High Weissenberg number simulations with incompressible Smoothed Particle Hydrodynamics and the log-conformation formulation

TL;DR

This paper introduces a novel 2D incompressible SPH algorithm that incorporates the log-conformation formulation, enabling stable and accurate simulations of high Weissenberg number viscoelastic flows, including complex free-surface and internal flows.

Contribution

The paper presents the first implementation of the log-conformation formulation within SPH for viscoelastic flows, significantly improving stability at high Weissenberg numbers.

Findings

Simulates flows at Wi=85 for Poiseuille flow

Handles both internal and free-surface flows

Applicable to various constitutive models

Abstract

Viscoelastic flows occur widely, and numerical simulations of them are important for a range of industrial applications. Simulations of viscoelastic flows are more challenging than their Newtonian counterparts due to the presence of exponential gradients in polymeric stress fields, which can lead to catastrophic instabilities if not carefully handled. A key development to overcome this issue is the log-conformation formulation, which has been applied to a range of numerical methods, but not previously applied to Smoothed Particle Hydrodynamics (SPH). Here we present a 2D incompressible SPH algorithm for viscoelastic flows which, for the first time, incorporates a log-conformation formulation with an elasto-viscous stress splitting (EVSS) technique. The resulting scheme enables simulations of flows at high Weissenberg numbers (accurate up to Wi=85 for Poiseuille flow). The method is robust, and able to handle both internal and free-surface flows, and a range of linear and non-linear constitutive models. Several test cases are considerd included flow past a periodic array of cylinders and jet buckling. This presents a significant step change in capabilties compared to previous SPH algorithms for viscoelastic flows, and has the potential to simulate a wide range of new and challenging applications.