Lagrangian Split-Step Method for Viscoelastic Flows.

This research addresses and resolves current challenges in meshless Lagrangian methods for simulating viscoelastic materials. A split-step scheme, or pressure Poisson reformulation of the Navier-Stokes equations, is introduced for incompressible viscoelastic flows in a Lagrangian context. The Lagrangian differencing dynamics (LDD) method, which is a thoroughly validated Lagrangian method for Newtonian and non-Newtonian incompressible flows, is extended to solve the introduced split-step scheme to simulate viscoelastic flows based on the Oldroyd-B constitutive model. To validate and evaluate the new method's capabilities, the following benchmarks were used: lid-driven cavity flow, droplet impact response, 4:1 planar sudden contraction, and die swelling. These findings highlight the LDD method's effectiveness in accurately simulating viscoelastic flows and capturing large deformations and memory effects. Even though the extra stress was directly modeled without any regularization approach, the method produced stable simulations for high Weissenberg numbers. The stability and performance of the the Lagrangian numerics for complex temporal evolution of material properties and stress responses encourage its use for industrial problems dealing with polymers.