Identification of a particle collision as a finite-time blowup in turbulence

Lee, Seulgi; Lee, Chang‐Hoon

doi:10.1038/s41598-022-27305-5

Cited by 4 publications

(1 citation statement)

References 53 publications

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“…The imagination of finite-time singularities as an event (often termed blow-up) with catastrophic consequences for a numerical method, implying its unavoidable breakdown once such a singularity occurs, is not un-common, see e.g. [9,10]. It seems as if the picture drawn currently in the literature contains further contradictions.…”

Section: Motivationmentioning

confidence: 99%

From anomalous dissipation through Euler singularities to stabilized finite element methods for turbulent flows

Fehn,

Kronbichler,

Lube

2024

Preprint

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It is well-known that kinetic energy produced artificially by an inadequate numerical discretization of nonlinear transport terms may lead to a blow-up of the numerical solution in simulations of fluid dynamical problems such as incompressible turbulent flows. However, the community seems to be divided whether this problem should be resolved by the use of discretely energy-preserving or dissipative discretization schemes. The rationale for discretely energy-preserving schemes is often based on the expectation of exact conservation of kinetic energy in the inviscid limit, which mathematically relies on the assumption of sufficient regularity of the solution. There is the (contradictory) phenomenological observation in turbulence that flows dissipate energy in the limit of vanishing molecular viscosity, an "anomalous" phenomenon termed dissipation anomaly or the zeroth law of turbulence. As already conjectured by Onsager, the Euler equations may dissipate kinetic energy through the formation of singularities of the velocity field. With the proof of Onsager's conjecture in recent years, a consequence for designing numerical methods for turbulent flows is that the smoothness assumption behind conservation of energy in the inviscid limit becomes indeed critical for turbulent flows. The velocity field rather has to be expected to show singular behavior towards the inviscid limit, supporting the dissipation of kinetic energy. Our main argument is that designing numerical methods against the background of this physical behavior is a strong rationale for the construction of dissipative (or dissipation-aware) numerical schemes for convective terms. From that perspective, numerical dissipation does not appear artificial, but as an important ingredient to overcome problems introduced by energy-conserving numerical methods such as the inability to represent anomalous dissipation as well as the accumulation of energy in small scales, which is known as thermalization. This work discusses stabilized H1, L2, and H(div)-conforming finite element methods with a focus on the energy-stability of the numerical method and its dissipation mechanisms to predict inertial dissipation. Finally, we discuss the achievable convergence rate for the kinetic energy in under-resolved turbulent flow simulations.

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Section: Motivationmentioning

confidence: 99%

From anomalous dissipation through Euler singularities to stabilized finite element methods for turbulent flows

Fehn,

Kronbichler,

Lube

2024

Preprint

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On the formation of thermal caustics in turbulent particle-laden flows

Zandi Pour,

Iovieno

2024

Physics of Fluids

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This study investigates the development of thermal caustics within particle-laden turbulent flows, a concept recently proposed to elucidate the non-smooth behavior of particle temperature during fluid–particle thermal interactions, drawing a parallel to the creation of caustics. The temperature variations observed between closely spaced particles, which are linked to thermal caustics, stem from the history of their different paths. This work delves into the emergence of thermal caustics by analyzing the dynamics of the gradient of particle temperature in the configuration space, highlighting the influence of both particle and thermal inertia. The analysis indicates that thermal caustics arise concurrently with caustics, with the exception of the condition of zero thermal inertia, which represents a singular scenario where particle temperature decouples from velocity.

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Caustic formation in a non-Gaussian model for turbulent aerosols

Meibohm,

Sundberg,

Mehlig

et al. 2024

Phys. Rev. Fluids

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Caustics in the dynamics of heavy particles in turbulence accelerate particle collisions. The rate J at which these singularities form depends sensitively on the Stokes number St, the nondimensional inertia parameter. Exact results for this sensitive dependence have been obtained using Gaussian statistical models for turbulent aerosols. However, direct numerical simulations of heavy particles in turbulence yield much larger caustic-formation rates than predicted by the Gaussian theory. To understand the possible mechanisms explaining this difference, we analyze a non-Gaussian statistical model for caustic formation in the limit of small St. We show that at small St, J depends sensitively on the tails of the distribution of Lagrangian fluid-velocity gradients. This explains why different authors obtained different St-dependencies of J in numerical-simulation studies. The most likely gradient fluctuation that induces caustics at small St, by contrast, is the same in the non-Gaussian and Gaussian models. Direct numerical simulation results for particles in turbulence show that the optimal fluctuation is similar, but not identical, to that obtained by the model calculations. Published by the American Physical Society 2024

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Identification of a particle collision as a finite-time blowup in turbulence

Cited by 4 publications

References 53 publications

From anomalous dissipation through Euler singularities to stabilized finite element methods for turbulent flows

From anomalous dissipation through Euler singularities to stabilized finite element methods for turbulent flows

On the formation of thermal caustics in turbulent particle-laden flows

Caustic formation in a non-Gaussian model for turbulent aerosols

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