Finite element simulation of flows of fluids with integral constitutive equations

Finite element procedures to compute solutions to steady flow problems with ‘memory fluids’ have been developed. While many aspects of these methods are still under development, they have reached the stage at which they can be implemented in general‐purpose nonlinear fluid mechanics codes which use the penalty form of the ‘v‐p’ formulation. The key to the success of such methods is the use of a very special element which allows virtually exact determination of the streamlines, and large‐strain elastic deformation tensors of the motion implied by the velocity field, which are required by the constitutive theories in question. This paper describes the constitutive equations and the numerical treatment of them which can be used to compute steady, two‐dimensional flow solutions. Some new results concerning hole pressures in plane flows over transverse slots are presented.