Two-dimensional Hydrodynamic Model Research Articles

A spatially distributed hydrodynamic model framework for urban flood hydrological and hydraulic processes involving drainage flow quantification

Two-dimensional hydrodynamic models are increasingly used to predict overland surface water flooding in urban catchments. The complexity of urban surfaces and subsurface drainage systems poses great challenges to modelling urban rainfall-runoff and flood hydraulics. This work develops a spatially distributed hydrodynamic model framework incorporating both hydrological and hydraulic processes of surface and subsurface drainage processes during urban flooding. The model is built upon 2D full shallow water equations solved by a Godunov-type finite volume method with robust treatments of the bed source term. To properly involve drainage flow effects, we present three methods to quantify the drainage flow discharge and its delay time which affect both urban hydrology and surface inundation. Besides, a simple OpenMPI-based parallel algorithm is applied to accelerate the model and ensure computational efficiency when applied to real-world events. The model framework is justified through the validations with five benchmark cases. Benchmark results indicate that the well-balanced treatment of bed source term ensures the model applicability in irregular urban surfaces, the model can predict both urban surface inundation and flood hydrograph, and the proposed drainage flow treatments can well reproduce drainage flow hydrograph. The model framework is successfully applied to simulate rainstorm-induced flood events in a rural–urban catchment, the upper Shenzhen River catchment. Results further demonstrate the robust capability of the model in the quantification of flow exchange between surface and subsurface systems to some extent even in the absence of drainage information. Our framework provides a practical solution for urban flood simulation even when pipe data are scarce.

Assessing the impact of climate change on fluvial flood losses in urban areas: a case study of Pamplona (Spain)

ABSTRACT Climate change is expected to increase the frequency and magnitude of flooding. Furthermore, in recent years, there has been an increase in city extent and population densities. This study considers the metropolitan area of Pamplona (Spain) as a case study. The delta changes in precipitation quantiles in the Arga River catchment, obtained from 12 climate models, have been transformed into peak flow delta changes using the Real-time Interactive Basin Simulator (RIBS) model. Also, three percentiles of flood quantile delta changes are selected. Water depths and flood extents expected in future flood events have been obtained using the two-dimensional Iber hydrodynamic model. The Safer_DAMAGE algorithm has been used to assess flood losses in urban areas at the building scale. The results show that flood losses are expected to be smaller for low return periods and greater for high return periods.

Application of a Linked Hydrodynamic–Groundwater Model for Accurate Groundwater Simulation in Floodplain Areas: A Case Study of Irtysh River, China

The rich biodiversity in the floodplain area is influenced by both floodplain floods and groundwater (GW). To protect the ecological environment in the floodplain area, it is essential to study the interaction between floodplain floods and GW. The objective of this paper is to propose a coupling strategy between a hydrodynamic model and a GW model to provide an accurate simulation tool for quantifying the interaction between floodplain floods and GW. The case study is conducted in the floodplain area of the middle reaches of the Irtysh River in northwest China. Firstly, a two-dimensional hydrodynamic model based on TELEMAC-2D is constructed to accurately simulate floodplain floods under wetting and drying conditions. Secondly, a GW model based on MODFLOW is developed. Finally, a coupling strategy is proposed to achieve accurate and efficient integration between the hydrodynamic model and the GW model. The calibration and verification results of the model demonstrate high accuracy, with root mean squared error (RMSE) values of 0.51 m and 0.77 m between observed and calculated GW levels for the hydrodynamic–GW coupled model. The water balance results indicate that floodplain floods serve as the largest GW recharge source in the study area, while phreatic evaporation is the primary GW discharge item. This paper represents a novel attempt to couple a two-dimensional hydrodynamic model with a GW model. The research results provide a scientific tool for the ecological restoration of floodplain areas considering both surface water and GW, as well as the comprehensive management and regulation of wetland water resources and the water environment.

Dynamic risk assessment of urban flood disasters based on functional area division—A case study in Shenzhen, China

The assessment of urban flood risk plays a vital role in disaster prevention and mitigation. This work aims to assess the dynamic risk of urban flood triggered by population movements through dividing urban functional zoning from the perspective of collective cognition. Firstly, the urban functional areas are identified using Points of Interest data and then the population movements mobile is detected based on functional areas using mobile signaling big data. Then, one-dimensional and two-dimensional hydrodynamic models are employed to simulate the 50-year flood scenario in Futian District, Shenzhen. Finally, a spatio-temporal dynamic assessment model for urban flood risk is constructed based on the extent of inundation, water depth, population density, and the disaster-bearing capacity of functional areas. The research findings are as follows: (1) Futian District's urban planning showcases harmonious integration of single-function and mixed-function areas. Utilizing the 50% perception standard efficiently identifies distinct functional types across diverse urban zones. The results are highly consistent with the actual situation. (2) During morning peak hours, the population exhibits a nuanced pattern of dispersal, concentration, and transition. Lunchtime witnesses multiple central clusters forming and gradually dispersing, while the evening peak witnesses population regrouping, covering broader geographical extents. Dynamic utilization of functional areas and mobile phone signaling data outperforms static population metrics, offering deeper insights into the complexities of human activity. (3) Between 12:00 and 13:00, lunchtime movements lead to a surge of 6 high-risk zones in the central area and 5 in the Meiling area. The dynamic flood risk assessment model, based on functional area delineation, effectively identifies disparities and fluctuations in flood risk across diverse functional areas during rainfall scenarios, ensuring heightened precision and accuracy in risk assessment.

Applying flow convergence routing to control sediment erosion and deposition locations in a dam's backwater zone

Despite studies showing that dams have significant effects on the sediment dynamics and evolution of a river upstream of a dam, the knowledge of relationships between river topography and sediment transport in a dam's backwater zone has hardly been applied in reservoir sedimentation management. This study investigated the potential of an alternating sequence of engineered topographic nozzles and oversized landforms, utilizing flow convergence routing theory, to redistribute sediment erosion foci in a dam's backwater zone for remote mountain reservoirs with a sediment storage capacity of ~105 m3. To test scientific ideas and engineering alternatives, the current topography of the backwater zone upstream from Our House Dam on the confined, mountainous Middle Yuba River, California, was virtually re-contoured into different scenarios for numerical experimentation. As most of the dam's backwater zone is filled with sediment (a common global problem) in a narrow, confined canyon, two-dimensional hydrodynamic modeling was useful for evaluating erosion patterns resulting from different manipulations. The results found that high velocity concentrates through nozzles and dissipates through oversized landforms, resulting in the latter exhibiting hydraulics indicative of functioning as sediment settling basins. These basins can be located away from the dam where key infrastructure needs clearance from sedimentation. As flow increases through the sequence of nozzles and oversized landforms, each nozzle's hydraulic jet will persist farther into the oversized area. Moderate in-channel flow (daily recurrence of ~5–30 %) was best for creating conditions to force deposition of sediment in oversized landforms. At high enough discharge (recurrence of <1–5 %) significant sediment erosion can occur throughout the constructed terrain in the backwater zone, so the whole topographic scheme can become overwhelmed and ineffective. Thus, the performance of re-contouring as an aid in reservoir sedimentation management is location and flow-dependent, necessitating careful design refinement for local conditions and assessment of financial benefits and costs. Overall, this study opens a new realm of sediment management for dam operators and regulators hard-pressed to know what to do when a moderate-sized mountain reservoir with poor accessibility has a sediment storage capacity of ~105 m3.

Understanding the effect of long term and short term hydrological components on landscape ecosystem

Modifications in river morphology are witnessed due to the hydrological fluctuations leading to braided rivers and sandbar developments. Understanding the hydrological alterations could offer crucial insight into the ecosystem's landscape pattern. To comprehend flood and drought in an agricultural ecosystem, we investigated the impact of short-term water level changes from 1999 to 2015. Numerical simulations were carried out on the fluctuant streamflow at different seasons in a braided river using a two-dimensional hydrodynamic model. The number of consecutive wet days (CWD), average wet days (AWD), consecutive dry days (CDD), and average dry days (ADD) were computed. The Standardized Streamflow Index (SSFI-4) was determined at a seasonal time scale, which is used to quantify the streamflow-based hydrological droughts. The calibration and validation of the hydrodynamic model was done with the measured velocity. To understand the planform geometry of the river, satellite images were derived for the historical period from 1976 to 80 till 2016–17. The Planform Index (PI) and Sinuosity Index (SI) were used to assess and classify the river into straight, braided and meander categories. Speedy modifications were observed across the longitudinal profile, with PFI varying between 3.72 and 42.8. Sandbars being an imperative asset for floodplain communities and dwellers, the effect of these fluctuations was studied in different landscape classes. We analyzed the changes in the spatial and temporal characteristics of dynamic landscape patterns between 2004 and 2014 at quinquennial and decadal scales. We found that a substantial-high water level from a 2010 flood led to a drastic change in the landscape pattern of the ecosystem. In addition, consecutive dry days witnessed over the sandbar regions affect the agriculture cropping patterns. Post flooding, the expansion of land under agriculture could be inferred from the fact that sediment was fertile and deposited after the flood recession; agriculture was dominantly practiced in the region. Overall, the study demonstrated that various hydrological components typically impact the spatial distribution characteristics of landscape patterns.

Two dimensional Hydrodynamic Simulation in Labuan Bajo Waters, Indonesia.

Based on its strategic location, Labuan Bajo is a golden triangle between Komodo Island and Toraja Land as a national tourism sector. This makes information about the condition of Labuan Bajo waters very important. One of the oceanographic parameters that have an important role in determining the condition of a body of water is ocean currents. Ocean currents are the movement or displacement of water masses caused by waves, wind, water density, and pressure. In their movement, currents have a direction and speed that can form ocean current patterns. One method that can see patterns of sea surface currents is two-dimensional hydrodynamic modeling. This study aims to identify patterns of surface currents and tides that occur in Labuan Bajo waters. The method used in this study is quantitative descriptive with a two-dimensional hydrodynamic modeling approach along with nested-model techniques to provide the model results with a smaller resolution to get the phenomenon that occurs in those waters. The data used is bathymetry, wind, tide, and High-Frequency Radar (HF Radar) data as current validation. The results of surface current simulation in Labuan Bajo waters have the highest current of >1.12 m/s in the Western season and the lowest speed of 0.88 m/s in the Transition I season. The wind pressure gradient in the Western season affects the current speed in that season.

Spectral energy distributions of classical Cepheids in the Magellanic Clouds

In this study, we constructed spectral energy distributions (SEDs) for a sample of 142 Large Magellanic Cloud (LMC) and 77 Small Magellanic Cloud (SMC) fundamental-mode classical Cepheids (CCs) using photometric data from the literature. When possible, the data were taken to be representative of mean light or averaged over the light curve. The sample was built from stars that either have a metallicity determination from high-resolution spectroscopy or have been used in Baade-Wesselink types of analyses, or have a radial velocity curve published in Gaia DR3 or have Walraven photometry, or have their light- and radial-velocity curves modelled by pulsation codes. The SEDs were fitted with stellar photosphere models to derive the best-fitting luminosity and effective temperature. Distance and reddening were taken from the literature. Only one star with a significant infrared (IR) excess was found in the LMC and none in the SMC. IR excess in MW CCs is not uncommon suggesting that IR excess may be more prominent in MW cepheids than in the Magellanic Clouds. The stars were plotted in a Hertzsprung-Russell diagram (HRD) and compared to evolutionary tracks for CCs and to theoretical instability strips. For the large majority of stars, the position in the HRD is consistent with the instability strip. Period-luminosity (PL) and period-radius relations were derived and compared to these relations in the MW. For a fixed slope, the zero point of the bolometric PL relation does not depend on metallicity, contrary to recent findings of a significant metallicity term when considering the PL relation in different photometric bands. The mass-luminosity (ML) relation is derived and it points to an over luminosity of about +0.3 dex with respect to a canonical ML relation. The most intriguing result concerns the flux-weighted gravity (FWG, a quantity derived from gravity and effective temperature) and its relation to period and luminosity. Both relations agree with theory, with the results for the MW and with the independent estimates from the six known LMC eclipsing binaries that contain CCs. However, the FWG (as determined from dedicated high-resolution spectroscopy for the sample) is too low by about 0.8 dex in 90% of the cases. Recent works on time-series data on 20 CCs in the MW were analysed finding a similar (but less extreme) offset in gravity and the FWG. Most importantly, other time-series data on the same 20 CCs are in full agreement with the FWG-period relation. The observed time-series of spectroscopic data and from a two-dimensional hydrodynamical cepheid model was used to investigate the so-called effective gravity, that is, the gravity corrected for a dynamical term related to the time derivative of the radial velocity. There is a reasonable good correspondence between the predicted effective gravity and the observed gravity as a function of pulsation phase, which would potentially allow for an independent estimate of the projection factor, but the dynamical term is too small to explain the overall difference between the observed (flux-weighted) gravity and the (flux-weighted) gravity derived from the SED modelling and stellar mass estimates.

The Hydrodynamic Impact of the South-to-North Water Diversion Project on the Lower-reach Lake of Nansi Lake

In order to study the changes in hydrodynamic characteristics of the lower-reach lake of Nansi Lake, this paper established a two-dimensional hydrodynamic model of the lower-reach lake of Nansi Lake based on topography, like rainfall, evaporation, and wind field of the lower-reach lake of Nansi Lake, and carried out water level verification, which is representative and can reflect the process of water level and flow velocity changes of the lower-reach lake of Nansi Lake before and after the South-to-North Water Transfer. The model results show that, before the Nansi Lake was connected to water, the lake area of Zhaoyang Lake in the north was long and narrow and the water level was high. The overall flow velocity of Weishan Lake was low, and the stagnant water area and low flow velocity area accounted for a large proportion. After the opening of the southern four lakes, the high-water level area is concentrated in the wide Weishan Lake area, the water level in the Zhaoyang Lake area is reduced, and the changes between different water level gradients tend to be gentler, and the mobility of the water body is greatly improved.

Modeling Cyanotoxin Production, Fate, and Transport in Surface Water Bodies Using CE-QUAL-W2

Cyanobacteria are frequently associated with forming toxic blooms. The toxins produced by cyanobacteria, cyanotoxins, are harmful to both humans and animals. Rising temperatures due to global climate change are expected to increase the occurrence of cyanobacteria, and it is vital that we protect our drinking water supplies and natural water resources. Modeling the production, fate, and transport of these toxins is an important step in limiting exposure to them and evaluating management strategies to mitigate their impact. The research provided here offers an overview of some of the main cyanotoxins of concern and presents preliminary models for the transport and fate of these toxins. Cyanotoxins can be either intracellular or extracellular, and a model for each was developed. The models were incorporated into the two-dimensional (longitudinal and vertical) hydrodynamic and water quality model CE-QUAL-W2. The toxin models were tested using a model of Henry Hagg Lake (Oregon, USA). The models were able to produce similar trends as found in published data, but since the toxin data available at Henry Hagg Lake was minimal, no direct comparisons between model results and field data were made. Four scenarios were conducted to test the functionality of the toxin models in CE-QUAL-W2. The predicted results from each test scenario matched the expected outcomes based on the parameters used in each scenario. Further applications of the toxin models to other water bodies with more consistent toxin data will help verify the accuracy of the models. This research provides a first step at modeling cyanotoxins using CE-QUAL-W2 and provides a framework to further develop the models through continued research of the cyanotoxins.

Correction to: Two-dimensional hydrodynamic modeling for prediction of bank erosion and bed incision in the Indus River

Correction to: Two-dimensional hydrodynamic modeling for prediction of bank erosion and bed incision in the Indus River

Ecological and navigational impact of the construction and operation of the Qingyuan dam

Dam construction has important impact on the ecological environment and navigation conditions of a river. Therefore, evaluating the degree of impact of such engineering constructions and seeking the optimum management are vital. This study considered the example of the construction of the Qingyuan Dam on the Beijiang River (China). The flow condition was calculated using a two-dimensional hydrodynamic model, and a habitat suitability model and navigation risk indicators were used to conduct quantitative assessment of the impact of different scenarios. The spawning ground habitat of Megalobrama terminalis was taken as an ecological measurement index. The gray correlation analysis method was used to quantify the influence of four flow indexes (i.e., water surface slope, backflow, flow velocity, and water depth) on navigation safety. The simulation results showed that construction of the Qingyuan Dam had serious negative impact on the ecological environment in the dry season, but that dry season navigation conditions have been improved greatly. Following construction of the dam, with increase in the Feilaixia Hydro-junction discharge, the ecological and navigable usable area both first increased and then decreased. With comprehensive consideration of the usable area and the spatial distributions of habitat suitability and navigation risk, when the Feilaixia Hydro-junction discharge is 3000 m3/s and the water level in front of the Qingyuan Dam is 10 m, the ecological and navigation benefits of the studied river reach were determined to be optimal. These research results could provide guidance for the management of the Feilaixia–Qingyuan river section, and help deliver optimum ecological and navigational benefits.

Two-dimensional hydrodynamic modeling for prediction of bank erosion and bed incision in the Indus River

Two-dimensional hydrodynamic modeling for prediction of bank erosion and bed incision in the Indus River

Multiparameter flood hazard, socioeconomic vulnerability and flood risk assessment for densely populated coastal city

In the current study, flood risk assessment of densely populated coastal urban Surat City, on the bank of the lower Tapi River in India, was conducted by combining the hydrodynamic model-based flood hazard and often neglected socioeconomic vulnerability. A two-dimensional (2D) hydrodynamic (HD) model was developed using physically surveyed topographic data and the existing land use land cover (LULC) of the study area (5248 km2). The satisfactory performance of the developed model was ascertained by comparing the observed and simulated water levels/depths across the river and floodplain. The 2D HD model outputs with geographic information system (GIS) applications were further used to develop probabilistic multiparameter flood hazard maps for coastal urban city. During a 100-year return period flood (Peak discharge = 34,459 m3/s), 86.5% of Surat City and its outskirt area was submerged, with 37% under the high hazard category. The north and west zones are the worst affected areas in Surat City. The socioeconomic sensitivity and adaptive capacity indicators were selected at the city's lowest administrative (ward) level. The socioeconomic vulnerability was evaluated by employing the robust data envelopment analysis (DEA) technique. Fifty-five of 89 wards in Surat City, covering 60% of the area under the jurisdiction of the Municipal Corporation, are highly vulnerable. Finally, the flood risk assessment of the city was conducted using a bivariate technique describing the distinctive contribution of flood hazard and socioeconomic vulnerability to risk. The wards adjoining the river and creek are at high flood risk, with an equal contribution of hazard and vulnerability. The ward-level hazard, vulnerability, and risk assessment of the city will help local and disaster management authorities to priorities high risk areas while planning flood management and mitigation strategies.

Numerical investigation on the coupled vibrations of piezoelectric energy harvester with a liquid-filled proof mass

Replacing the solid tip mass of a piezoelectric cantilever beam with a liquid-filled mass can increase its frequency bandwidth due to the effect of nonlinear liquid sloshing. To investigate the coupled vibrations of the piezoelectric beam and the sloshing liquid, as well as their contributions to the output power, a coupled two-dimensional finite element method-smoothed particle hydrodynamics model has been developed in this study. Using this model, the dynamic behavior of a piezoelectric beam with a liquid-filled rectangular container as the tip mass, subjected to vertical harmonic excitation, has been investigated. The effects of parametric sloshing, excitation level, and geometric nonlinearity on the output voltages have been studied in detail. The simulation results indicate that: (a) the parametric sloshing in the liquid container exhibits subharmonic characteristics, which can be triggered by matching the excitation frequency to twice the natural frequency of the sloshing mode; (b) the piezoelectric beam exhibits subharmonic or harmonic oscillations at parametric resonance; (c) due to the effect of coupled vibrations, the energy harvester with a liquid-filled proof mass has a broader bandwidth compared to the traditional harvester; (d) the frequency response diagram of the output voltage shows multiple peaks at high excitation amplitudes, and the bifurcations are caused by parametric sloshing.

Magnitude of formative flows in stream potholes

Although it is generally recognized that geomorphic work is tied to bedrock channel reshaping, the importance of low vs. high flow stages that cause the most geomorphic impact remains unclear. The objective of the research is to study the concept of “formative flow” in bedrock channels and determine, through morphological studies, if those flows have any impact on sculpted features such as potholes and how this relationship relates to various inputs such as flow stages (magnitude and frequency), shear stress, and sediment size. Here, we studied the distribution of the main pothole typologies and tried to understand why potholes are found along bedrock river channels. Specifically, we examined stream potholes from three locations along the Spanish Central System: Alberche, Tietar, and Manzanares rivers. We conducted the research by taking precise geometric measurements, classifying potholes, analyzing flow magnitude and frequency, and using a two-dimensional (2D) hydrodynamic model to assess key variables in Manzanares river. This research demonstrated that bankfull depths completely cover all pothole typologies in all the analyzed sites but are not sufficient to achieve its formative flow depth (FFD). Using a detailed 2D hydrodynamic model in Manzanares river, we discovered that dimensions of cylindrical potholes are closely related to bankfull discharge and that this depth is connected to FFD. Other potholes, such as erosive-compound and erosive-lateral, are historical remnants, and their shapes are not related to any particular FFD and are likely associated with rare events and catastrophic breaks. A collection of laterals that exhibit FFD near bankfull flows appear to represent a part of the recent evolution of a knickpoint. To summarize, it can be inferred from the findings that the utility of morphological analysis in conjunction with the 2D hydrodynamic model is to examine the fraction of erosional/active features to determine the degree of senescence and/or change in natural conditions in a river reach.

Coseismic river avulsion on surface rupturing faults: Assessing earthquake-induced flood hazard.

Surface-rupturing earthquakes can produce fault displacements that abruptly alter the established course of rivers. Several notable examples of fault rupture-induced river avulsions (FIRAs) have been documented, yet the factors influencing these phenomena have not been examined in detail. Here, we use a recent case study from New Zealand's 2016 Kaikōura earthquake to model the coseismic avulsion of a major braided river subjected to ~7-m vertical and ~4-m horizontal offset. We demonstrate that the salient characteristics of the avulsion can be reproduced with high accuracy by running a simple two-dimensional hydrodynamic model on synthetic (pre-earthquake) and "real" (post-earthquake) deformed lidar datasets. With adequate hydraulic inputs, deterministic and probabilistic hazard models can be precompiled for fault-river intersections to improve multihazard planning. Flood hazard models that ignore present and potential future fault deformation may underestimate the extent, frequency, and severity of inundation following large earthquakes.

Rainwater harvesting systems: An urban flood risk mitigation measure in arid areas

Rainwater harvesting (RWH) systems have been developed to compensate for shortage in the water supply worldwide. Such systems are not very common in arid areas, particularly in the Gulf Region, due to the scarcity of rainfall and their reduced efficiency in covering water demand and reducing water consumption rates. In spite of this, RWH systems have the potential to reduce urban flood risks, particularly in densely populated areas. This study aimed to assess the potential use of RWH systems as urban flood mitigation measures in arid areas. Their utility in the retention of stormwater runoff and the reduction of water depth and extent were evaluated. The study was conducted in a residential area in Bahrain that experienced waterlogging after heavy rainfall events. The water demand patterns of housing units were analyzed, and the daily water balance for RWH tanks was evaluated. The effect of the implementation of RWH systems on the flood volume was evaluated with a two-dimensional hydrodynamic model. Flood simulations were conducted in several rainfall scenarios with different probabilities of occurrence. The results showed significant reductions in the flood depth and flood extent, but these effects were highly dependent on the rainfall intensity of the event. RWH systems are effective flood mitigation measures, particularly in urban arid regions short of proper stormwater control infrastructure, and they enhance the resilience of the built environment to urban floods.

Development of a Two-Dimensional Hybrid Sediment-Transport Model

This paper presents the development of a two-dimensional hydrodynamic sediment transport model using the finite volume method based on a collocated unstructured hybrid-mesh system consisting of triangular and quadrilateral cells. The model is a single-phase nonequilibrium sediment-transport model for nonuniform and noncohesive sediments in unsteady turbulent flows that considers multiple sediment-transport processes such as deposition, erosion, transport, and bed sorting. This model features a hybrid unstructured mesh system for easy mesh generation in complex domains. To avoid interpolation from vertices in conventional unstructured models, this model adopted a second-order accurate edge-gradient evaluation method to consider the mesh irregularities based on Taylor’s series expansion. In addition, the multipoint momentum interpolation corrections were integrated to avoid possible nonphysical oscillations during the wetting-and-drying process, common in unsteady sediment transport problems, to ensure both numerical stability and numerical accuracy. The developed sediment transport model was validated by a benchmark degradation case for the erosion process with armoring effects, a benchmark aggradation case for the deposition process, and a naturally meandering river for long-term unsteady sediment-transport processes. Finally, the model was successfully applied to simulate sediment transport in a reservoir that was significantly affected by typhoon events.

Analysis of Flow Characteristics around a Square Cylinder with Boundary Constraint

Based on the two-dimensional hydrodynamic model of the finite volume method and structured multigrid, the flow characteristics around a square cylinder with boundary constraint are analysed. The gap ratio G/D (G is the distance from the cylinder to the channel boundary, and D is the side length of the square cylinder) does not change the four flow patterns. Under the laminar vortex street phase, the boundary constraint only reduces the scale of the vortices. The vortex centres are pressed toward the boundaries of the channel, and a low velocity zone is formed near the boundary, but the law of vorticity attenuation along the flow direction is not changed. The flow pattern classification map shows that the boundary constraint increases the Reynolds number required to generate the turbulence flow pattern, and the range of the Reynolds number in the flow pattern of the laminar vortex street has a maximum increase range. The correlation between the time-averaged drag coefficient or the vortex shedding frequency and Reynolds number under different gap ratios indicates that the resistance of the square cylinder and the vortex shedding frequency increase accordingly with the strengthening of the boundary constraint. When G/D &lt; 3.5, the increase is particularly obvious. Meanwhile, the correlation characteristics between the resistance or the vortex shedding frequency of the square cylinder and the Reynolds number are unrelated to the boundary constraint strength.