Bed Evolution Research Articles

Improving the bed movement physics of inclined grate biomass CFD simulations

Extensive research has been performed in the field of biomass combustion, particularly in terms of numerical simulations. However, only a few studies have deepened the understanding of the dynamics of packed beds and boiler grates.This paper presents and assesses a new physical solution under a comprehensive Eulerian model that tackles the complex problem of biomass movements inside a packed boiler bed. In addition, this paper improves the precision of the obtained results, expanding the application cases of the simulation model produced by the GTE research group at the University of Vigo (Spain). The modelling algorithms are based on mechanisms that represent the crumbling of biomass particles due to gravity and the movements caused by the push generated by the feeding system. The movements’ logic affects the variables involved in the biomass thermal conversion formulation, which is integrated with other combustion models previously presented by the authors.To test the performance of the presented models, a 3D experimental grate was printed and fed with biomass pellets. The performance was compared to that of the evolution of the simulated bed. Several experiments were performed to analyse parameters, such as the bed size, slope and residence time of different fuel batches. The results of the comparison show agreement in the behaviour of the model in terms of the bed size, shape and slope for different instances of the feeding process. Otherwise, the experiments show that the internal distribution of the bed layers of different batches presents some differences with the predictions. Therefore, possible improvements, such as considering a friction factor, may be applied to the model to upgrade its performance.

A Wave Input-Reduction Method Incorporating Initiation of Sediment Motion

The long-term prediction of morphological bed evolution has been of interest to engineers and scientists for many decades. Usually, process-based models are employed to simulate bed-level changes in the scale of years to decades. To compensate for the major computational effort required by these models, various acceleration techniques have been developed, namely input-reduction, model-reduction and behaviour-oriented modelling. The present paper presents a new input-reduction method to obtain representative wave conditions based on the Shields criterion of incipient motion and subsequent calculation of the sediment pick-up rate. Elimination of waves unable to initiate sediment movement leads to additional reduction of model run-times. The proposed method was implemented in the sandy coastline adjusted to the port of Rethymno, Greece, and validated against two datasets consisting of 7 and 20 and 365 days, respectively, using the model MIKE21 Coupled Model FM. The method was compared with a well-established method of wave schematization and evaluation of the model’s skill deemed the simulations based on the pick-up rate schematization method as “excellent”. Additionally, a model run-time reduction of about 50% was observed, rendering this input-reduction method a valuable tool for the medium to long-term modelling of bed evolution.

Sediment transport and bed evolution in a 180∘curved channel with lateral intake: Numerical simulations using Eulerian and Discrete Phase models

Lateral intakes are hydraulic structures used for domestic, agricultural and industrial water conveyance, characterized by a very complex three-dimensional morphodynamic behavior: since streamlines near the lateral intake are deflected, some vortices form, pressure gradient, shear and centrifugal forces at the intake generate flow separation and a secondary movement, responsible for local scour and sediment deposition. On the other side, the modeling of flows, besides the sediment transport, in curved channels implies some more complications in comparison with straight channels. In this research, this complex process has been investigated experimentally and numerically, with the mechanism of sediment transport, bed topography evolution, flow pattern and their interactions. Experiments were performed in the Laboratory of Tarbiat Modares University, Iran, where a U-shaped channel with a lateral intake was installed and dry sediment was injected at constant rate into a steady flow. Due to the spiral flow, the bed topography changes significantly and the bed forms in turn affect the sediment entering the intake. Different from the previous works on this topic which were mainly based on laboratory experiments, here, Computational Fluid Dynamics (CFD) numerical simulations with FLUENT software were also performed, specifically with the two-phase Eulerian Model (EM) and Discrete Phase Model (DPM), at the aim of evaluating their performance in reproducing the observed physical processes. This software is used for a large variety of CFD problems, but not much for simulating sediment transport phenomena and bed topography evolution. The comparison of the results obtained through the two models against the laboratory experimental data proved a good performance of both the models in reproducing the main features of the flow, for example, the longitudinal and vertical streamlines and the mechanism of particles movement. However, the EM reveals a better performance than DPM in the prediction of the secondary flows and, consequently, of the bed topography evolution, whereas the DPM well depicts the particles pattern, predicts the location of trapped particles and determines the percentage of sediment entering the intake.The numerical models so calibrated and validated were applied to other cases with different positions of the intake in the bend. The results show that mechanism of sediment entrance into the intake varies in different position. If the intake is installed in the second half of the bend, the sediment accumulates along the inner bank of the bend and enters the intake from downstream edge of intake; on the other side, if it is placed in the first half of the bend, the sediment accumulates along both the inner and the outer bends and, therefore, more sediment enters the intake. Also the results of the simulations performed with the DPM model for different positions of the lateral intake show that for all discharge ratios, the position of 120∘is the one which guarantees the minimum ratio of sediment diverted to the intake (Gr).

Crystallization and jamming in narrow fluidized beds

A fluidized bed is basically a suspension of granular material by an ascending fluid in a tube, and it has a rich dynamics that includes clustering and pattern formation. When the ratio between the tube and grain diameters is small, different behaviors can be induced by high confinement effects. Some unexpected and curious behaviors that we investigate in this paper are the crystallization and jamming of grains in liquids with velocities higher than those for incipient fluidization, supposed to maintain the grains fluidized. In our experiments, performed in a vertical tube of transparent material, different grains, water velocities, resting times, and velocity decelerations were used. An analysis of the bed evolution based on image processing shows that, after a decreasing flow that reaches a velocity still higher than that for incipient fluidization, grains become organized in lattice structures of high compactness, where they are trapped though with small fluctuations. These structures are initially localized and grow along time, in a similar manner as happens in phase transitions and glass formation. After a certain time, if the liquid velocity is slightly increased, jamming occurs, with grains being completely blocked and their fluctuation disappearing. We show that different lattice structures appear depending on the grain type. Our results provide new insights into fluidization conditions, glass-like formation, and jamming.

Role of the chemical homogenization on the microstructural and mechanical evolution of prolonged heat-treated laser powder bed fused Inconel 625

Ni-based superalloy components for high-temperature applications rely on the long term stability of the microstructure and mechanical properties at service temperatures. Nowadays, the production of such types of components is frequently performed via Additive Manufacturing (AM) technologies. Nevertheless, few studies are dedicated to understanding the behavior of AM Ni-based superalloys upon prolonged exposure to high temperatures. This work aims at studying the effect of prolonged thermal exposures on the microstructure and mechanical properties of Inconel 625 processed by laser powder bed fusion. Thermal exposures within the range of 600 °C and 900 °C for 200 h were performed on this material. The as-built and solution annealed Inconel 625 conditions were selected. The solution annealed state implies a complete chemical homogenization, typically recommended for working at high temperatures, whereas the initial as-built state is characterized by segregations and fine dendritic structures. Upon the studied prolonged thermal exposures, the peculiar as-built microstructure formed a higher quantity of phases with smaller dimensions with respect to the solution annealed condition under thermal exposures. The smaller phases of the as-built state resulted in similar mechanical properties evolution under different temperatures. Differently, the prolonged heat-treated solution annealed conditions exhibited more marked mechanical properties variations due to coarser phases.

A 2D well-balanced, coupled model of water flow, sediment transport, and bed evolution based on unstructured grids with efficient variable storage strategy

In recent decades, a few Godunov-type, finite volume two-dimensional (2D) unstructured grid, coupled flow, and sediment models (GF2DUCM) have been developed for flows over erodible beds. These kinds of models are generally analyzed as a Vertex Model (VM) that define topography at the cell vertex, which can lead to the non-conservation of mass regarding flow, sediment, and bed evolution. Here, a full cell-cantered variable storage method (Central Model or CM) is applied as the solution of the GF2DUCM. In this method, terrain elevation is defined at the cell centroids; this accurately describes the physical relations between the water depth and topography deformation. This approach can fully eliminate calculation errors in topography deformation at local cells caused by the interpolation of topography deformation at the cell vertex, and reduced uncertainty in the computation of the GF2DUCM. The model performance is systematically tested using a series of laboratory experiments, which demonstrate the mass conservation feature and high accuracy in reproducing hydrodynamic and morphological processes.

Riverbed Changes of the Uppermost Atchafalaya River, USA—A Case Study of Channel Dynamics in Large Man-Controlled Alluvial River Confluences

River confluences are important nodes for downstream sediment transport and geomorphological development. Previous studies have established the knowledge that under natural conditions, river confluence zones experience channel scour followed with middle channel bar development. Less care is however given to the intensity of a confluence scour zone under man-controlled conditions, such as discharge regulation and levee confinement. In general, our knowledge about long-term bed evolution downstream of large alluvial river confluences is limited. Here we conducted a study focused on the 69-km uppermost channel of the Atchafalaya River, the largest distributary of the Mississippi River, to test the hypothesis that the channel downstream of two large tributaries sustains longer-term, extensive bed scouring owing to increased discharge in the main channel and, therefore, mid-channel bars in such a confluence zone cannot be built under confined channel conditions. The Atchafalaya River carries the total flow from the Red River and approximately 25% of the Mississippi River flow, traveling southwards 230 km before emptying into the Gulf of Mexico. We utilized long-term records on water surface elevation and discharge during 1935–2016, as well as channel bathymetry survey data during 1998–2006 to determine changes in hydraulic head and morphologic deformation in the confluence zone. The results from this study show that the combined flow from the Red River and Mississippi River into the Atchafalaya River steadily increased to approximately 5848 cubic meters per second (m3 s−1) in the recent decades, and the channel bed of the uppermost Atchafalaya River experienced considerable erosion since the 1930s. At a specific discharge of 8000 ± 100 m3 s−1, the river stage decreased by 5.8, 5.6, and 4.9 m from 1935 to 2016 at (from upstream to downstream) Simmesport, Melville, and Krotz Springs gauging stations, respectively. The average bed elevation reduced by 1.9 m from 1998 to 2006, although its thalweg increased by 0.3 m. Based on the channel bed assessment, a total volume of 6.6 × 107 m3 sediment was eroded from the uppermost 69 km of the Atchafalaya over the 8 years. The findings suggest that confluence zones of large alluvial rivers under controlled flow and confined levee conditions can experience extensive, long-lasting channel erosion. This can be especially progressive if the channel below a confluence is confined by levees, which can increase drag forces and prevent middle channel deposition. Further studies are needed to determine if the eroded sediment from the uppermost Atchafalaya is carried out to the river mouth or is deposited in the lower Atchafalaya. Such knowledge will have both scientific and practical relevance in river engineering and management.

Análisis hidro-sedimentológico 2d del comportamiento de un campo de espigones para la protección de márgenes en un río meandriforme

ABSTRACT Alluvial rivers show a highly dynamic morphological patterns, which cause problems in the operation and maintenance of infrastructure located in their environment. In these cases, it is necessary to design structures to control bank morphodynamic processes. This article describes the hydro-sedimentology of the meandering channel called río del Valle (Argentina), for which bank protection was implemented on its outer bank. This study zone was selected for the cutting of an embankment located on the outer bank of the channel due to the excessive lateral migration of the meander. Flow structure and bed morphology patterns are analyzed and discussed using the results of the application of the TELEMAC 2D model coupled to the Sisyphe morphological module. These results allow us to identify vector patterns of velocity and streamlines in the groyne field, showing the development of a recirculation flow between groynes, as well as the influence in the displacement of the core of maximum velocity towards the center of the channel along the bend apex. The bed evolution shows the vertical regrowth of the bed in the groyne field and the reduction of the point bar in the bend entrance.

A robust two-dimensional model for highly sediment-laden unsteady flows of variable density over movable beds

AbstractIn this work, a novel 2D depth-integrated numerical model for highly sediment-laden shallow flows over non-uniform erodible beds is presented, including variable density and exchange between the bed layer and the water–sediment mixture flow. The system of equations is formed by the 2D conservation equations for the mass and momentum of the mixture, the mass conservation equation for the different sediment size-classes transported in the flow and the bed evolution equation. The depth-averaged mixture density varies according to the volumetric concentration of the different sediment size-classes that can be incorporated from the bed to the flow and transported as suspended materials. The rheological behaviour of the flow is directly controlled by the properties of the mixture. A new x-split augmented Roe (xA-Roe) scheme is derived to solve the coupled flow and suspended solid-phase equations in both structured and unstructured meshes. The numerical scheme is defined to properly include density variations and momentum source terms, retaining a well-balanced flux formulation in steady states and the correct treatment of the wet–dry fronts. The numerical scheme is assessed with steady and transient cases involving highly sediment-laden flows, demonstrating its accuracy, stability and robustness in the presence of complex bed topography, wetting–drying fronts and rapid morphological changes.

A 2D HLL-based weakly coupled model for transient flows on mobile beds

Abstract We propose a finite-volume model that aims at improving the ability of 2D numerical models to accurately predict the morphological evolution of sandy beds when subjected to transient flows like dam-breaks. This model solves shallow water and Exner equations with a weakly coupled approach while the fluxes at the interfaces of the cells are calculated thanks to a lateralized HLLC flux scheme. Besides describing the model, we ran it for four different test cases: a steady flow on an inclined bed leading to aggradation or degradation, a dam-break leading to high interaction between the flow and the bed, a dam-break with a symmetrical enlargement close to the gate and a dam-break in a channel with a 90° bend. The gathered results are discussed and compared to an existing fully coupled approach based on HLLC fluxes. Although both models equally perform regarding water levels, the weakly coupled model looks to better predict the bed evolution for the four test cases. In particular, its results are not affected by an excessive numerical diffusion encountered by the coupled model. Moreover, it usually better estimates the amplitudes of the maximum deposits and scours. It is also more stable when subject to high bed–flow interaction.

Review of imaging-based measurement techniques for free surface flows involving sediment transport and morphological changes

Abstract In order to validate the numerical methods aimed at the simulation of fast transient flows involving sediment transport and morphological changes, data are required. However, field data are scarce, or, if existing, are often inaccurate or incomplete, due to the difficulty of taking reliable measurements in such difficult flow conditions. Laboratory experiments constitute a good alternative to obtain validation data for numerical models. When performing simplified experiments, a limited number of well-identified flow features can be highlighted if appropriate measurements are taken. Advances in experimental techniques in the last decades have significantly enlarged the field of possible data acquisition, especially thanks to the development of non-intrusive techniques such as digital imagery. Non-intrusive techniques are of paramount importance when considering sediment transport because a measurement device interacting with the flow would also modify the observed morphological features. In this paper, several imaging-based techniques are presented for water-level and bed evolution measurements. The key features and advantages are discussed but also the drawbacks of those techniques. The discussion is illustrated by different examples that have resulted in data sets commonly used by scientists all over the world to test their numerical simulation tools.

A coupled 1-D/2-D model for simulating river sediment transport and bed evolution

AbstractThe paper details the method to couple a 1-D hydro-sedimentary model to a 2-D hydro-sedimentary model in order to represent the hydrodynamics and morphological processes during a flood event along a river. Tested on two field cases, the coupled model is stable even in the case of generalized overflow over the riverbanks or of levee breaching. For lateral coupling, the coupled model allows saving computational time compared to a full 2-D model and to provide valuable results concerning the flooding features as well as the evolution of the bed topography. However, despite a similar simplified representation of the sediment features in the 1-D and 2-D models, some discrepancies appear in the case of upstream/downstream coupling along a cross section perpendicular to the flow direction because the assumption of homogeneous velocity and concentration is not valid for estimating sediment transport. Further research is necessary to be able to define a suitable distribution of the sediments on the 1-D side of the boundary between the two models.

A short note on the simulation of turbulent stratified flow and mobile bed interaction using the continuum coupled flow and morphodynamics model

This paper aims at addressing issues related to the misrepresentation of the turbulent stratified flow for sand wave simulation using the continuum coupled flow and morphodynamics modeling approach. continuum flow and morphodynamics frameworks often consider the contributions of (i) suspended sediment-load in the sediment mass-balance equation and (ii) stratification in the equations of fluid motion. We argue that omitting these contributions could impact the numerical simulation results of transverse sand wave development at the late stages of bed evolution. We support our argument by presenting a numerical analysis, which attempts to quantify the impact of the stratification and suspended sediment-load on the calculated bed topography during various stages of transverse sand wave evolution in a mobile bed flume.

Comparison of Local and Global Optimization Methods for Calibration of a 3D Morphodynamic Model of a Curved Channel

In curved channels, the flow characteristics, sediment transport mechanisms, and bed evolution are more complex than in straight channels, owing to the interaction between the centrifugal force and the pressure gradient, which results in the formation of secondary currents. Therefore, using an appropriate numerical model that considers this fully three-dimensional effect, and subsequently, the model calibration are substantial tasks for achieving reliable simulation results. The calibration of numerical models as a subjective approach can become challenging and highly time-consuming, especially for inexperienced modelers, due to dealing with a large number of input parameters with respect to hydraulics and sediment transport. Using optimization methods can notably facilitate and expedite the calibration procedure by reducing the user intervention, which results in a more objective selection of parameters. This study focuses on the application of four different optimization algorithms for calibration of a 3D morphodynamic numerical model of a curved channel. The performance of a local gradient-based method is compared with three global optimization algorithms in terms of accuracy and computational time (model runs). The outputs of the optimization methods demonstrate similar sets of calibrated parameters and almost the same degree of accuracy according to the achieved minimum of the objective function. Accordingly, the most efficient method concerning the number of model runs (i.e., local optimization method) is selected for further investigation by setting up additional numerical models using different sediment transport formulae and various discharge rates. The comparisons of bed topography changes in several longitudinal and cross-sections between the measured data and the results of the calibrated numerical models are presented. The outcomes show an acceptable degree of accuracy for the automatically calibrated models.

Scour Characteristics of the Underwater Crossing of Trunk Gas Pipeline Across the River Lena

The design data of the underwater crossing of the trunk gas pipeline (TGPL), which is an extension of the main gas pipeline of Hatassy GDS-2, for gasification of regions on the eastern side of the river Lena of the Republic of Sakha (Yakutia) are considered. Scours behaviour of the underwater crossing of TGPL across the river Lena is examined taking into account hydromorphological factors. The influence of hydrological and exogenous processes on the state of the underwater passage of Hatassy-Pavlovsk TGPL is shown by the example of the line-II. Changes of the river bottom profiles in the area of TGPL fixed at four discharge section lines, as well as water consumption were analyzed. It is shown that the presence of the underwater gas pipeline significantly affects the nature of the movement of micro- and meso-forms of the river bottom. It has been established that the constantly changing hydrological and hydromorphological processes resulted in sagging of the inverted siphon section in the line-II of the underwater crossing of Hatassy-Pavlovsk TGPL. During the designing and construction of the first line of the underwater gas pipeline across the river Lena, major omissions were committed, the peculiarities of the hydromorphological and hydrologic features of the river bed evolution in the section of the underwater passage of Tabaga-Kangalassy TGPL across the river Lena had not been taken into account. The effects of hydrodynamic and permafrost processes, heaving phenomena on floodplain and shore slope together increase the non-functional loads on the underwater gas pipeline. As a result of these factors, high longitudinal tensile stresses arise, especially in the welded joints of the inverted siphon pipes, and lead to accidents and incidents at the underwater gas pipeline across the river Lena.

Long term sediment transport simulation of the Danube, Sava, and Tisa rivers

The aim of this paper is to evaluate a newly developed one dimensional unsteady flow, sediment transport and bed evolution model for a looped river network through a long term simulation of a real-life scenario. The model was assessed by verifying it for the Danube, Tisa, and Sava rivers in Serbia for a five year time interval. The total length of the modeled domain was 741.94 km from which 486.48 km is the length of the modeled Danube River reach, 132.50 km the modeled section of the Sava and 122.96 km the length of the modeled Tisa River reach. The simulated domain included smaller tributaries such as the Kolubara, Mlava, Nera, Pek, Porecka, Tamis, and Great Morava rivers. Due to the size of the domain that was included in the model, the work also includes extensive research regarding the available measurements, issues with measurement errors, and suggestions on overcoming incomplete measurements by developing different types of correlations. The attained results were analyzed by comparing the simulation results with measured water levels, discharges, and suspended sediment concentrations. The implemented evaluation of the results confirmed the developed model's reliability.

Sediment transport and bed evolution model for complex river systems.

This work presents the theoretical background, development, and preliminary evaluation of a one-dimensional unsteady sediment transport and bed evolution model for a looped river network. The sediment transport and bed evolution model employs a concept that differentiates sediment particles moving in the form of suspended sediment, and near bed, and bed sediment. Applying the active layer concept, the developed model utilizes the appropriate exchange mechanisms between the suspended sediment and active layer material, which are presented in great detail. The governing transport equations were solved using the split operator approach that resulted in two successive steps. The advection equations were solved using the characteristics method, whereas the diffusion equations were discretized using the Crank-Nicholson scheme. The obtained system was complemented with additional auxiliary equations in order to allow sediment transport and bed evolution simulation at nodes, thus enabling the same in a looped river network. The derived equations were applied to develop an open-channel flow, sediment transport, and bed evolution model that was subjected to a series of preliminary numerical tests.

Modelling hyperconcentrated floods in the Middle Yellow River using an improved river network model

In the section of the Middle Yellow River from Longmen to the Sanmenxia Dam, the prediction to hyperconcentrated flood processes is difficult because of the abrupt change of channel geometry along the river and the high variability of the amount of flood water and sediment load from the main river and tributaries. A river network model based on a Godunov-type FVM scheme is proposed in order to investigate the flow dynamics, sediment transport and bed evolution during hyperconcentrated floods. A quasi 2D algorithm is adopted to calculate the velocity at the junction cell, which is then used for providing the interior boundary conditions. The computation for each reach can be executed simultaneously and the solution procedure is parallelized using OpenMP. The speedup factor compared with a serial program increases linearly in theory with the number of reaches in the river network. Two flood events, featuring significant erosion and deposition respectively, were simulated to validate the model. The calculated water levels, discharges and fractional concentrations of non-uniform suspended load were in agreement with the measurements. A comparison was made between the proposed model and an existing model neglecting the momentum conservation principle at the junction, with the former showing better prediction of the peak water levels near the confluence. Numerical experiments were conducted to analyze the influences of reservoir operation and discharge capacity of the dam on flood routing and bed evolution in the river network. It is demonstrated that decreasing pool level during flood season and increasing discharge capacity are both valid measures to alleviate sedimentation in the Sanmenxia Reservoir, and the former measure is a prerequisite. Therefore, the model presented here can help to enhance the understanding of river network system subject to high sediment input and inspire better strategies on sustainable reservoir management.

Responses of river bed evolution to flow-sediment process changes after Three Gorges Project in middle Yangtze River: A case study of Yaojian reach

The Three Gorges Project (TGP) has changed the flow-sediment process in the middle Yangtze River. For navigation purposes, there is an urgent need to study the changes of the river regime over a long-term period and the shoal-channel evolution over different seasons since the completion of the TGP. Based on analysis of the measured data and the results of a two-dimensional mathematical model, the changes of the river regime and river bed evolution in the Yaojian reach downstream of the TGP were studied. Results show that a high sediment transport flux helps to keep the main flow in the North Branch, while a low sediment transport flux helps to keep the main flow in the South Branch. Thus, the main branch will not change in the near future because of the low sediment transport load. In this study, the flow-sediment process adjusted by the TGP was restored to the conditions before the TGP, and the river bed evolution under the adjusted and non-adjusted flow-sediment conditions was calculated. After the completion of the TGP, the reservoir storage accelerated the flood recession process and decreased the erosion by 11.9% under the flow-sediment conditions in 2010, and the deposition in the flood season decreased by 56.4%.

A GPU-based numerical model coupling hydrodynamical and morphological processes

Sediment transport simulations are important in practical engineering. In this study, a graphics processing unit (GPU)-based numerical model coupling hydrodynamical and morphological processes was developed to simulate water flow, sediment transport, and morphological changes. Aiming at accurately predicting the sediment transport and sediment scouring processes, the model resolved the realistic features of sediment transport and used a GPU-based parallel computing technique to the accelerate calculation. This model was created in the framework of a Godunov-type finite volume scheme to solve the shallow water equations (SWEs). The SWEs were discretized into algebraic equations by the finite volume method. The fluxes of mass and momentum were computed by the Harten, Lax, and van Leer Contact (HLLC) approximate Riemann solver, and the friction source terms were calculated by the proposed a splitting point-implicit method. These values were evaluated using a novel 2D edge-based MUSCL scheme. The code was programmed using C++ and CUDA, which could run on GPUs to substantially accelerate the computation. The aim of the work was to develop a GPU-based numerical model to simulate hydrodynamical and morphological processes. The novelty is the application of the GPU techniques in the numerical model, making it possible to simulate the sediment transport and bed evolution in a high-resolution but efficient manner. The model was applied to two cases to evaluate bed evolution and the effects of the morphological changes on the flood patterns with high resolution. This indicated that the GPU-based high-resolution hydro-geomorphological model was capable of reproducing morphological processes. The computational times for this test case on the GPU and CPU were 298.1 and 4531.2 s, respectively, indicating that the GPU could accelerate the computation 15.2 times. Compared with the traditional CPU high-grid resolution, the proposed GPU-based high-resolution numerical model improved the reconstruction speed more than 2.0–12.83 times for different grid resolutions while remaining computationally efficient.