Adaptive Grid Method for Problems in Fluid Mechanics and Heat Transfer

Abstract

A new method for generating adaptive grids for time-dependent and steady problems in multidimensional fluid mechanics and heat transfer has been developed. The method can be used with many existing grid generation schemes or can be used as an independent grid generation technique. The present adaptive method is based upon the placement of grid points in proportion to the gradients that appear in the dependent variable. The multidimensional results presented in the paper are for the unsteady heat conduction equation and have included steep gradients due to geometry and unsteady boundary conditions. The method has performed in an impressive fashion, although there is a need to control grid skewness better. A study of one-dimensional problems associated with combustion and cell Reynolds number has demonstrated the technique's accuracy and versitility. The paper also discusses the relationship of the method to other grid generation techniques, as well as extensions of the new method.