The result of these differing paths is that many numerical analysts spend their effort constructing elegant solvers for simple models of little practical use, while computational scientists study highly-realistic systems but “solve” them using ad hoc methods with questionable accuracy and stability. While early simulation approaches could be well-understood using standard mathematical techniques, applied mathematics has unfortunately not kept up with the fast pace of scientific simulation development.
During this time, the complexity of scientific simulations has evolved from relatively simplistic calculations involving only a handful of basic equations, to massive models that combine vast arrays of physical processes. In recent decades computation has rapidly assumed its role alongside theory and experiment as the third pillar of the scientific method.
