Finite element methods for viscoelastic flow

Finite element methods to compute approximate solutions to flow problems involving the flows of viscoelastic fluids are discussed. The primary goals of such investigations are at least three: First, to evaluate the predictions of the many proposed constitutive theories for viscoelastic fluids. Second, to model measurement flows in various rheological measurement devices in order to quantify the deviation of the actual flow from the flow which must be presumed to interpret the measurement. Third, it is hoped that these methods will prove sufficiently robust to allow the simulation of idealized polymer processes with the aim of aiding in the design of such processes and the required apparatus. The focus of the current research of the author and a growing number of others is on two-dimensional, isothermal, steady flows of incompressible fluids. While these restrictions will be seen to be non-essential in theory, even the simplest calculations of non-visometric flow solutions will be seen to require a high degree of computational complexity in practice. Nevertheless, the current finite element procedures seem to show promise in the continuing endeavor to understand this challenging class of problems.