Fully coupled implicit finite-volume algorithm for viscoelastic interfacial flows
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
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2026
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| _version_ | 1866918328740610048 |
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| author | Mazloum, Ayman Gennari, Gabriele Denner, Fabian van Wachem, Berend |
| author_facet | Mazloum, Ayman Gennari, Gabriele Denner, Fabian van Wachem, Berend |
| contents | A fully coupled implicit finite-volume algorithm for incompressible viscoelastic interfacial flows is proposed, whereby the viscoelasticity of the flow is described by an upper-convected Maxwell constitutive model, including limited extensibility and shear-thinning behaviour. The governing equations describing the conservation of continuity and momentum, as well as the constitutive model are discretized using standard finite-volume methods and are solved for pressure, velocity and the polymer stress tensor in a single linear system of equations. Treating all terms of the linearized and discretized governing equations implicit in velocity, pressure and/or the components of the polymer stress tensor, a tightly coupled system of equations is obtained. The interface separating the interacting bulk phases and the surface tension acting at the fluid interface are modelled using a state-of-the-art front-tracking method. We demonstrate the capabilities of the proposed numerical framework with four representative test cases, including the deformation of a viscoelastic droplet in shear flow at large Weissenberg numbers of up to Wi=10^4, and the jump discontinuity of the rise velocity of a bubble rising in a viscoelastic liquid as a result of a "negative wake". Contrary to previous studies using segregated algorithms, the proposed fully coupled implicit algorithm does not apply or require a log-conformation approach to predict these flows. Overall, the fully implicit coupled front-tracking formulation provides a robust framework to reliable numerical predictions of strongly elastic interfacial flows at large Weissenberg numbers. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2602_08645 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Fully coupled implicit finite-volume algorithm for viscoelastic interfacial flows Mazloum, Ayman Gennari, Gabriele Denner, Fabian van Wachem, Berend Fluid Dynamics Computational Physics A fully coupled implicit finite-volume algorithm for incompressible viscoelastic interfacial flows is proposed, whereby the viscoelasticity of the flow is described by an upper-convected Maxwell constitutive model, including limited extensibility and shear-thinning behaviour. The governing equations describing the conservation of continuity and momentum, as well as the constitutive model are discretized using standard finite-volume methods and are solved for pressure, velocity and the polymer stress tensor in a single linear system of equations. Treating all terms of the linearized and discretized governing equations implicit in velocity, pressure and/or the components of the polymer stress tensor, a tightly coupled system of equations is obtained. The interface separating the interacting bulk phases and the surface tension acting at the fluid interface are modelled using a state-of-the-art front-tracking method. We demonstrate the capabilities of the proposed numerical framework with four representative test cases, including the deformation of a viscoelastic droplet in shear flow at large Weissenberg numbers of up to Wi=10^4, and the jump discontinuity of the rise velocity of a bubble rising in a viscoelastic liquid as a result of a "negative wake". Contrary to previous studies using segregated algorithms, the proposed fully coupled implicit algorithm does not apply or require a log-conformation approach to predict these flows. Overall, the fully implicit coupled front-tracking formulation provides a robust framework to reliable numerical predictions of strongly elastic interfacial flows at large Weissenberg numbers. |
| title | Fully coupled implicit finite-volume algorithm for viscoelastic interfacial flows |
| topic | Fluid Dynamics Computational Physics |
| url | https://arxiv.org/abs/2602.08645 |