arXiv subjects

A. Brunk

Publications and source records attributed to A. Brunk.

3 recordsLinked to original sources

arXiv2026

Surface-tension calibration for N-phase mixtures

Diffuse-interface (phase-field) models are a widely used framework for interfacial dynamics in complex fluids, in which sharp interfaces are replaced by smooth transition layers and interfacial forces follow from a free-energy functional. In these models, surface tensions and diffuse thicknesses are not prescribed directly but are encoded implicitly by the bulk multiwell potential and the gradient-energy term through one-dimensional equilibrium profiles. While this link is classical in the binary Cahn--Hilliard setting, calibrating multiphase models is substantially more delicate because multiple pairwise surface tensions must be matched simultaneously and the relevant equilibrium paths are constrained by the Gibbs simplex. The practical problem is therefore: given a chosen bulk potential and a set of target pairwise surface tensions, determine gradient-energy coefficients that reproduce these targets in the full multiphase model. Here we present a thermodynamically consistent calibration procedure for N-phase diffuse-interface free energies of Cahn--Hilliard type. The method determines a symmetric capillary matrix that matches prescribed pairwise surface tensions through the model's equilibrium profiles. We further introduce a rescaling strategy that adjusts diffuse interface widths to mesh-resolvable values while preserving the calibrated surface tensions. The resulting calibrated free-energy closure can be incorporated directly into N-phase mixture simulations, and we demonstrate this by applying it to N-phase Navier--Stokes--Cahn--Hilliard flows.

physics.flu-dyn↗

arXiv2026

Symmetric structure-preserving discretization of N-phase incompressible fluid mixtures with arbitrary density ratios

Diffuse-interface models are a widely used framework for interfacial dynamics in complex fluids, in which interfaces are represented through smooth transition layers and capillary effects are encoded by a free-energy functional. For incompressible mixtures with more than two phases, however, robust computation is substantially more difficult because the numerical method should preserve the balance structure of the continuum model, maintain the saturation constraint, dissipate energy, and treat all phases symmetrically even when density ratios are arbitrary. Existing structure-preserving methods are largely developed for binary flows or for formulations that distinguish a reference phase, so a genuinely symmetric N-phase discretization remains lacking. The practical problem is therefore to construct a fully-discrete method for N-phase incompressible Navier--Stokes--Cahn--Hilliard mixture models that retains the key thermodynamic and conservation properties of the continuum equations for arbitrary density ratios. Here we propose a symmetric fully-discrete method for the N-phase incompressible Navier--Stokes--Cahn--Hilliard mixture model with arbitrary density ratios. The method yields a fully-discrete problem in which every solution satisfies exact phase volume conservation, phase mass conservation, total volume conservation, total mass conservation, and a discrete energy-dissipation law. In addition, if the volume-saturation constraint holds for the initial data, then it is preserved at every time step. We numerically verify these structure-preserving properties and demonstrate the robustness of the method in representative multiphase flow problems. The resulting scheme provides a computational framework for incompressible N-phase mixture flows with complex interfacial dynamics and arbitrary density contrasts.

math.NA↗

arXiv2026

Mixture-aware closure of the N-phase Navier--Stokes--Cahn--Hilliard mixture model

Diffuse-interface (phase-field) models are widely used to describe multiphase mixtures and their interfacial dynamics. In multiphase settings, however, the constitutive closure should remain meaningful across different representations of the same mixture. Existing N-phase phase-field constructions commonly enforce reduction only when a phase is absent (restriction to a face of the Gibbs simplex), but do not address the natural requirement that physically identical phases can be merged without changing the governing equations. This requires characterizing thermodynamically admissible, mixture-aware constitutive closures that are consistent with merging identical phases at the PDE level. Here, we show that, under a small set of structural axioms, PDE-level reduction consistency uniquely fixes the admissible free-energy structure to an ideal-mixing contribution to an ideal-mixing contribution, a symmetric mean-field interaction term, and a constant-coefficient quadratic gradient penalty. yielding a thermodynamic closure that includes Maxwell--Stefan-type mobilities as a special case. The same requirement constrains the Onsager mobility matrix to a pairwise-exchange form with bilinear degeneracy in the volume fractions, yielding a thermodynamic closure that includes Maxwell--Stefan-type mobilities as a special case. These results provide a consistent closure for N-phase Navier--Stokes--Cahn--Hilliard mixture models and, in the bulk-only setting, for multiphase Maxwell--Stefan diffusion systems. Numerical experiments confirm the predicted mixture-aware reduction properties and illustrate the capabilities of the N-phase Navier--Stokes--Cahn--Hilliard framework in representative multiphase-flow computations.

physics.flu-dyn↗