Adaptive gridding for finite difference solutions to heat and mass transfer problems

The present investigation is concerned with a review of some recent work regarding the calculation of optimal meshes for the solution of parabolic and elliptic partial differential equations (PDE). The solutions to the physical problems presented cover a range of flow and chemical systems. In all of the problems there is the common simplification of uncoupling the fluid mechanics from the heat and mass transfer. Adaptive grid methods are considered, taking into account the positive weight function concept, steady-state problems and the variable node method, time-dependent problems, coordinate transformation methods, and linear algebra considerations. Some example problems are discussed, giving attention to steady premixed flames, the two-dimensional elliptic boundary-value problem, unsteady two-dimensional flame propgation, and a coordinate transformation method.