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The head-on collision of two identical droplets is investigated based on the BGK-Boltzmann equation. Gauss-Hermite quadratures with different degree of precision are used to solve the kinetic equation, so that the continuum (solution truncated at the Navier-Stokes order) and non-continuum (rarefied gas dynamics) solutions can be compared. When the kinetic equation is solved with adequate accuracy, prominent variations of the vertical velocity (the collision is in the horizontal direction), the viscous stress components, and droplet morphology are observed during the formation of liquid bridge, which demonstrates the importance of the rarefaction effects and the failure of the Navier-Stokes equation. The rarefaction effects change the topology of streamlines near the droplet surface, suppress the high-magnitude vorticity concentration inside the interdroplet region, and promote the vorticity diffusion around outer droplet surface. Two physical mechanisms responsible for the local energy conversion between the free and kinetic energies are identified, namely, the total pressure-dilatation coupling effect and the interaction between the density gradient and strain rate tensor. An energy conversion analysis is performed to show that the rarefaction effects can enhance the conversion from free energy to kinetic energy and facilitate the discharge of interdroplet gas film along the vertical direction, thereby boosting droplet coalescence.

Based on the properties of large-scale plume currents, an injection/suction control strategy is introduced to enhance the strength of plume currents and the turbulent transport of passive scalar in rotating plane Poiseuille flow. The control keeps the classical non-penetrative condition on the stable side, and prescribes spanwise varying wall-normal velocity on the unstable side. Direct numerical simulations show that at medium rotation numbers, very weak injection/suction (the root-mean-square velocity on the controlled side is below $1\%$ of the bulk mean velocity) with properly distributed slots could significantly enhance the large-scale plume currents which have the same spatial distribution as the injection slots. In addition, if the distance between plume currents are increased, the turbulent transport efficiency can be promoted. Therefore, taking the strength and transport efficiency into account, the distance between injection slots should be slightly larger than the intrinsic distance between plume currents to achieve maximum enhancement of turbulent transport. For comparison, the control with non-penetrative condition on the unstable side and injection/suction on the stable side is also examined with simulations. It is found that the injection/suction on the stable side has much weaker influence compared with that on the unstable side. This is because that plumes are generated on the unstable side, and that controlling the origin of plumes is more effective.

For the first time, the non-equilibrium time-relaxation kinetic model (NTRKM) is proposed for compressible turbulence modeling on unresolved grids. Within the non-equilibrium time-relaxation framework, NTRKM is extended in the form of modified Bhatnagar-Gross-Krook model. Based on the first-order Chapman-Enskog expansion, NTRKM connects with the six-variable macroscopic governing equations. The first five governing equations correspond to the conservative laws in mass, momentum and total energy, while the sixth equation governs the evolution of unresolved turbulence kinetic energy Kutke. The unknowns in NTRKM, including turbulent relaxation time and source term, are determined by essential gradient-type assumption and standard dynamic modeling approach. Current generalized kinetic model on unresolved grids consequently offers a profound mesoscopic understanding for one-equation subgrid-scale turbulence kinetic energy Ksgs model in compressible large eddy simulation. To solve NTRKM accurately and robustly, a non-equilibrium gas-kinetic scheme is developed, which succeeds the well-established gas-kinetic scheme for simulating Navier-Stokes equations. Three-dimensional decaying compressible isotropic turbulence and temporal compressible plane mixing layer on unresolved grids are simulated to evaluate the generalized kinetic model and non-equilibrium gas-kinetic scheme. The performance of key turbulent quantities up to second-order statistics confirms that NTRKM is comparable with the widely-used eddy-viscosity Smagorinsky model (SM) and dynamic Smagorinsky model (DSM). Specifically, compared with the DNS solution in temporal compressible plane mixing layer, the performance of NTRKM is much closer with DSM and better than SM. This study provides a workable approach for compressible turbulence modeling on unresolved grids., Comment: 35 pages

The decompositions of the skin-friction and heat transfer coefficients based on the two-fold repeated integration in hypersonic transitional and turbulent boundary layers are analyzed to explain the generations of the wall skin friction and heat transfer. The Reynolds analogy factor slightly increases as the wall temperature decreases, especially for the extremely cooled wall. The integral analysis is applied to explain the overshoot behaviours of the skin-friction and heat transfer coefficients in hypersonic transitional boundary layers. The overshoot of the skin-friction coefficient is mainly caused by the drastic change of the mean velocity profiles, and the overshoot of the heat transfer coefficient is primarily due to the viscous dissipation. In the hypersonic turbulent boundary layers, the skin-friction and heat transfer coefficients increase significantly as the wall temperature decreases. The effects of the mean velocity gradients and the Reynolds shear stress contribute dominantly to the wall skin friction, and have weak correlations with the wall temperature, except for the strongly cooled wall condition. The strongly cooled wall condition and high Mach number can enhance the effect of the Reynolds shear stress, and weaken the impact of the mean velocity gradients. Furthermore, the magnitudes of the dominant relative contributions of the mean temperature gradients, pressure dilatation, viscous dissipation and the Reynolds heat flux to the heat transfer coefficient increase as the wall temperature increases in the hypersonic turbulent boundary layers.

Graph Convolutional Networks (GCNs) are powerful for processing graph-structured data and have achieved state-of-the-art performance in several tasks such as node classification, link prediction, and graph classification. However, it is inevitable for deep GCNs to suffer from an over-smoothing issue that the representations of nodes will tend to be indistinguishable after repeated graph convolution operations. To address this problem, we propose the Graph Partner Neural Network (GPNN) which incorporates a de-parameterized GCN and a parameter-sharing MLP. We provide empirical and theoretical evidence to demonstrate the effectiveness of the proposed MLP partner on tackling over-smoothing while benefiting from appropriate smoothness. To further tackle over-smoothing and regulate the learning process, we introduce a well-designed consistency contrastive loss and KL divergence loss. Besides, we present a graph enhancement technique to improve the overall quality of edges in graphs. While most GCNs can work with shallow architecture only, GPNN can obtain better results through increasing model depth. Experiments on various node classification tasks have demonstrated the state-of-the-art performance of GPNN. Meanwhile, extensive ablation studies are conducted to investigate the contributions of each component in tackling over-smoothing and improving performance.

Finding extended hydrodynamics equations valid from the dense gas region to the rarefied gas region remains a great challenge. The key to success is to obtain accurate constitutive relations for stress and heat flux. Data-driven models offer a new phenomenological approach to learning constitutive relations from data. Such models enable complex constitutive relations that extend Newton's law of viscosity and Fourier's law of heat conduction by regression on higher derivatives. However, the choices of derivatives in these models are ad-hoc without a clear physical explanation. We investigated data-driven models theoretically on a linear system. We argue that these models are equivalent to non-linear length scale scaling laws of transport coefficients. The equivalence to scaling laws justified the physical plausibility and revealed the limitation of data-driven models. Our argument also points out that modeling the scaling law could avoid practical difficulties in data-driven models like derivative estimation and variable selection on noisy data. We further proposed a constitutive relation model based on scaling law and tested it on the calculation of Rayleigh scattering spectra. The result shows our data-driven model has a clear advantage over the Chapman-Enskog expansion and moment methods., Comment: 10 pages, 4 figures

In this paper, a high-order gas-kinetic scheme in general curvilinear coordinate (HGKS-cur) is developed for the numerical simulation of compressible turbulence. Based on the coordinate transformation, the Bhatnagar-Gross-Krook (BGK) equation is transformed from physical space to computational space. To deal with the general mesh given by discretized points, the geometrical metrics need to be constructed by the dimension-by-dimension Lagrangian interpolation. The multidimensional weighted essentially non-oscillatory (WENO) reconstruction is adopted in the computational domain for spatial accuracy, where the reconstructed variables are the cell averaged Jacobian and the Jacobian-weighted conservative variables. The two-stage fourth-order method, which was developed for spatial-temporal coupled flow solvers, is used for temporal discretization. The numerical examples for inviscid and laminar flows validate the accuracy and geometrical conservation law of HGKS-cur. As a direct application, HGKS-cur is implemented for the implicit large eddy simulation (iLES) in compressible wall-bounded turbulent flows, including the compressible turbulent channel flow and compressible turbulent flow over periodic hills. The iLES results with HGKS-cur are in good agreement with the refereed spectral methods and high-order finite volume methods. The performance of HGKS-cur demonstrates its capability as a powerful tool for the numerical simulation of compressible wall-bounded turbulent flows and massively separated flows., Comment: high-order gas-kinetic scheme, general curvilinear coordinate, implicit large eddy simulation, wall-bounded turbulent flows, compressible turbulence

Graph representation learning has long been an important yet challenging task for various real-world applications. However, their downstream tasks are mainly performed in the settings of supervised or semi-supervised learning. Inspired by recent advances in unsupervised contrastive learning, this paper is thus motivated to investigate how the node-wise contrastive learning could be performed. Particularly, we respectively resolve the class collision issue and the imbalanced negative data distribution issue. Extensive experiments are performed on three real-world datasets and the proposed approach achieves the SOTA model performance.

In this paper, we propse a series expansion of the baroclinic torque in low-Mach-number flows, so that the accuracy and universality of any buoyancy term could be examined analytically, and new types of buoyancy terms could be constructed and validated. We first demonstrate that the purpose of introducing a buoyancy term is to approximate the baroclinic torque, and straightforwardly the accuracy of any buoyancy term could be measured by the deviation of its curl from the baroclinic torque. Then a regular perturbation method is introduced for the elliptic equation of the hydrodynamic pressure in low-Mach-number flows, resulting in a sequence of Poisson equations, whose solutions lead to the series representation of the baroclinic torque and the new types of buoyancy terms. With the error definition of buoyancy terms and the series representation of the baroclinic torque, the classical gravitational and centrifugal buoyancy term, as well as some other previously proposed buoyancy terms are revisited. Finally, numerical simulations confirm that, with a decreasing density variation or an increasing order of our newly proposed buoyancy term, the simplified equations with one of the new types of buoyancy terms can converge to the original low-Mach-number equations.

With the rising of modern data science, data--driven turbulence modeling with the aid of machine learning algorithms is becoming a new promising field. Many approaches are able to achieve better Reynolds stress prediction, with much lower modeling error ($\epsilon_M$), than traditional RANS models but they still suffer from numerical error and stability issues when the mean velocity fields are estimated using RANS equations with the predicted Reynolds stresses, illustrating that the error of solving the RANS equations ($\epsilon_P$) is also very important. In the present work, the error $\epsilon_P$ is studied separately by using the Reynolds stresses obtained from direct numerical simulation and we derive the sources of $\epsilon_P$. For the implementations with known Reynolds stresses solely, we suggest to run an adjoint RANS simulation to make first guess on $\nu_t^*$ and $S_{ij}^0$. With around 10 iterations, the error could be reduced by about one-order of magnitude in flow over periodic hills. The present work not only provides one robust approach to minimize $\epsilon_P$, which may be very useful for the data-driven turbulence models, but also shows the importance of the nonlinear part of the Reynolds stresses in flow problems with flow separations., Comment: 12 pages, 5 figures