Development of a hybrid particle-mesh method for simulating free-surface flows

In this work the feasibility of a numerical wave tank using a hybrid particle-mesh method is investigated.Based on the fluid implicit particle method（FLIP）a formulation for the hybrid method is presented for incompressible multiphase flows involving large density jumps and wave generating boundaries.The performance of the method is assessed for a standing wave and for the generation and propagation of a solitary wave over a flat and a sloping bed.A comparison is made with results obtained with a well-established SPH package.The tests demonstrate that the method is a promising and attractive tool for simulating the nearshore propagation of waves.

Effect of Viscosity on Free-Surface Waves in Oseen Flows

Based on the complex dispersion relation for the two-dimensional free-surface waves generated by a moving body in the steady Oseen flows, the effect of viscosity on wavelength and wave amplitude was investigated by means of an asymptotic method and a numerical analysis. A comparison between the asymptotic and numerical analysis for the viscous decay factor demonstrates the validity of the perturbation expansions for the wave profile. The numerical result shows that the wavelength of viscous wave is slightly elongated in comparison with that of inviscid wave.

THREE-DIMENSIONAL NON-HYDROSTATIC MODEL FOR FREE-SURFACE FLOWS WITH UNSTRUCTURED GRID

The three-dimensional Navier-Stokes equations were solved with the fractional step method where the hydrostatic pressure component was determined first, while the non-hydrostatic component of the pressure was computed from the pressure Poisson equation in which the coefficient matrix is positive definite and symmetric. The eddy viscosity was calculated from the efficient k-ε turbulence model. The resulting model is computationally efficient and unrestricted to the CFL condition. Computations with and without hydrostatic approximation were compared for the same cases to test the validity of the conventional hydrostatic pressure assumption. The model was verified against analytical solutions and experimental data, with excellent agreement.

Large eddy simulation of free-surface flows

This paper introduces and discusses numerical methods for flee-surface flow simulations and applies a large eddy simula- tion （LES） based flee-surface-resolved CFD method to a couple of flows of hydraulic engineering interest. The advantages, dis- advantages and limitations of the various methods are discussed. The review prioritises interface capturing methods over interface tracking methods, as these have shown themselves to be more generally applicable to viscous flows of practical engineering interest, particularly when complex and rapidly changing surface topologies are encountered. Then, a LES solver that employs the level set method to capture flee-surface deformation in 3-D flows is presented, as are results from two example calculations that concern com- plex low submergence turbulent flows over idealised roughness elements and bluff bodies. The results show that the method is capable of predicting very complex flows that are characterised by strong interactions between the bulk flow and the free-surface, and permits the identification of turbulent events and structures that would be very difficult to measure experimentally.

A new three-dimensional terrain-following tidal model of free-surface flows

A three-dimensional hydrodynamic model is presented which combines a terrain-following vertical coordinate with a horizontally orthogonal curvilinear coordinate system to fit the complex bottom topography and coastlines near estuaries, continental shelves, and harbors. To solve the governing equations more efficiently, we improve the alternating direction implicit method, which is extensively used in the numerical modeling of horizontal two-dimensional shallow water equations, and extend it to a three-dimensional tidal model with relatively little computational effort. Through several test cases and realistic applications, as presented in the paper, it can be demonstrated that the model is capable of simulating the periodic to-and-fro currents, wind-driven flow, Ekman spirals, and tidal currents in the near-shore region.

Lubrication theory for free-surface flows with finite slopes and fluxes

It is known that free-surface flows with small slopes can be described by classical lubrication theory.By replacing the assumption of quasi-parallel flows with local wedge flows,the classical lubrication theory has been generalized to the situation with finite surface slopes and vanishing fluxes,e.g.,steady capillary flows with moving contact lines.In this work,this theory is further extended by imposing the contribution of finite fluxes,which can be modeled by a source/sink flow in a wedge.The resulting lubrication equation is used to investigate the surface morphologies observed in dip coating of an inclined plate,including the Landau-Levich-Derjaguin film,dimple and capillary shock.Dependence of these structures on the inclination angle and relative speed with respect to the plate is discussed in detail.Numerical solutions of the lubrication equation agree well with available asymptotic theory.

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.

A unified fractional flow framework for predicting the liquid holdup in two-phase pipe flows

Two-phase pipe flow occurs frequently in oil&gas industry,nuclear power plants,and CCUS.Reliable calculations of gas void fraction(or liquid holdup)play a central role in two-phase pipe flow models.In this paper we apply the fractional flow theory to multiphase flow in pipes and present a unified modeling framework for predicting the fluid phase volume fractions over a broad range of pipe flow conditions.Compared to existing methods and correlations,this new framework provides a simple,approximate,and efficient way to estimate the phase volume fraction in two-phase pipe flow without invoking flow patterns.Notably,existing correlations for estimating phase volume fraction can be transformed and expressed under this modeling framework.Different fractional flow models are applicable to different flow conditions,and they demonstrate good agreement against experimental data within 5%errors when compared with an experimental database comprising of 2754 data groups from 14literature sources,covering various pipe geometries,flow patterns,fluid properties and flow inclinations.The gas void fraction predicted by the framework developed in this work can be used as inputs to reliably model the hydraulic and thermal behaviors of two-phase pipe flows.

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.

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.

Computational modeling of free-surface slurry flow problems using particle simulation method

The particle simulation method is used to solve free-surface slurry flow problems that may be encountered in several scientific and engineering fields.The main idea behind the use of the particle simulation method is to treat granular or other materials as an assembly of many particles.Compared with the continuum-mechanics-based numerical methods such as the finite element and finite volume methods,the movement of each particle is accurately described in the particle simulation method so that the free surface of a slurry flow problem can be automatically obtained.The major advantage of using the particle simulation method is that only a simple numerical algorithm is needed to solve the governing equation of a particle simulation system.For the purpose of illustrating how to use the particle simulation method to solve free-surface flow problems,three examples involving slurry flow on three different types of river beds have been considered.The related particle simulation results obtained from these three examples have demonstrated that:1) The particle simulation method is a promising and useful method for solving free-surface flow problems encountered in both the scientific and engineering fields;2) The shape and irregular roughness of a river bed can have a significant effect on the free surface morphologies of slurry flow when it passes through the river bed.

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.

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.

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.

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.

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.

Dissipative free-surface solver for potential flow around hydrofoil distributed with doublets

A doublet integral equation is formulated for the two-dimensional dissipative potential flow around a hydrofoil submerged below a free-water surface. The free-water surface is assumed to involve energy dissipation, and thus it is the source of damping. A doublet panel method is developed from incorporation of the dissipative Green function approach and the doublet distributions on the hydrofoil surface. Numerical computations are implemented, and the derived numerical results are in good agreement with analytic solutions and experimental measurements.

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”.

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.