A Backwards-Tracking Lagrangian-Eulerian Method for Viscoelastic Two-Fluid Flows
Journal article, 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.

computational fluid dynamics

viscoelastic flow

volume of fluid

immersed boundary methods


Simon Ingelsten

Chalmers, Industrial and Materials Science, Engineering Materials

Fraunhofer-Chalmers Centre

Andreas Mark

Fraunhofer-Chalmers Centre

Roland Kádár

Chalmers, Industrial and Materials Science, Engineering Materials

Fredrik Edelvik

Fraunhofer-Chalmers Centre

Applied Sciences

20763417 (eISSN)

Vol. 11 1 1-25 439

Subject Categories

Applied Mechanics

Computational Mathematics

Textile, Rubber and Polymeric Materials

Fluid Mechanics and Acoustics

Areas of Advance


Materials Science



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