The investigator proposes to develop novel computational schemes for the study of flows of viscoelastic liquids in three spatial dimensions. A new formulation that transforms the constitutive equation for viscoelastic stress into a conservative form is proposed. This new formulation is amenable to the use of a state-of-the-art adaptive mesh refinement method on octree finite-volume meshes. The goal of this proposal is to develop discretization and solution algorithms that are designed to not only maintain the higher order accuracy, but also guarantee that the discrete set of algebraic equations possess particular characteristics that are contained in the differential form of the constitutive equations. Different constitutive models for viscoelastic liquids are incorporated into the computational framework, allowing the investigation of the effects of constitutive laws on improved fitting to the experimental measurements, especially in flows which contain stress singularities. Parallelized algorithms combined with adaptive mesh refinement and GPU optimization are expected to significantly improve the efficiency of the direct simulations.
The numerical methodologies constructed in this proposed research, while focusing on addressing two-phase viscoelastic flows, will be broadly-useful in simulating and investigating a number of different complex flow applications such as polymer processing, biological flows in microfluidic devices, and emulsion flows in polymer blending. In nano/microscale geometries, flows of two immiscible liquids are often dominated by surface tension. Moreover, the interface of two liquids may undergo large deformation rates as it moves in networks of nano/microchannels. While the surface tension force discretization proposed in this work overcomes the former, the improvements proposed for discretizing the viscoelastic constitutive equations allow practical direct simulation of viscoelastic flows with strong elasticity.
