We review progress and open challenges for a number of problems related to the Oldroyd B
model which are of current interest to the mathematical community. We discuss existence …

We present a comprehensive three-dimensional numerical investigation of the von Kármán
swirling flow between two parallel plates using the Oldroyd-B model and characterize the …

We demonstrate through numerical solutions of the Oldroyd-B model in a two-dimensional
Taylor–Couette geometry that the onset of elastic turbulence in a viscoelastic fluid can be …

In this work, we show that the double-periodic boundary conditions typically applied in
numerical simulations of elastic turbulence can lead to significantly incorrect results if not …

Polymer solutions in the semi-dilute regime are of considerable industrial importance. The
complex rheological properties of such highly viscoelastic fluids and the complexity of their …

Reduced-order models (ROMs) have been widely adopted in fluid mechanics, particularly in
the context of Newtonian fluid flows. These models offer the ability to predict complex …

Dense suspensions of swimming bacteria exhibit chaotic flow patterns that promote the
mixing and transport of resources and signaling chemicals within cell colonies. While the …

This paper presents a multi-fidelity reduced-order model (MFROM) and global optimization
method for rapid and accurate simulation and design of microfluidic concentration gradient …

In this study, a numerical technique based on the Lattice Boltzmann method is presented to
model viscoelastic fluid interaction with complex boundaries which are commonly seen in …

In this paper, an improved nonlinear reduced-order modeling technique capable of
describing the parameterized shape defect is presented. In the proposed framework, a set of …