of the strong natural coupling of their physical variables. For example, conservation equations in heat transfer problems are frequently coupled. Classical solution methods are based on numerical decoupling: cross terms at a given iteration step are calculated by using the values of the potentials previously calculated. This procedure increases the magnitude of source terms with respect to the main diagonal terms and requires very small time steps to ensure numerical stability. This article presents a generic multitridiagonal-matrix algorithm (MTDMA) to simultaneously solve the heat and mass transfer governing equations in porous media, with strong coupling among the dependent variables. It is shown that, in addition to considerably reducing the running time, it assures stable solutions for much higher time steps. To verify its performance, a combined heat and mass transfer problem through a porous medium is presented and comparisons with the TriDiagonal-Matrix Algorithm (TDMA) are made in terms of numerical stability and computer run time. The algorithm has shown itself to be a very effective solver for applications where two or more set of linear equations are strongly coupled.