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

Abstract : The authors' purpose in writing this paper is to review some of their recent work in the calculation of optimal meshes for the solution of parabolic and elliptic partial differential equations (PDE). They first explain our strategies for the adaptive placement of mesh points. In addition, they make some speculation as to promising avenues for future research in mesh adaptation. Finally, they discuss examples of the application of adaptive gridding to problems of heat and mass transfer. They draw these examples from our work in combustion modeling. In obtaining numerical solutions of PDEs, the spatial derivatives are often approximated by discrete representations on a mesh network. The accuracy of any numerical solution depends in an important way on the relationship of the location of the mesh points to changes in the dependent variables. The authors objective is to investigate finite difference methods in which the mesh networks adapt themselves dynamically to obtain accurate solutions. Such methods represent an important advance in overcoming a major shortcoming of traditional fixed mesh methods which are often unable to resolve accurately steep fronts or sharp peaks.