Cahn-Hilliard Navier-Stokes simulations for marine free-surface flows

Kühl, Niklas; Hinze, Michael; Rung, Thomas

doi:10.1007/s42757-020-0101-3

Cited by 5 publications

(18 citation statements)

References 39 publications

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“…Though the non-zero RHS of (1) appears to increase the complexity, it is beneficial for various reasons, cf. Kühl et al [2021a]: It naturally includes surface tension effects, supports the use of stability-preserving, upwindbiased convective approximations, and facilitates consistent yet robust primal/adjoint formulations. The latter is particularly relevant for the present study.…”

Section: Concentration Transportmentioning

confidence: 96%

“…They are distinguished by mass or volume conservative strategies and essentially augment the Lagrangian concentration transport equation by a velocity-divergence term and a non-linear, diffusive right-hand side of order four, which is zero outside the interface region, cf. Ding et al [2007] and Kühl et al [2021a]…”

Section: Concentration Transportmentioning

confidence: 99%

“…Here M (c) refers to a mobility parameter of dimension [m 4 /(N s)] and ψ(c, ∆c) denotes to a chemical potential of dimension [Pa]. Following Kühl et al [2021a], the present study employs a mass conservative strategy together with an appropriate choice of M and a frequently used "double-well potential" which yields…”

Section: Concentration Transportmentioning

confidence: 99%

“…m(c = 1[0]) = 1[0], cf. Kühl et al [2021a], Kühl [2021]. The simplest conceivable EoS m (1) corresponds to a bounded linear interpolation between the limit states.…”

Section: Equation Of Statementioning

confidence: 99%

“…Mass conservative CH formulations yield non-solenoidal velocity fields unless f ρ vanishes, cf. Kühl et al [2021a]. This in turn suggests to employ the hyperbolic EoS which can compress the non-solenoidal regime to a small layer controlled by γ m .…”

Section: Equation Of Statementioning

confidence: 99%

See 4 more Smart Citations

Adjoint Node-Based Shape Optimization of Free Floating Vessels

Kühl¹,

Nguyen²,

Palm³

et al. 2022

Preprint

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The paper is concerned with a node-based, gradient-driven, continuous adjoint two-phase flow procedure to optimize the shapes of free-floating vessels and discusses three topics. First, we aim to convey that elements of a Cahn-Hilliard formulation should augment the frequently employed Volume-of-Fluid twophase flow model to maintain dual consistency. It is seen that such consistency serves as the basis for a robust primal/adjoint coupling in practical applications at huge Reynolds and Froude numbers. The second topic covers different adjoint coupling strategies. A central aspect of the application is the floating position, particularly the trim and the sinkage, that interact with a variation of hydrodynamic loads induced by the shape updates. Other topics addressed refer to the required level of density coupling and a more straightforward -yet non-frozen-adjoint treatment of turbulence. The third part discusses the computation of a descent direction within a node-based environment. We will illustrate means to deform both the volume mesh and the hull shape simultaneously and at the same time obey technical constraints on the vessel's displacement and its extensions. The Hilbert-space approach provides smooth shape updates using the established coding infrastructure of a computational fluid dynamics algorithm and provides access to managing additional technical constraints. Verification and validation follow from a submerged 2D cylinder case. The application includes a full-scale offshore supply vessel at Re = 3 • 10 8 and Fn = 0.37. Results illustrate that the fully parallel procedure can automatically reduce the drag of an already pre-optimized shape by 9-13% within ≈ O(10 000-30 000) CPUh depending on the considered couplings and floatation aspects.

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Section: Concentration Transportmentioning

confidence: 96%

Section: Concentration Transportmentioning

confidence: 99%

Section: Concentration Transportmentioning

confidence: 99%

“…m(c = 1[0]) = 1[0], cf. Kühl et al [2021a], Kühl [2021]. The simplest conceivable EoS m (1) corresponds to a bounded linear interpolation between the limit states.…”

Section: Equation Of Statementioning

confidence: 99%

Section: Equation Of Statementioning

confidence: 99%

See 3 more Smart Citations

Adjoint Node-Based Shape Optimization of Free Floating Vessels

Kühl¹,

Nguyen²,

Palm³

et al. 2022

Preprint

Self Cite

View full text Add to dashboard Cite

show abstract

Adjoint node-based shape optimization of free-floating vessels

Kühl

Nguyen

Palm

et al. 2022

Struct Multidisc Optim

Self Cite

View full text Add to dashboard Cite

The paper is concerned with a node-based, gradient-driven, continuous adjoint two-phase flow procedure to optimize the shapes of free-floating vessels and discusses three topics. First, we aim to convey that elements of a Cahn–Hilliard formulation should augment the frequently employed Volume-of-Fluid two-phase flow model to maintain dual consistency. It is seen that such consistency serves as the basis for a robust primal/adjoint coupling in practical applications at huge Reynolds and Froude numbers. The second topic covers different adjoint coupling strategies. A central aspect of the application is the floating position, particularly the trim and the sinkage, that interact with a variation of hydrodynamic loads induced by the shape updates. Other topics addressed refer to the required level of density coupling and a more straightforward—yet non-frozen—adjoint treatment of turbulence. The third part discusses the computation of a descent direction within a node-based environment. We will illustrate means to deform both the volume mesh and the hull shape simultaneously and at the same time obey technical constraints on the vessel’s displacement and its extensions. The Hilbert-space approach provides smooth shape updates using the established coding infrastructure of a computational fluid dynamics algorithm and provides access to managing additional technical constraints. Verification and validation follow from a submerged 2D cylinder case. The application includes a full-scale offshore supply vessel at $$\mathrm{Re} = 3 \times 10^8$$ Re = 3 × 10 8 and $$\mathrm{Fn} = 0.37$$ Fn = 0.37 . Results illustrate that the fully parallel procedure can automatically reduce the drag of an already pre-optimized shape by 9–13% within $$\approx\,{\mathcal{O}}$$ ≈ O (10,000-30,000) CPUh depending on the considered couplings and floatation aspects.

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Two-phase flow simulations of surface waves in wind-forced conditions

et al. 2023

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The paper is devoted to two-phase flow simulations and investigates the ability of a diffusive interface Cahn–Hilliard volume-of-fluid model to capture the dynamics of the air–sea interface at geophysically relevant Reynolds numbers. It employs a hybrid filtered/averaging improved detached eddy simulation method to model turbulence and utilizes a continuum model to account for surface tension if the diffuse interface is under-resolved by the grid. A numerical wind-wave tank is introduced, and results obtained for two known wind-wave conditions are analyzed in comparison to experimental data at matched Reynolds numbers. The focus of the comparison is on both time-averaged and wave-coherent quantities, and includes pressure, velocity as well as modeled and resolved Reynolds stresses. In general, numerical predictions agree well with the experimental measurements and reproduce many wave-dependent flow features. Reynolds stresses near the water surface are found to be especially important in modulating the critical layer height. It is concluded that the diffusive interface approach proves to be a promising method for future studies of air–sea interface dynamics in geophysically relevant flows.

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Cahn-Hilliard Navier-Stokes simulations for marine free-surface flows

Cited by 5 publications

References 39 publications

Adjoint Node-Based Shape Optimization of Free Floating Vessels

Adjoint Node-Based Shape Optimization of Free Floating Vessels

Adjoint node-based shape optimization of free-floating vessels

Two-phase flow simulations of surface waves in wind-forced conditions

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