THE NONLINEAR STABILITY OF PLANE PARALLEL SHEAR FLOWS WITH RESPECT TO TILTED PERTURBATIONS

The nonlinear stability of plane parallel shear flows with respect to tilted perturbations is studied by energy methods.Tilted perturbation refers to the fact that perturbations form an angleθ∈(0,π/2)with the direction of the basic flows.By defining an energy functional,it is proven that plane parallel shear flows are unconditionally nonlinearly exponentially stable for tilted streamwise perturbation when the Reynolds number is below a certain critical value and the boundary conditions are either rigid or stress-free.In the case of stress-free boundaries,by taking advantage of the poloidal-toroidal decomposition of a solenoidal field to define energy functionals,it can be even shown that plane parallel shear flows are unconditionally nonlinearly exponentially stable for all Reynolds numbers,where the tilted perturbation can be either spanwise or streamwise.

Depth-Guided Vision Transformer With Normalizing Flows for Monocular 3D Object Detection

Monocular 3D object detection is challenging due to the lack of accurate depth information.Some methods estimate the pixel-wise depth maps from off-the-shelf depth estimators and then use them as an additional input to augment the RGB images.Depth-based methods attempt to convert estimated depth maps to pseudo-LiDAR and then use LiDAR-based object detectors or focus on the perspective of image and depth fusion learning.However,they demonstrate limited performance and efficiency as a result of depth inaccuracy and complex fusion mode with convolutions.Different from these approaches,our proposed depth-guided vision transformer with a normalizing flows(NF-DVT)network uses normalizing flows to build priors in depth maps to achieve more accurate depth information.Then we develop a novel Swin-Transformer-based backbone with a fusion module to process RGB image patches and depth map patches with two separate branches and fuse them using cross-attention to exchange information with each other.Furthermore,with the help of pixel-wise relative depth values in depth maps,we develop new relative position embeddings in the cross-attention mechanism to capture more accurate sequence ordering of input tokens.Our method is the first Swin-Transformer-based backbone architecture for monocular 3D object detection.The experimental results on the KITTI and the challenging Waymo Open datasets show the effectiveness of our proposed method and superior performance over previous counterparts.

Arbitrary High-Order Fully-Decoupled Numerical Schemes for Phase-Field Models of Two-Phase Incompressible Flows

Due to the coupling between the hydrodynamic equation and the phase-field equation in two-phase incompressible flows,it is desirable to develop efficient and high-order accurate numerical schemes that can decouple these two equations.One popular and efficient strategy is to add an explicit stabilizing term to the convective velocity in the phase-field equation to decouple them.The resulting schemes are only first-order accurate in time,and it seems extremely difficult to generalize the idea of stabilization to the second-order or higher version.In this paper,we employ the spectral deferred correction method to improve the temporal accuracy,based on the first-order decoupled and energy-stable scheme constructed by the stabilization idea.The novelty lies in how the decoupling and linear implicit properties are maintained to improve the efficiency.Within the framework of the spatially discretized local discontinuous Galerkin method,the resulting numerical schemes are fully decoupled,efficient,and high-order accurate in both time and space.Numerical experiments are performed to validate the high-order accuracy and efficiency of the methods for solving phase-field models of two-phase incompressible flows.

Bound-Preserving Discontinuous Galerkin Methods with Modified Patankar Time Integrations for Chemical Reacting Flows

In this paper,we develop bound-preserving discontinuous Galerkin(DG)methods for chemical reactive flows.There are several difficulties in constructing suitable numerical schemes.First of all,the density and internal energy are positive,and the mass fraction of each species is between 0 and 1.Second,due to the rapid reaction rate,the system may contain stiff sources,and the strong-stability-preserving explicit Runge-Kutta method may result in limited time-step sizes.To obtain physically relevant numerical approximations,we apply the bound-preserving technique to the DG methods.Though traditional positivity-preserving techniques can successfully yield positive density,internal energy,and mass fractions,they may not enforce the upper bound 1 of the mass fractions.To solve this problem,we need to(i)make sure the numerical fluxes in the equations of the mass fractions are consistent with that in the equation of the density;(ii)choose conservative time integrations,such that the summation of the mass fractions is preserved.With the above two conditions,the positive mass fractions have summation 1,and then,they are all between 0 and 1.For time discretization,we apply the modified Runge-Kutta/multi-step Patankar methods,which are explicit for the flux while implicit for the source.Such methods can handle stiff sources with relatively large time steps,preserve the positivity of the target variables,and keep the summation of the mass fractions to be 1.Finally,it is not straightforward to combine the bound-preserving DG methods and the Patankar time integrations.The positivity-preserving technique for DG methods requires positive numerical approximations at the cell interfaces,while Patankar methods can keep the positivity of the pre-selected point values of the target variables.To match the degree of freedom,we use polynomials on rectangular meshes for problems in two space dimensions.To evolve in time,we first read the polynomials at the Gaussian points.Then,suitable slope limiters can be applied to enforce the positivity of the solutions at those points,which can be preserved by the Patankar methods,leading to positive updated numerical cell averages.In addition,we use another slope limiter to get positive solutions used for the bound-preserving technique for the flux.Numerical examples are given to demonstrate the good performance of the proposed schemes.

Debris Fan Produced by Failure of Canyon-Blocking Pyroclastic Flows

Ash-rich pyroclastic flows from the cataclysmic eruption of Mount Mazama (~7700 yr. B. P.), Cascade volcanic arc, Oregon, entered and blocked the narrow, bedrock-lined canyon of the Williamson River approximately 35 to 44 km from the source volcano. The blockage impounded a body of water which then released producing four stratigraphic units in the downstream debris fan. The four stratigraphic units are a boulder core comprised of locally sourced bedrock boulders and three sand-rich units including a fine-grained sand unit, a sandy pumice gravel (±basalt/hydrovolcanic tuff) unit, and a pumice pebble-bearing, crystal-rich sand unit. Hand-drilled auger holes up to ~1.6 m deep were used to obtain samples of the sand-rich units. Units were delimited using surface and down-hole observations, composition and texture, estimated density, statistical parameters of grain size, and vertical and lateral distribution of properties. Overtopping followed by rapid incision into the ash-rich pyroclastic flows progressively cleared the canyon, but a bedrock knickpoint near the head of the canyon limited the volume of debris available for transport to about 0.04 km3 to 0.08 km3. Co-deposition of bedrock boulders and lithic-rich sand was followed by rapid deposition with minimal reworking of remobilized pyroclastics. Continued draining of the impounded lake sent hyperconcentrated flows onto the debris fan depositing pumice-rich gravels that graded upward to crystal-rich sands.

Stochastic Analysis and Modeling of Velocity Observations in Turbulent Flows

Highly turbulent water flows,often encountered near human constructions like bridge piers,spillways,and weirs,display intricate dynamics characterized by the formation of eddies and vortices.These formations,varying in sizes and lifespans,significantly influence the distribution of fluid velocities within the flow.Subsequently,the rapid velocity fluctuations in highly turbulent flows lead to elevated shear and normal stress levels.For this reason,to meticulously study these dynamics,more often than not,physical modeling is employed for studying the impact of turbulent flows on the stability and longevity of nearby structures.Despite the effectiveness of physical modeling,various monitoring challenges arise,including flow disruption,the necessity for concurrent gauging at multiple locations,and the duration of measurements.Addressing these challenges,image velocimetry emerges as an ideal method in fluid mechanics,particularly for studying turbulent flows.To account for measurement duration,a probabilistic approach utilizing a probability density function(PDF)is suggested to mitigate uncertainty in estimated average and maximum values.However,it becomes evident that deriving the PDF is not straightforward for all turbulence-induced stresses.In response,this study proposes a novel approach by combining image velocimetry with a stochastic model to provide a generic yet accurate description of flow dynamics in such applications.This integration enables an approach based on the probability of failure,facilitating a more comprehensive analysis of turbulent flows.Such an approach is essential for estimating both short-and long-term stresses on hydraulic constructions under assessment.

Exploring the Element Integration of Urban and Rural“Space of Flows”in the Context of Consumption Upgrading:A Case Study of Changsi Village in Anhui Province

The mobility and interaction between urban and rural areas are becoming more and more intensive,and their links and exchanges are increasingly closer due to constant flow of factors such as information,capital,personnel and technology.In this context,the element integration of urban and rural“space of flows”can promote the integrated development of urban and rural areas,improve the consumption environment and experience,and promote the industrial upgrading and technological progress.To realize the element integration of urban and rural“space of flows”,it is necessary to explore and innovate in infrastructure construction,information technology application,industrial cooperation and cultural exchanges.Government departments,enterprises and social organizations also need to work together to give play to their respective advantages and jointly promote the process of element integration of urban and rural“space of flows”.

Numerical Simulation of Dam-Break Flows Using Radial Basis Functions: Application to Urban Flood Inundation

Dam-break flows pose significant threats to urban areas due to their potential for causing rapid and extensive flooding. Traditional numerical methods for simulating these events struggle with complex urban landscapes. This paper presents an alternative approach using Radial Basis Functions to simulate dam-break flows and their impact on urban flood inundation. The proposed method adapts a new strategy based on Particle Swarm Optimization for variable shape parameter selection on meshfree formulation to enhance the numerical stability and convergence of the simulation. The method’s accuracy and efficiency are demonstrated through numerical experiments, including well-known partial and circular dam-break problems and an idealized city with a single building, highlighting its potential as a valuable tool for urban flood risk management.

On the analytical solution of transient friction in channel flows

The transient friction in channel mean flows is the sum of two contributions,i.e.,the underlying laminar flow(ULF)and the purely turbulent component(PTC),and the contributions are analyzed separately by theoretical experiments.It is found that,the transient friction may be higher or remarkably lower than that in equal-Reynolds number steady-state flows.The universal time constant for plane-parallel laminar flows is reported,and the role of the time constant in a turbulent mean flow is examined.It is shown that the time constant is related to the turbulence's frozen time.Finally,a study of the logarithmic layer during the transient flow is accomplished,which shows that the logarithmic layer is destroyed.

Verification and Validation of High-Resolution Inviscid and Viscous Conical Nozzle Flows

Capturing elaborated flow structures and phenomena is required for well-solved numerical flows.The finite difference methods allow simple discretization of mesh and model equations.However,they need simpler meshes,e.g.,rectangular.The inverse Lax-Wendroff(ILW)procedure can handle complex geometries for rectangular meshes.High-resolution and high-order methods can capture elaborated flow structures and phenomena.They also have strong mathematical and physical backgrounds,such as positivity-preserving,jump conditions,and wave propagation concepts.We perceive an effort toward direct numerical simulation,for instance,regarding weighted essentially non-oscillatory(WENO)schemes.Thus,we propose to solve a challenging engineering application without turbulence models.We aim to verify and validate recent high-resolution and high-order methods.To check the solver accuracy,we solved vortex and Couette flows.Then,we solved inviscid and viscous nozzle flows for a conical profile.We employed the finite difference method,positivity-preserving Lax-Friedrichs splitting,high-resolution viscous terms discretization,fifth-order multi-resolution WENO,ILW,and third-order strong stability preserving Runge-Kutta.We showed the solver is high-order and captured elaborated flow structures and phenomena.One can see oblique shocks in both nozzle flows.In the viscous flow,we also captured a free-shock separation,recirculation,entrainment region,Mach disk,and the diamond-shaped pattern of nozzle flows.

Fiber Bundle Topology Optimization for Surface Flows

This paper presents a topology optimization approach for the surface flows on variable design domains.Via this approach,the matching between the pattern of a surface flow and the 2-manifold used to define the pattern can be optimized,where the 2-manifold is implicitly defined on another fixed 2-manifold named as the base manifold.The fiber bundle topology optimization approach is developed based on the description of the topological structure of the surface flow by using the differential geometry concept of the fiber bundle.The material distribution method is used to achieve the evolution of the pattern of the surface flow.The evolution of the implicit 2-manifold is realized via a homeomorphous map.The design variable of the pattern of the surface flow and that of the implicit 2-manifold are regularized by two sequentially implemented surface-PDE filters.The two surface-PDE filters are coupled,because they are defined on the implicit 2-manifold and base manifold,respectively.The surface Navier-Stokes equations,defined on the implicit 2-manifold,are used to describe the surface flow.The fiber bundle topology optimization problem is analyzed using the continuous adjoint method implemented on the first-order Sobolev space.Several numerical examples have been provided to demonstrate this approach,where the combination of the viscous dissipation and pressure drop is used as the design objective.

Fixed-Time Gradient Flows for Solving Constrained Optimization: A Unified Approach

The accelerated method in solving optimization problems has always been an absorbing topic.Based on the fixedtime(FxT)stability of nonlinear dynamical systems,we provide a unified approach for designing FxT gradient flows(FxTGFs).First,a general class of nonlinear functions in designing FxTGFs is provided.A unified method for designing first-order FxTGFs is shown under Polyak-Łjasiewicz inequality assumption,a weaker condition than strong convexity.When there exist both bounded and vanishing disturbances in the gradient flow,a specific class of nonsmooth robust FxTGFs with disturbance rejection is presented.Under the strict convexity assumption,Newton-based FxTGFs is given and further extended to solve time-varying optimization.Besides,the proposed FxTGFs are further used for solving equation-constrained optimization.Moreover,an FxT proximal gradient flow with a wide range of parameters is provided for solving nonsmooth composite optimization.To show the effectiveness of various FxTGFs,the static regret analyses for several typical FxTGFs are also provided in detail.Finally,the proposed FxTGFs are applied to solve two network problems,i.e.,the network consensus problem and solving a system linear equations,respectively,from the perspective of optimization.Particularly,by choosing component-wisely sign-preserving functions,these problems can be solved in a distributed way,which extends the existing results.The accelerated convergence and robustness of the proposed FxTGFs are validated in several numerical examples stemming from practical applications.

A Novel Model for the Prediction of Liquid Film Thickness Distribution in Pipe Gas-Liquid Flows

A model is proposed for liquid film profile prediction in gas-liquid two-phase flow,which is able to provide the film thickness along the circumferential direction and the pressure gradient in the flow direction.A two-fluid model is used to calculate both gas and liquid phases’flow characteristics.The secondary flow occurring in the gas phase is taken into account and a sailing boat mechanism is introduced.Moreover,energy conservation is applied for obtaining the liquid film thickness distribution along the circumference.Liquid film thickness distribution is calculated accordingly for different cases;its values are compared with other models and available experimental data.As a result,the newly proposed model is tested and good performances are demonstrated.The liquid film thickness distribution in small pipes and inclined pipes is also studied,and regime transition is revealed by liquid film profile evolution.The observed inflection point demonstrates that the liquid film thickness decreases steeply along the circumference,when the circle angle ranges between 30°and 50°for gas-liquid stratified flow with small superficial velocities.

A flexible multiscale algorithm based on an improved smoothed particle hydrodynamics method for complex viscoelastic flows

Viscoelastic flows play an important role in numerous engineering fields,and the multiscale algorithms for simulating viscoelastic flows have received significant attention in order to deepen our understanding of the nonlinear dynamic behaviors of viscoelastic fluids.However,traditional grid-based multiscale methods are confined to simple viscoelastic flows with short relaxation time,and there is a lack of uniform multiscale scheme available for coupling different solvers in the simulations of viscoelastic fluids.In this paper,a universal multiscale method coupling an improved smoothed particle hydrodynamics(SPH)and multiscale universal interface(MUI)library is presented for viscoelastic flows.The proposed multiscale method builds on an improved SPH method and leverages the MUI library to facilitate the exchange of information among different solvers in the overlapping domain.We test the capability and flexibility of the presented multiscale method to deal with complex viscoelastic flows by solving different multiscale problems of viscoelastic flows.In the first example,the simulation of a viscoelastic Poiseuille flow is carried out by two coupled improved SPH methods with different spatial resolutions.The effects of exchanging different physical quantities on the numerical results in both the upper and lower domains are also investigated as well as the absolute errors in the overlapping domain.In the second example,the complex Wannier flow with different Weissenberg numbers is further simulated by two improved SPH methods and coupling the improved SPH method and the dissipative particle dynamics(DPD)method.The numerical results show that the physical quantities for viscoelastic flows obtained by the presented multiscale method are in consistence with those obtained by a single solver in the overlapping domain.Moreover,transferring different physical quantities has an important effect on the numerical results.

An Improved Coupled Level Set and Continuous Moment-of-Fluid Method for Simulating Multiphase Flows with Phase Change

An improved algorithm for computing multiphase flows is presented in which the multimaterial Moment-of-Fluid(MOF)algorithm for multiphase flows,initially described by Li et al.(2015),is enhanced addressing existing MOF difficulties in computing solutions to problems in which surface tension forces are crucial for understanding salient flow mechanisms.The Continuous MOF(CMOF)method is motivated in this article.The CMOF reconstruction method inherently removes the"checkerboard instability"that persists when using the MOF method on surface tension driven multiphase(multimaterial)flows.The CMOF reconstruction algorithm is accelerated by coupling the CMOF method to the level set method and coupling the CMOF method to a decision tree machine learning(ML)algorithm.Multiphase flow examples are shown in the two-dimensional(2D),three-dimensional(3D)axisymmetric"RZ",and 3D coordinate systems.Examples include two material and three material multiphase flows:bubble formation,the impingement of a liquid jet on a gas bubble in a cryogenic fuel tank,freezing,and liquid lens dynamics.

On the Vortex Sheets of Compressible Flows

This paper provides a review of the recent results on the stability of vortex sheets in compressible flows.Vortex sheets are contact discontinuities of the underlying flows.The vortex sheet problem is a free boundary problem with a characteristic boundary and is challenging in analysis.The formulation of the vortex sheet problem will be introduced.The linear stability and nonlinear stability for both the two-dimensional two-phase compressible flows and the two-dimensional elastic flows are summarized.The linear stability of vortex sheets for the three-dimensional elastic flows is also presented.The difficulties of the vortex sheet problems and the ideas of proofs are discussed.

Spatial Structure of China's E-commerce Express Logistics Network Based on Space of Flows

The intermediate link compression characteristics of e-commerce express logistics ne tworks influence the tradition al mode of circulation of goods and economic organization,and alter the city spatial pattern.Based on the theory of space of flows,this study adopts China Smart Logistics Network relational data to build China's e-commerce express logistics network and explore its spatial structure characteristics through social network analysis(SNA),the PageRank technique,and geospatial methods.The results are as follows:the network density is 0.9270,which is close to 1;hence,indicating that e-commerce express logistics lines between Chinese cities are nearly complete and they form a typical network structure,thereby eliminating fragmented spaces.Moreover,the average minimum number of edges is 1.1375,which indicates that the network has a small world effect and thus has a high flow efficiency of logistics elements.A significant hierarchical diffusion effect was observed in dominant flows with the highest edge weights.A diamond-structured network was formed with Shanghai,Guangzhou,Chongqing,and Beijing as the four core nodes.Other node cities with a large logistics scale and importance in the network are mainly located in the 19 city agglomerations of China,revealing the fact that the development of city agglomerations is essential for promoting the separation of experience space and changing the urban spatial pattern.This study enriches the theory of urban networks,reveals the flow laws of modern logistics elements,and encourages coordinated development of urban logistics.

Coarse-to-Fine Video Instance Segmentation With Factorized Conditional Appearance Flows

We introduce a novel method using a new generative model that automatically learns effective representations of the target and background appearance to detect,segment and track each instance in a video sequence.Differently from current discriminative tracking-by-detection solutions,our proposed hierarchical structural embedding learning can predict more highquality masks with accurate boundary details over spatio-temporal space via the normalizing flows.We formulate the instance inference procedure as a hierarchical spatio-temporal embedded learning across time and space.Given the video clip,our method first coarsely locates pixels belonging to a particular instance with Gaussian distribution and then builds a novel mixing distribution to promote the instance boundary by fusing hierarchical appearance embedding information in a coarse-to-fine manner.For the mixing distribution,we utilize a factorization condition normalized flow fashion to estimate the distribution parameters to improve the segmentation performance.Comprehensive qualitative,quantitative,and ablation experiments are performed on three representative video instance segmentation benchmarks(i.e.,YouTube-VIS19,YouTube-VIS21,and OVIS)and the effectiveness of the proposed method is demonstrated.More impressively,the superior performance of our model on an unsupervised video object segmentation dataset(i.e.,DAVIS19)proves its generalizability.Our algorithm implementations are publicly available at https://github.com/zyqin19/HEVis.

Influence of Cavitation on Unsteady Vortical Flows in a Side Channel Pump

Previous investigation on side channel pump mainly concentrates on parameter optimization and internal unsteady vortical flows.However,cavitation is prone to occur in a side channel pump,which is a challenging issue in promoting performance.In the present study,the cavitating flow is investigated numerically by the turbulence model of SAS combined with the Zwart cavitation model.The vapors inside the side channel pump firstly occur in the impeller passage near the inlet and then spread gradually to the downstream passages with the decrease of NPSHa.Moreover,a strong adverse pressure gradient is presented at the end of the cavity closure region,which leads to cavity shedding from the wall.The small scaled vortices in each passage reduce significantly and gather into larger vortices due to the cavitation.Comparing the three terms of vorticity transport equation with the vapor volume fraction and vorticity distributions,it is found that the stretching term is dominant and responsible for the vorticity production and evolution in cavitating flows.In addition,the magnitudes of the stretching term decrease once the cavitation occurs,while the values of dilatation are high in the cavity region and increase with the decreasing NPSHa.Even though the magnitude of the baroclinic torque term is smaller than vortex stretching and dilatation terms,it is important for the vorticity production along the cavity surface and near the cavity closure region.The pressure fluctuations in the impeller and side channel tend to be stronger due to the cavitation.The primary frequency of monitor points in the impeller is 24.94 Hz and in the side channel is 598.05 Hz.They are quite corresponding to the shaft frequency of 25 Hz(fshaft=1/n=25 Hz)and the blade frequency of 600 Hz(fblade=Z/n=600 Hz)respectively.This study complements the investigation on cavitation in the side channel pump,which could provide the theoretical foundation for further optimization of performance.

Corrigendum to “The transition from conservative to dissipative flows in class-B laser model with fold-Hopf bifurcation andcoexisting attractors”

Recently, we received a letter from Prof. G. L. Oppo, which indicated that he had doubts about the transformation of the system in the article Chin. Phys. B 31 060503 (2022) and gave other considerations. After inspection, we found that there was a clerical error in the article. Based on this, we have made corrections and supplements to the original article.