A Backwards-Tracking Lagrangian-Eulerian Method for Viscoelastic Two-Fluid Flows
Artikel i vetenskaplig tidskrift, 2021

A new Lagrangian–Eulerian method for the simulation of viscoelastic free surface flow is proposed. The approach is developed from a method in which the constitutive equation for viscoelastic stress is solved at Lagrangian nodes, which are convected by the flow, and interpolated to the Eulerian grid with radial basis functions. In the new method, a backwards-tracking methodology is employed, allowing for fixed locations for the Lagrangian nodes to be chosen a priori. The proposed method is also extended to the simulation of viscoelastic free surface flow with the volume of fluid method. No unstructured interpolation or node redistribution is required with the new approach. Furthermore, the total amount of Lagrangian nodes is significantly reduced when compared to the original Lagrangian–Eulerian method. Consequently, the method is more computationally efficient and robust. No additional stabilization technique, such as both-sides diffusion or reformulation of the constitutive equation, is necessary. A validation is performed with the analytic solution for transient and steady planar Poiseuille flow, with excellent results. Furthermore, the proposed method agrees well with numerical data from the literature for the viscoelastic die swell flow of an Oldroyd-B model. The capabilities to simulate viscoelastic free surface flow are also demonstrated through the simulation of a jet buckling case.

viscoelastic flow

computational fluid dynamics

immersed boundary methods

volume of fluid


Simon Ingelsten

Chalmers, Industri- och materialvetenskap, Konstruktionsmaterial

Andreas Mark

Chalmers, Mekanik och maritima vetenskaper, Strömningslära

Roland Kádár

Chalmers, Industri- och materialvetenskap, Konstruktionsmaterial

Fredrik Edelvik

Applied Sciences

1454-5101 (ISSN)

Vol. 11 1 439


Teknisk mekanik


Textil-, gummi- och polymermaterial

Strömningsmekanik och akustik



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