Details
| Original language | English |
|---|---|
| Pages (from-to) | 1457-1481 |
| Number of pages | 25 |
| Journal | International Journal for Numerical Methods in Fluids |
| Volume | 97 |
| Issue number | 12 |
| Publication status | Published - 5 Nov 2025 |
Abstract
The modeling of fluids is an important field for mechanics of materials. In this work, we demonstrate that Hamilton's principle, which is well-known for the modeling of solids, can also be formulated to derive the Navier–Stokes equations, which paves the way for easy inclusion of complex material constraints. Furthermore, we expand Hamilton's principle to enable the introduction of “internal variables”, which describe the space- and time-dependent evolution of the material properties. Hereby, a novel strategy for the modeling of non-Newtonian fluids is given. Eventually, Hamilton's principle inherently enables a space-time formulation with the automatic derivation of the correct formal functional setting, which covers different scales of viscosity through the internal variable. The resulting system is a space-time multiscale model for fluid flow, which is based on an additional partial differential equation. The model constitutes thus a much more adaptive description of the complex processes in non-Newtonian fluid flow as possible for classical models based on algebraic constitutive laws. This also includes a spatially and temporally local evolution of the effective viscosity, depending on the local flow conditions rather than material parameters and resulting in both shear-thinning and shear-thickening behavior. Numerical examples substantiate our proposed setting by some studies from Newtonian flow to non-Newtonian regimes with fading or increasing viscosity.
Keywords
- Hamilton's principle, non-Newtonian fluids, numerical simulation, variational modelling
ASJC Scopus subject areas
- Engineering(all)
- Computational Mechanics
- Engineering(all)
- Mechanics of Materials
- Engineering(all)
- Mechanical Engineering
- Computer Science(all)
- Computer Science Applications
- Mathematics(all)
- Applied Mathematics
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In: International Journal for Numerical Methods in Fluids, Vol. 97, No. 12, 05.11.2025, p. 1457-1481.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Space-Time Modeling and Numerical Simulations of Non-Newtonian Fluids Using Internal Variables
AU - Junker, Philipp
AU - Wick, Thomas
N1 - Publisher Copyright: © 2025 The Author(s). International Journal for Numerical Methods in Fluids published by John Wiley & Sons Ltd.
PY - 2025/11/5
Y1 - 2025/11/5
N2 - The modeling of fluids is an important field for mechanics of materials. In this work, we demonstrate that Hamilton's principle, which is well-known for the modeling of solids, can also be formulated to derive the Navier–Stokes equations, which paves the way for easy inclusion of complex material constraints. Furthermore, we expand Hamilton's principle to enable the introduction of “internal variables”, which describe the space- and time-dependent evolution of the material properties. Hereby, a novel strategy for the modeling of non-Newtonian fluids is given. Eventually, Hamilton's principle inherently enables a space-time formulation with the automatic derivation of the correct formal functional setting, which covers different scales of viscosity through the internal variable. The resulting system is a space-time multiscale model for fluid flow, which is based on an additional partial differential equation. The model constitutes thus a much more adaptive description of the complex processes in non-Newtonian fluid flow as possible for classical models based on algebraic constitutive laws. This also includes a spatially and temporally local evolution of the effective viscosity, depending on the local flow conditions rather than material parameters and resulting in both shear-thinning and shear-thickening behavior. Numerical examples substantiate our proposed setting by some studies from Newtonian flow to non-Newtonian regimes with fading or increasing viscosity.
AB - The modeling of fluids is an important field for mechanics of materials. In this work, we demonstrate that Hamilton's principle, which is well-known for the modeling of solids, can also be formulated to derive the Navier–Stokes equations, which paves the way for easy inclusion of complex material constraints. Furthermore, we expand Hamilton's principle to enable the introduction of “internal variables”, which describe the space- and time-dependent evolution of the material properties. Hereby, a novel strategy for the modeling of non-Newtonian fluids is given. Eventually, Hamilton's principle inherently enables a space-time formulation with the automatic derivation of the correct formal functional setting, which covers different scales of viscosity through the internal variable. The resulting system is a space-time multiscale model for fluid flow, which is based on an additional partial differential equation. The model constitutes thus a much more adaptive description of the complex processes in non-Newtonian fluid flow as possible for classical models based on algebraic constitutive laws. This also includes a spatially and temporally local evolution of the effective viscosity, depending on the local flow conditions rather than material parameters and resulting in both shear-thinning and shear-thickening behavior. Numerical examples substantiate our proposed setting by some studies from Newtonian flow to non-Newtonian regimes with fading or increasing viscosity.
KW - Hamilton's principle
KW - non-Newtonian fluids
KW - numerical simulation
KW - variational modelling
UR - http://www.scopus.com/inward/record.url?scp=105010693333&partnerID=8YFLogxK
U2 - 10.1002/fld.5406
DO - 10.1002/fld.5406
M3 - Article
AN - SCOPUS:105010693333
VL - 97
SP - 1457
EP - 1481
JO - International Journal for Numerical Methods in Fluids
JF - International Journal for Numerical Methods in Fluids
SN - 0271-2091
IS - 12
ER -