Time integration of three-dimensional numerical transport models
Several variants of the method of lines for the numerical solution of a 3D diffusion-convection equation are considered and compared, the equation being possibly nonlinear through a fall velocity of suspended material. The domain is extended to one of rectangular shape by adding dummy points. The specific methods surveyed are special second-order Runge-Kutta (necessitating stringend time step restrictions), locally one-dimensional methods (unconditionally stable, easily to vectorize and parallelize, but not accurate enough), operator splitting methods (probably the most often used type in practical applications), point and line hopscotch methods (implicit along vertical lines), and, finally, predictor-corrector methods combined with splitting. The numerical comparison includes storage needed, number of tridiagonal systems to be solved per time step, ease of vectorization and parallelization. Regretfully enough neither predictor-corrector nor operator splitting methods are considered in this part of the paper. Based on their experiments on a Cray YMP4, the authors conclude that line hopscotch is most efficient for the studied problem.
scientific article; zbMATH DE number 721002
scientific article