In this study, we present the development of a two-dimensional finite element solver for the simulation of fluids exhibiting both elastic and plastic constitutive properties. We achieve this by combining the constitutive models of the Oldroyd-B model for viscoelastic fluids and the Papanastasiou model for Bingham fluids within a single Eulerian numerical framework. Our aim within this approach is to approximate the given velocity, pressure, and elastic stresses. We employ a higher order finite element method for the velocity-stress approximation and a discontinuous pressure element. This specific element pair has proven highly effective for accurately capturing the behavior of both Oldroyd-B and Bingham fluids, including non-linear viscosity functions. Our study consists of three main steps. Firstly, we validate the numerical results for each module component of the constitutives to ensure the accuracy of the approximations and calculations. This step is crucial for establishing the reliability and robustness of our approach. Subsequently, in the second step, we apply the solver to simulate elastoviscoplastic fluid behavior in a porous medium and flow around a cylinder benchmark. Finally, we compute the drag and lift for the flow around the cylinder simulation to validate our numerical methodology against established benchmark results. Through the analysis of the above mentioned benchmark problems, we highlight the potential of the proposed solver to reliably capture the complex interplay of elastic, viscous, and plastic effects in non-Newtonian fluid dynamics.
Muhammad Tayyab Bin Saghir (Wed,) studied this question.