The iterative solution of fully implicit discretizations of three-dimensional transport models
The authors consider systems of spatially three-dimensional weakly coupled advection-diffusion-reaction equations. By spatial difference-discretization (of three-point type in each spatial variable with special upwind modification for the advection terms) they obtain a system of ordinary differential equations for which they discuss in detail a few fully implicit methods of Runge-Kutta type. They investigate some iterative methods of solving the systems of (nonlinear) equations arising at each new time level, with particular emphasis on advantages possible by use of parallel vector computers. Furthermore, they discuss questions of stability of their methods and conclude their paper by displaying results of numerical case studies.
scientific article; zbMATH DE number 1088832
scientific article