Simulation of Microstructured Fluids in Production and Biomedical Engineering
Many incompressible flows of engineering interest involve fluids that are governed by complex constitutive relations. For viscoelastic fluids in particular, the advective nature of the constitutive equation requires numerical stabilization. Moreover, the use of three distinct variable fields means that two separate compatibility conditions must be satisfied. A stabilized stress-velocity-pressure formulation of Galerkin/Least-Squares type can provide stability at high Weissenberg numbers, and circumvents the compatibility condition on the velocity and stress interpolations. Further improvement can be achieved using a reformulation based on the logarithm of the conformation tensor. Development of such numerical methods is motivated by challenging applications in production technology, including shape optimization of plastics extrusion dies, and in bioengineering, including blood-handling devices such as heart pumps.