CONVERGENCE RATE OF SOLUTIONS TO STRONG CONTACT DISCONTINUITY FOR THE ONE-DIMENSIONAL COMPRESSIBLE RADIATION HYDRODYNAMICS MODEL

This paper is concerned with a singular limit for the one-dimensional compress- ible radiation hydrodynamics model. The singular limit we consider corresponds to the physical problem of letting the Bouguer number infinite while keeping the Boltzmann number constant. In the case when the corresponding Euler system admits a contact discontinuity wave, Wang and Xie （2011） [12] recently verified this singular limit and proved that the solution of the compressible radiation hydrodynamics model converges to the strong contact 1 discontinuity wave in the L∞-norm away from the discontinuity line at a rate of ε1/4, as the reciprocal of the Bouguer number tends to zero. In this paper, Wang and Xie＇s convergence rate is improved to ε7/8 by introducing a new a priori assumption and some refined energy estimates. Moreover, it is shown that the radiation flux q tends to zero in the L∞-norm away from the discontinuity line, at a convergence rate as the reciprocal of the Bouguer number tends to zero.

ONE-AND TWO-DIMENSIONAL COUPLED HYDRODYNAMICS MODEL FOR DAM BREAK FLOW

1-D and 2-D mathematical models for dam break flow were established and verified with the measured data in laboratory. The 1-D and 2-D models were then coupled, and used to simulate the dam break flow from the reservoir tail to the dam site, the propagation of dam break waves in the downstream channel, and the submergence of dam break flow in the downstream town with the hydrodynamics method. As a numerical example, the presented model was employed to simulate dam break flow of a hydropower station under construction. In simulation, different dam-break durations, upstream flows and water levels in front of dam were considered, and these influencing factors of dam break flow were analyzed, which could be referenced in planning and designing hydropower stations.

A Vertical Two-Dimensional Model to Simulate TidalHydrodynamics in A Branched Estuary

A vertical (laterally averaged) two-dimensional hydrodynamic model is developed for tides, tidal current, and salinity in a branched estuarine system. The governing equations are solved with the hydrostatic pressure distribution assumption and the Boussinesq approximation. An explicit scheme is employed to solve the continuity equations. The momentum and mass balance equations are solved implicitly in the Cartesian coordinate system. The tributaries are governed by the same dynamic equations. A control volume at the junctions is designed to conserve mass and volume transport in the finite difference schemes, based on the physical principle of continuum medium of fluid. Predictions by the developed model are compared with the analytic solutions of steady wind-driven circulatory flow and tidal flow. The model results for the velocities and water surface elevations coincide with analytic results. The model is then applied to the Tanshui River estuarine system. Detailed model calibration and verification have been conducted with measured water surface elevations, tidal current, and salinity distributions. The overall performance of the model is in qualitative agreement with the available field data. The calibrated and verified numerical model has been used to quantify the tidal prism and flushing rate in the Tanshui River-Tahan Stream, Hsintien Stream, and Keelung River.

Numerical analysis of submarine landslides using a smoothed particle hydrodynamics depth integral model

Submarine landslides can cause severe damage to marine engineering structures. Their sliding velocity and runout distance are two major parameters for quantifying and analyzing the risk of submarine landslides.Currently, commercial calculation programs such as BING have limitations in simulating underwater soil movements. All of these processes can be consistently simulated through a smoothed particle hydrodynamics（SPH） depth integrated model. The basis of the model is a control equation that was developed to take into account the effects of soil consolidation and erosion. In this work, the frictional rheological mode has been used to perform a simulation study of submarine landslides. Time-history curves of the sliding body＇s velocity, height,and length under various conditions of water depth, slope gradient, contact friction coefficient, and erosion rate are compared; the maximum sliding distance and velocity are calculated; and patterns of variation are discussed.The findings of this study can provide a reference for disaster warnings and pipeline route selection.

Analytical model of non-uniform charge distribution within the gated region of GaN HEMTs

A physics-based analytical expression that predicts the charge,electrical field and potential distributions along the gated region of the GaN HEMT channel has been developed.Unlike the gradual channel approximation(GCA),the proposed model considers the non-uniform variation of the concentration under the gated region as a function of terminal applied volt-ages.In addition,the model can capture the influence of mobility and channel temperature on the charge distribution trend.The comparison with the hydrodynamic(HD)numerical simulation showed a high agreement of the proposed model with numerical data for different bias conditions considering the self-heating and quantization of the electron concentration.The ana-lytical nature of the model allows us to reduce the computational and time cost of the simulation.Also,it can be used as a core expression to develop a complete physics-based transistorⅣmodel without GCA limitation.

GLOBAL SOLUTIONS TO A HYDRODYNAMIC MODEL FOR SEMICONDUCTORS WITH VELOCITY RELAXATION

In this paper,we apply the method given in the paper“Zero relaxation time limits to a hydrodynamic model of two carrier types for semiconductors”(Mathematische Annalen,2022,382:1031–1046)to study the Cauchy problem for a one dimensional inhomogeneous hydrodynamic model of two-carrier types for semiconductors with the velocity relaxation.

A novel lattice model integrating the cooperative deviation of density and optimal flux under V2X environment

A novel lattice hydrodynamic model is proposed by integrating the cooperative deviation of density and optimal flux under vehicle to X(V2X) environment. According to the theoretical analysis, the stability conditions and the mKdV equations affected by the cooperative deviation of traffic information are explored. And the density wave, hysteresis loop and energy consumption of the traffic flow have been investigated via numerical simulation. The results indicate that the cooperative deviation of density and optimal flux can effectively alleviate the traffic congestion. More importantly, our new consideration can reduce fuel consumption and exhaust emission under the V2X environment.

Lagrangian coherent structure analysis on transport of Acetes chinensis along coast of Lianyungang,China

Spatial heterogeneity or“patchiness”of plankton distributions in the ocean has always been an attractive and challenging scientific issue to oceanographers.We focused on the accumulation and dynamic mechanism of the Acetes chinensis in the Lianyungang nearshore licensed fishing area.The Lagrangian frame approaches including the Lagrangian coherent structures theory,Lagrangian residual current,and Lagrangian particle-tracking model were applied to find the transport pathways and aggregation characteristics of Acetes chinensis.There exist some material transport pathways for Acetes chinensis passing through the licensed fishing area,and Acetes chinensis is easy to accumulate in the licensed fishing area.The main mechanism forming this distribution pattern is the local circulation induced by the nonlinear interaction of topography and tidal flow.Both the Lagrangian coherent structure analysis and the particle trajectory tracking indicate that Acetes chinensis in the licensed fishing area come from the nearshore estuary.This work contributed to the adjustment of licensed fishing area and the efficient utilization of fishery resources.

Numerical simulation of typhoon- induced storm surge on the coast of Jiangsu Province,China,based on coupled hydrodynamic and wave models

In order to facilitate engineering design and coastal flooding protection, the potential storm surge induced by a typhoon is studied.Using an unstructured mesh, a coupled model which combines the advanced circulation （ ADCIRC ） hydrodynamic model and simulating waves nearshore （ SWAN ） model is applied to analyze the storm surge and waves on the coast of Jiangsu Province.The verifications of wind velocity, tidal levels and wave height show that this coupling model performs well to reflect the characteristics of the water levels and waves in the studied region.Results show that the effect of radiation stress on storm surge is significant, especially in shallow areas such as the coast of Jiangsu Province and the Yangtze estuary.By running the coupled model, the simulated potential flooding results can be employed in coastal engineering applications in the Jiangsu coastal area, such as storm surge warnings and extreme water level predictions.

AUV Modeling and Motion Control Strategy Design

To provide a suitable model for AUV simulation and control purposes, a general nonlinear dynamic model including a novel thruster hydrodynamics model was derived. Based on the modeling method, the "AUV-XX" simulation platform was established to carry out fundamental tests on its motion characteristics, stability, and controllability. A motion control strategy consisting of both position and speed control in a horizontal plane was designed for different task assignments of underwater vehicles. Combined control of heave and pitch was adopted to compensate for the reduction of vertical tunnel thrusters when the vehicle is moving at a high speed. An improved S-surface controller based on the capacitor plate model was developed with flexible gain selections made possible by different forms of restricting the error and changing the rate of the error. Simulation results show that the derived general mathematical model together with simulation platform can provide a test bed for fundamental tests of motion control. Additionally, the capacitor plate model S-surface control shows a good performance in guiding the vehicle to achieve the desired position and speed with sufficient accuracy.

Full 2D Hydrodynamic Modelling of Rainfall-induced Flash Floods

Mountain catchments are prone to flash flooding due to heavy rainfall. Enhanced understanding of the generation and evolution processes of flash floods is essential for effective flood risk management. However, traditional distributed hydrological models based on kinematic and diffusion wave approximations ignore certain physical mechanisms of flash floods and thus bear excessive uncertainty. Here a hydrodynamic model is presented for flash floods based on the full two-dimensional shallow water equations incorporating rainfall and infiltration. Laboratory experiments of overland flows were modelled to illustrate the capability of the model. Then the model was applied to resolve two observed flash floods of distinct magnitudes in the Lengkou catchment in Shanxi Province, China. The present model is shown to be able to reproduce the flood flows fairly well compared to the observed data. The spatial distribution of rainfall is shown to be crucial for the modelling of flash floods. Sensitivity analyses of the model parameters reveal that the stage and discharge hydrographs are more sensitive to the Manning roughness and initial water content in the catchment than to the Green-Ampt head. Most notably, as the flash flood augments due to heavier rainfall, the modelling results agree with observed data better, which clearly characterizes the paramount role of rainfall in dictating the floods. From practical perspectives, the proposed model is more appropriate for modelling large flash floods.

Water Quality Model Establishment for Middle and Lower Reaches of Hanshui River,China

With the development of industry and agriculture,nitrogen,phosphorus and other nutrients in the Hanshui River greatly increase and eutrophication has become an important threat to the water quality of the Hanshui River,especially in the middle and lower reaches.The primary objective of this study was to establish the water quality model for the middle and lower reaches of the Hanshui River based on the model of MIKE 11.The main pollutants migration and transformation process could be simulated using the water quality model.The rainfall-runoff model,hy-drodynamic model and water quality model were established using MIKE 11.The pollutants,such as chemical oxygen demand(COD),biochemical oxygen demand(BOD),ammonia nitrogen,nitrate nitrogen,phosphorus,dissolved oxy-gen(DO),were simulated and predicted using the above three models.A set of methods computing non-point source pollution load of the Hanshui River Basin was proposed in this study.The simulated and observed values of COD,BOD5,ammonia,nitrate,DO,and total phosphorus were compared after the parameter calibration of the water quality model.The simulated and observed results match better,thus the model can be used to predict water quality in the fu-ture for the Hanshui River.The pollution trend could be predicted using the water quality model according pollution load generation.It is helpful for government to take effective measures to prevent the water bloom and protect water quality in the river.

RELAXATION TIME LIMITS PROBLEM FOR HYDRODYNAMIC MODELS IN SEMICONDUCTOR SCIENCE

In this article, two relaxation time limits, namely, the momentum relaxation time limit and the energy relaxation time limit are considered. By the compactness argument, it is obtained that the smooth solutions of the multidimensional nonisentropic Euler-Poisson problem converge to the solutions of an energy transport model or a drift diffusion model, respectively, with respect to different time scales.

Lattice models of traffic flow considering drivers' delay in response

This paper proposes two lattice traffic models by taking into account the drivers＇ delay in response. The lattice versions of the hydrodynamic model are described by the differential-difference equation and difference-difference equation, respectively. The stability conditions for the two models are obtained by using the linear stability theory. The modified KdV equation near the critical point is derived to describe the traffic jam by using the reductive perturbation method, and the kink-antikink soliton solutions related to the traffic density waves are obtained. The results show that the drivers＇ delay in sensing headway plays an important role in jamming transition.

Flow difference effect in the lattice hydrodynamic model

In this paper, a new lattice hydrodynamic model based on Nagatani＇s model INagatani T 1998 Physica A 261 5991 is presented by introducing the flow difference effect. The stability condition for the new model is obtained by using the linear stability theory. The result shows that considering the flow difference effect leads to stabilization of the system compared with the original lattice hydrodynamic model. The jamming transitions among the freely moving phase, the coexisting phase, and the uniform congested phase are studied by nonlinear analysis. The modified KdV equation near the critical point is derived to describe the traffic jam, and kink -antikink soliton solutions related to the traffic density waves are obtained. The simulation results are consistent with the theoretical analysis for the new model.

Study on Model Tests and Hydrodynamic Force Models for Free Spanning Submarine Pipelines Subjected to Earthquakes

A test rig is built to model the dynamic response of submarine pipelines with an underwater shaking table in the State Key Laboratory of Coastal and Offshore Engineering, Dalian University of Technology, China. Model tests are carried out to consider the effects of exciting wave directions and types. Based on the experimental results, two hydrodynamic force models derived from Morisen equation and Wake model are presented respectively. By use of hydrodynamic force models suitable for free spanning submarine pipelines under earthquakes, diseretized equations of motion are obtained and finite element models are established to analyze dynamic response of free spanning submarine pipeline subjected to multi-support seismic excitations. The comparison of numerical results with experimental results shows that the improved Morison and Wake hydrodynamic force models could satisfactorily predict dynamic response on the free spanning submarine pipelines subjected to earthquakes.

Density waves in a lattice hydrodynamic traffic flow model with the anticipation effect

By introducing the traffic anticipation effect in the real world into the original lattice hydrodynamic model, we present a new anticipation effect lattice hydrodynamic （AELH） model, and obtain the linear stability condition of the model by applying the linear stability theory. Through nonlinear analysis, we derive the Burgers equation and Korteweg-de Vries （KdV） equation, to describe the propagating behaviour of traffic density waves in the stable and the metastable regions, respectively. The good agreement between simulation results and analytical results shows that the stability of traffic flow can be enhanced when the anticipation effect is considered.

A new lattice hydrodynamic traffic flow model with a consideration of multi-anticipation effect

We present a new multi-anticipation lattice hydrodynamic model based on the traffic anticipation effect in the real world. Applying the linear stability theory, we obtain the linear stability condition of the model. Through nonlinear analysis, we derive the modified Korteweg-de Vries equation to describe the propagating behaviour of a traffic density wave near the critical point. The good agreement between the simulation results and the analytical results shows that the stability of traffic flow can be enhanced when the multi^anticipation effect is considered.

Coupled 2D Hydrodynamic and Sediment Transport Modeling of Megaflood due to Glacier Dam-break in Altai Mountains,Southern Siberia

One of the largest known megafloods on earth resulted from a glacier dam-break,which occurred during the Late Quaternary in the Altai Mountains in Southern Siberia.Computational modeling is one of the viable approaches to enhancing the understanding of the flood events.The computational domain of this flood is over 9460 km2 and about 3.784 × 106 cells are involved as a 50 m × 50 m mesh is used,which necessitates a computationally efficient model.Here the Open MP(Open Multiprocessing) technique is adopted to parallelize the code of a coupled 2D hydrodynamic and sediment transport model.It is shown that the computational efficiency is enhanced by over 80% due to the parallelization.The floods over both fixed and mobile beds are well reproduced with specified discharge hydrographs at the dam site.Qualitatively,backwater effects during the flood are resolved at the bifurcation between the Chuja and Katun rivers.Quantitatively,the computed maximum stage and thalweg are physically consistent with the field data of the bars and deposits.The effects of sediment transport and morphological evolution on the flood are considerable.Sensitivity analyses indicate that the impact of the peak discharge is significant,whilst those of the Manningroughness,medium sediment size and shape of the inlet discharge hydrograph are marginal.

STEADY-STATE SOLUTIONS FOR A ONE-DIMENSIONAL NONISENTROPIC HYDRODYNAMIC MODEL WITH NON-CONSTANT LATTICE TEMPERATURE

A one-dimensional stationary nonisentropic hydrodynamic model for semiconductor devices with non-constant lattice temperature is studied. This model consists of the equations for the electron density, the electron current density and electron temperature, coupled with the Poisson equation of the electrostatic potential in a bounded interval supplemented with proper boundary conditions. The existence and uniqueness of a strong subsonic steady-state solution with positive particle density and positive temperature is established. The proof is based on the fixed-point arguments, the Stampacchia truncation methods, and the basic energy estimates.