Virtual Flow Research Articles

Immersive Virtual Reality Collaboration Framework for Flow Field Visualization

<p indent="0mm">Aiming at the problems of the single collaboration mode and the high cost of building a collaboration environment of the existing flow field collaboration analysis application, according to the requirements of flow field collaboration analysis, an immersive virtual reality collaboration framework for flow field visualization is proposed. Firstly, the collaboration message that supports flow field collaboration synchronization is defined. Then a collaborative pipeline tree is proposed that supports the sharing of flow field visualization results. Finally the demonstration collaboration analysis mode and free collaboration analysis mode of immersive virtual reality flow field visualization collaborative analysis are designed and implemented. Users can choose the appropriate collaboration analysis mode according to the actual task, to support the team in the flow field collaboration analysis. By building a prototype system and performing a demonstration collaboration analysis and a free collaboration analysis on the flow field data respectively, from the perspective of observation of different users, the collaboration process of the two collaborative analysis modes is demonstrated.

Virtual embolization for treatment support of intracranial AVMs using an interactive desktop and VR application

PurposeThe treatment of intracranial arteriovenous malformations (AVM) is challenging due to their complex anatomy. For this vessel pathology, arteries are directly linked to veins without a capillary bed in between. For endovascular treatment, embolization is carried out, where the arteries that supply the AVM are consecutively blocked. A virtual embolization could support the medical expert in treatment planning.MethodWe designed and implemented an immersive VR application that allows the visualization of the simulated blood flow by displaying millions of particles. Furthermore, the user can interactively block or unblock arteries that supply the AVM and analyze the altered blood flow based on pre-computed simulations.ResultsIn a pilot study, the application was successfully adapted to three patient-specific cases. We performed a qualitative evaluation with two experienced neuroradiologist who regularly conduct AVM embolizations. The feature of virtually blocking or unblocking feeders was rated highly beneficial, and a desire for the inclusion of quantitative information was formulated.ConclusionThe presented application allows for virtual embolization and interactive blood flow visualization in an immersive virtual reality environment. It could serve as useful addition for treatment planning and education in clinical practice, supporting the understanding of AVM topology as well as understanding the influence of the AVM’s feeding arteries.

Research and Implementation of Lean Production Mode in Shipbuilding

This paper studies the production process of a shipbuilding enterprise. The company suffers from long manufacturing cycle, low utilization rate of personnel and an unbalanced production line. To solve these problems, the lean shipbuilding mode, mainly divided into shipbuilding work breakdown, production plan and virtual flow operation in this paper, is put forward, which combines the lean production and modern information management technology with shipbuilding. Supported by the theory of work breakdown structure and task package scheduling, the shipbuilding task package is reasonably divided. The priority of task package manufacturing is determined by calculating the task package manufacturing sequence coefficient, and a reasonable number of operators is calculated to ensure the continuity of segmented manufacturing. After determining the manufacturing priority of the task pack and the number of allocable personnel, the corresponding work can be scheduled. Production planning drives all production activities of the shipbuilding enterprise, and just-in-time production is achieved through the reasonable arrangement of these production plans, thus reducing the waste of personnel and time. Then, the virtual flow operation is carried out, which can achieve high efficiency of flow production and high flexibility of fixed workstation production during the production process of large-scale and heavy-duty products. The virtual assembly production system of the workshop is established according to the characteristics of shipbuilding operation and the actual production situation. On this basis, a lean shipbuilding manufacturing execution system for small and medium-sized shipbuilding enterprises is developed to achieve lean production in a shipbuilding workshop. Through the implementation of the lean shipbuilding mode based on task package scheduling and its manufacturing execution system, compared with the original data, the ship production cycle is reduced to 76.7%, the number of workers is reduced by 16.7% and the production balance rate is up to 81%.

Abstract 8984: Prediction of Functional Results of Percutaneous Coronary Interventions With Virtual Stenting and Quantitative Flow Ratio

Introduction: The clinical value of residual quantitative flow ratio (rQFR), a novel function of QFR technique aimed to predict residual ischemia after virtual percutaneous coronary intervention (vPCI) is unknown. Hypothesis: We hypothesized rQFR well predict functional results after PCI. Methods: This is a sub-study of the COE-PERSPECTIVE registry, which investigated the prognostic value of post-PCI fractional flow reserve (FFR). From pre-PCI angiograms, QFR and rQFR were analyzed and their diagnostic performance was assessed at blinded fashion using pre-PCI FFR and post-PCI FFR as reference, respectively. The prognostic value of rQFR after vPCI was assessed according to vessel-oriented composite outcome (VOCO) (a composite of cardiac death, vessel-specific myocardial infarction, and vessel-specific revascularization) at 2 years. Results: Two hundred and seventy-four patients (274 vessels) with FFR-based ischemic causing lesions were analyzed. Pre-PCI QFR and FFR were 0.63±0.10 and 0.66±0.11 (R=0.756, p&lt;0.001). rQFR after vPCI and FFR after real PCI were 0.93±0.06 and 0.86±0.07 (R=0.528, p&lt;0.001). Diagnostic performance of rQFR to predict actual post-PCI FFR was good (area under the curve (AUC): 0.856 [0.804-0.909], p&lt;0.001). rQFR predicted well the incidence of 2-year VOCO after index PCI (AUC: 0.712 [0.555-0.869], p=0.041), being similar to that of actual post-PCI FFR (AUC: 0.691 [0.512-0.870], p=0.061). rQFR ≤0.89 was associated with increased risk of 2-year VOCO (hazard ratio: 12.9 [2.32-71.3], P=0.0035). Conclusions: Residual QFR estimated from pre-PCI angiography and virtual coronary stenting predicts procedural functional results and long-term vessel-related clinical events.

Path Planning for Vehicle Active Collision Avoidance Based on Virtual Flow Field

Path Planning for Vehicle Active Collision Avoidance Based on Virtual Flow Field

Research on spatial difference and dynamic mechanism of virtual tourism flow based on online group purchase

&lt;p class="15"&gt;Taking the online group purchase of tourism products as the research perspective and the online group purchase virtual tourism flow of tourism products in 26 tourism destinations in China as the research data, this paper studies the spatial distribution differences and formation dynamic mechanism of virtual tourism flow through the method of spatial analysis. On the whole, the online group purchase virtual tourism flow shows weak discrete distribution characteristics, and some parts show certain aggregation. The virtual passenger flow is concentrated in the provinces with rich tourism resources in the south coast and central China, and the group purchase virtual tourism flow in the central and western regions, North China and Northeast China is small. The spatial distribution of group purchase virtual tourism flow is the result of the joint action of internal and external driving forces and environmental driving forces. The external driving forces include three main driving factors: product group purchase price, product type and network marketing spatial structure. Relevant analysis shows that group purchase price is the most important external driving factor, followed by product type and finally network marketing spatial structure. Taking group buying virtual tourism flow as the research perspective has a certain novelty, which makes up for the weakness of tourism flow in virtual space. The flow direction of virtual tourism flow can reflect the real tourism flow to a certain extent, and even guide the real tourism flow. The research of virtual tourism flow provides a predictive warning for the flow management and capacity management of scenic spots.&lt;/p&gt;

On gray-box modeling for virtual flow metering

A virtual flow meter (VFM) enables continuous prediction of flow rates in petroleum production systems. The predicted flow rates may aid the daily control and optimization of a petroleum asset. Gray-box modeling is an approach that combines mechanistic and data-driven modeling. The objective is to create a computationally feasible VFM for use in real-time applications, with high prediction accuracy and scientifically consistent behavior. This article investigates five different gray-box model types in an industrial case study using real, historical production data from 10 petroleum wells, spanning at most four years of production. The results are diverse with an oil flow rate prediction error in the range of 1.8%–40.6%. Further, the study casts light upon the nontrivial task of balancing learning from both physics and data. Therefore, providing general recommendations towards the suitability of different hybrid models is challenging. Nevertheless, the results are promising and indicate that gray-box VFMs can reduce the prediction error of a mechanistic VFM while remaining scientifically consistent. The findings motivate further experimentation with gray-box VFM models and suggest several future research directions to improve upon the performance and scientific consistency.

A Method for Solving Percolation Overflow Boundary Based on Maximum of Horizontal Energy Loss Rate

The determination of overflow boundary is a prerequisite for the accurate solution of the seepage field by the finite element method. In this paper, a method for solving overflow boundary according to the maximum value of horizontal energy loss rate is proposed, which based on the analysis of the physical meaning of functional and the water head distribution of seepage field under different overflow boundaries. This method considers that the overflow boundary that makes the horizontal energy loss rate reach the maximum value is the real boundary overflow. Compared with the previous iterative computation method of overflow point and free surface, the method of solving overflow boundary based on the maximum horizontal energy loss rate does not need iteration, so the problem of non-convergence does not exist. The relative error of the overflow points is only 1.54% and 0.98% by calculating the two-dimensional model of the glycerol test and the three-dimensional model of the electric stimulation test, respectively. Compared with the overflow boundary calculated by the node virtual flow method, improved cut-off negative pressure method, initial flow method, and improved discarding element method, this method has a higher accuracy.

Virtual (Computed) Fractional Flow Reserve: Future Role in Acute Coronary Syndromes.

The current management of acute coronary syndromes (ACS) is with an invasive strategy to guide treatment. However, identifying the lesions which are physiologically significant can be challenging. Non-invasive imaging is generally not appropriate or timely in the acute setting, so the decision is generally based upon visual assessment of the angiogram, supplemented in a small minority by invasive pressure wire studies using fractional flow reserve (FFR) or related indices. Whilst pressure wire usage is slowly increasing, it is not feasible in many vessels, patients and situations. Limited evidence for the use of FFR in non-ST elevation (NSTE) ACS suggests a 25% change in management, compared with traditional assessment, with a shift from more to less extensive revascularisation. Virtual (computed) FFR (vFFR), which uses a 3D model of the coronary arteries constructed from the invasive angiogram, and application of the physical laws of fluid flow, has the potential to be used more widely in this situation. It is less invasive, fast and can be integrated into catheter laboratory software. For severe lesions, or mild disease, it is probably not required, but it could improve the management of moderate disease in 'real time' for patients with non-ST elevation acute coronary syndromes (NSTE-ACS), and in bystander disease in ST elevation myocardial infarction. Its practicability and impact in the acute setting need to be tested, but the underpinning science and potential benefits for rapid and streamlined decision-making are enticing.

Computational Assessment of Hemodynamic Significance in Patients With Intramural Anomalous Aortic Origin of the Coronary Artery Using Virtually Derived Fractional Flow Reserve and Downstream Microvascular Resistance.

Anomalous aortic origin of a coronary artery (AAOCA) is the second most common cause of sudden cardiac death in young athletes. One of the hypothesized mechanisms of ischemia in these patients is the lateral compression of the anomalous artery with an intramural or interarterial course. The presence of a narrowing in the anomalous artery will cause physiologic changes in downstream resistance that should be included for computational assessment of possible clinical ramifications. In this study, we created different compression levels, i.e., proximal narrowing, in the intramural course of a representative patient model and calculated hyperemic stenosis resistance (HSR) as well as virtual fractional flow reserve (vFFR). Models also included the effect of the distal hyperemic microvascular resistance (HMR) on vFFR. Our results agreed with similar FFR studies indicating that FFR is increased with increasing HMR and that different compression levels could have similar FFR depending on the HMR. For example, vFFR at HSR: 1.0-1.3 and HMR: 2.30 mmHg/cm/s is 0.68 and close to vFFR at HSR: 0.6-0.7 and HMR: 1.6 mmHg/cm/s, which is 0.7. The current findings suggest that functional assessment of anomalous coronary arteries through FFR should consider the vascular resistance distal to the narrowing in addition to the impact of a proximal narrowing and provides computational approaches for implementation of these important considerations.

Feasibility of virtual fractional flow reserve derived from coronary angiography and its correlation with invasive functional assessment

Abstract Introduction Invasive functional assessment (iFA) of coronary artery disease (CAD) needs expensive devices, has potential procedure-related complications and is still underutilized. Virtual Fractional Flow Reserve (vFFR) derived from invasive coronary angiography (ICA) has the potential to overcome these limitations. Purpose To investigate the feasibility of vFFR analysis and its correlation with iFA (iFR, RFR or FFR). Methods Retrospective analysis of consecutive patients (pts) who underwent iFA in a tertiary center between 2019 and 2020. vFFR was calculated using a dedicated software (CAAS Workstation 8.4) based on standard non-hyperaemic coronary angiograms acquired in ≥2 different projections, by operators blinded to iFA results. Diagnostic performance and accuracy of vFFR were evaluated. vFFR was considered positive when &amp;lt;0.80. FFR &amp;lt;0.8 and iFR/RFR &amp;lt;0.90 were classified as positive according to current clinical standards. Results Out of 113 coronary arteries of 102 pts, vFFR was successfully analysed in 106 (94%). Reasons for vFFR analysis failure were: vessel projection overlap (48%), &amp;lt;2 angiographic projections (28%) and table movement while acquisition (24%). From 106 coronary arteries of 95 pts with analysable vFFR (78% male, mean age 67.8±9.7 years), 90 (85%) showed agreement with the respective iFA result. The vFFR predicted which lesions were physiologically significant and which were not with accuracy, sensitivity, specificity, positive and negative predictive values of 73%, 73%, 83%, 53%, and 92% respectively. The mean difference between vFFR and iFA were −0.0484±0.096 and Pearson's correlation coefficient was 0.533 (p&amp;lt;0.001). The ROC area under the curve was 0.839 (0.751–0.928, p&amp;lt;0.001). Conclusion FFR were feasible in 94% of cases analysed retrospectively. As compared to gold-standard iFA, vFFR had an overall moderate accuracy in detecting ischemia-producing lesions and a negative predictive value &amp;gt;90%. vFFR has the potential to substantially simplify physiological coronary lesion assessment and thus improve its current uptake. Funding Acknowledgement Type of funding sources: None. Bland-Altman plot between vFFR and IFA

Virtual fractional flow reserve derived from coronary angiography – artery and lesion specific correlations

Abstract Introduction Virtual Fractional flow reserve (vFFR) from standard non-hyperaemic invasive coronary angiography (ICA) has emerged as a promising non-invasive test to assess hemodynamic severity of coronary artery disease (CAD). Purpose To investigate the difference in vFFR analysis between vessels and specific lesions. Methods Retrospective analysis of consecutive patients (pts) who underwent invasive functional assessment (iFA) in a tertiary center between 2019 and 2020. vFFR was calculated using dedicated software (CAAS Workstation 8.4) based on coronary angiograms of the acquired in ≥2 different projections, by operators blinded to iFA results. Diagnostic performance of vFFR was evaluated and correlated with iFA, according to coronary vessel, vessel diameter at stenosis, diameter stenosis and area stenosis at lesion. vFFR was considered positive when &amp;lt;0.80. FFR &amp;lt;0.8 and iFR/RFR &amp;lt;0.90 were classified as positive according to current clinical standards. Results 106 coronary arteries of 95 pts (78% male, mean age 67.8±9.7 years) underwent vFFR evaluation. ICA indications were chronic coronary syndrome in 63% or acute coronary syndrome (non-culprit lesion) in the remaining pts. VFFR accuracy was good (AUC 0.839 (p&amp;lt;0.001) and Pearson's correlation coefficient 0.533 (p&amp;lt;0.001) when vFFR was measured in the distal vessel segment. The correlation improved when vFFR were assessed at lesion site (r=0.631, p&amp;lt;0.001) or up to 1cm below the stenosis (0.610, p&amp;lt;0.001). Binary concordance of 89% were observed in RCA and LAD (Sensibility -S 68%, Specificity-Sp 96%, False positive -FP 3.8%, False negative - FN 31%, predictive positive value-PPV 87%, predictive negative value- PNV 89%), while in the circumflex coronary artery binary concordance were of 77% (S 50%; Sp 82%; FP 18%; FN 50%; PPV 33% and PNV 90%). Correlation between vFFR and iFA was higher in vessels ≥2mm (r=0.730, p&amp;lt;0.001). and in lesions in the extremes of the severity spectrum (Table 1). Conclusion vFFR has a moderate to high linear correlation to iFA, depending on the artery and type of lesion studied. The higher correlation was found when vFFR were measured at lesion site, in non-circumflex artery stenosis, in vessels ≥2mm and in vessels with mild or severe stenosis. Funding Acknowledgement Type of funding sources: None.

Physiological and angiographic outcomes of PCI in calcified lesions after rotational atherectomy or intravascular lithotripsy

Abstract Background Percutaneous coronary interventions (PCI) in calcified coronary artery lesions is associated with impaired stent expansion, higher rate of periprocedural complications and cardiac mortality. Lesion preparation using dedicated calcium modifying techniques such as RA or IVL has been advocated. Studies comparing these technologies are lacking. Objectives To compare the in-stent pressure gradient, evaluated by virtual fractional flow-reserve, in calcific lesions treated using either rotational atherectomy (RA) or intravascular lithotripsy (IVL). Methods Patients undergoing either RA- or IVL-assisted PCI from two European centers were included. Propensity score matching (1:2) was performed to control for potential bias. Primary outcome was post- PCI in-stent pressure gradient calculated by virtual fractional flow reserve (vFFRgrad, calculated as the difference between the vFFR at the proximal minus distal edge of the stent). Secondary outcomes included the proportion of patients with complete functional revascularization defined as of distal vFFR post PCI (vFFRpost) ≥0.90. Results From a cohort of 210 patients, 105 matched patients (70 RA and 35 IVL) were included. Pre-PCI vFFR did not differ between groups (0,65±0,13 RA and 0,67±0,11 IVL). After PCI, in-stent pressure gradient was significantly lower in the IVL group (0.032±0.026 vs 0.043±0.026 in the RA group, p=0.024). The proportion of vessels with functional complete revascularization was similar between the two groups (32.9% vs. 37.1% in the RA and IVL group, respectively; p=0.669) Conclusions Calcific lesions preparation with IVL is effective and resulted in improved in-stent pressure gradient compared to RA. Approximately one third of the patients undergoing PCI for a severely calcified lesion achieved functional revascularization with no difference between rotational RA and IVL. Funding Acknowledgement Type of funding sources: None. In stent gradients after RA and IVL

The importance of three dimensional coronary artery reconstruction accuracy when computing virtual fractional flow reserve from invasive angiography

Three dimensional (3D) coronary anatomy, reconstructed from coronary angiography (CA), is now being used as the basis to compute ‘virtual’ fractional flow reserve (vFFR), and thereby guide treatment decisions in patients with coronary artery disease (CAD). Reconstruction accuracy is therefore important. Yet the methods required remain poorly validated. Furthermore, the magnitude of vFFR error arising from reconstruction is unkown. We aimed to validate a method for 3D CA reconstruction and determine the effect this had upon the accuracy of vFFR. Clinically realistic coronary phantom models were created comprosing seven standard stenoses in aluminium and 15 patient-based 3D-printed, imaged with CA, three times, according to standard clinical protocols, yielding 66 datasets. Each was reconstructed using epipolar line projection and intersection. All reconstructions were compared against the real phantom models in terms of minimal lumen diameter, centreline and surface similarity. 3D-printed reconstructions (n = 45) and the reference files from which they were printed underwent vFFR computation, and the results were compared. The average error in reconstructing minimum lumen diameter (MLD) was 0.05 (± 0.03 mm) which was < 1% (95% CI 0.13–1.61%) compared with caliper measurement. Overall surface similarity was excellent (Hausdorff distance 0.65 mm). Errors in 3D CA reconstruction accounted for an error in vFFR of ± 0.06 (Bland Altman 95% limits of agreement). Errors arising from the epipolar line projection method used to reconstruct 3D coronary anatomy from CA are small but contribute to clinically relevant errors when used to compute vFFR.

The impact of water scarcity on Chinese inter-provincial virtual water trade

Chinese water resources are limited and unevenly distributed across space, making the inter-provincial virtual water trade increasingly prosperous. Many studies have focused on the impact of virtual water trade on regional water scarcity, but little consideration has been paid to the impact of water scarcity on virtual water trade, particularly in China. To fill this gap, we addressed the Chinese inter-provincial virtual water trade in 2012, 2015 and 2017, and we combined a multi-regional input-output analysis with a gravity model supplemented by the instrumental variable method. Our results indicated water pressure values were higher in northern areas, and provinces with extreme water stress were distributed in the eastern coastal areas. Additionally, virtual water tends to be exported from water-poor regions to water-rich regions. The results of the gravity model show that the Chinese inter-provincial virtual water trade is significantly related to water scarcity. We found that virtual water flow is positively correlated with the water scarcity of exporting regions, such as Xinjiang, Heilongjiang, Anhui, and Jiangsu, and it is negatively correlated with the water scarcity of importing regions, such as Shandong, Guangdong and Zhejiang. Therefore, water scarcity affects the virtual water trade flow, and the trade in turn exacerbates the regional water shortage in the northern and eastern coast of China. In addition, the virtual water trade is affected by socio-economic factors and environmental factors. We suggest that related policies should be developed to terminate this malignant cycle. The virtual water trade should be guided towards becoming more adaptable to sustainable development rather than allowing for water-scarce areas to pursue economic development at the cost of scarce water resources.

Multi-task learning for virtual flow metering

Virtual flow metering (VFM) is a cost-effective and non-intrusive technology for inferring multiphase flow rates in petroleum assets. Inferences about flow rates are fundamental to decision support systems that operators extensively rely on. Data-driven VFM, where mechanistic models are replaced with machine learning models, has recently gained attention due to its promise of lower maintenance costs. While excellent performances in small sample studies have been reported in the literature, there is still considerable doubt about the robustness of data-driven VFM. In this paper, we propose a new multi-task learning (MTL) architecture for data-driven VFM. Our method differs from previous methods in that it enables learning across oil and gas wells. We study the method by modeling 55 wells from four petroleum assets and compare the results with two single-task baseline models. Our findings show that MTL improves robustness over single-task methods, without sacrificing performance. MTL yields a 25%–50% error reduction on average for the assets where single-task architectures are struggling.

Linear response in large deviations theory: a method to compute non-equilibrium distributions

We consider thermodynamically consistent autonomous Markov jump processes displaying a macroscopic limit in which the logarithm of the probability distribution is proportional to a scale-independent rate function (i.e. a large deviations principle is satisfied). In order to provide an explicit expression for the probability distribution valid away from equilibrium, we propose a linear response theory performed at the level of the rate function. We show that the first order non-equilibrium contribution to the steady state rate function, g( x ), satisfies where the vector field u ( x ) defines the macroscopic deterministic dynamics, and the scalar field equals the rate at which work is performed on the system in a given state x . This equation provides a practical way to determine g( x ), significantly outperforms standard linear response theory applied at the level of the probability distribution, and approximates the rate function surprisingly well in some far-from-equilibrium conditions. The method applies to a wealth of physical and chemical systems, that we exemplify by two analytically tractable models—an electrical circuit and an autocatalytic chemical reaction network—both undergoing a non-equilibrium transition from a monostable phase to a bistable phase. Our approach can be easily generalized to transient probabilities and non-autonomous dynamics. Moreover, its recursive application generates a virtual flow in the probability space which allows to determine the steady state rate function arbitrarily far from equilibrium.

Bayesian neural networks for virtual flow metering: An empirical study

Recent works have presented promising results from the application of machine learning (ML) to the modeling of flow rates in oil and gas wells. Encouraging results and advantageous properties of ML models, such as computationally cheap evaluation and ease of calibration to new data, have sparked optimism for the development of data-driven virtual flow meters (VFMs). Data-driven VFMs are developed in the small data regime, where it is important to question the uncertainty and robustness of models. The modeling of uncertainty may help to build trust in models, which is a prerequisite for industrial applications. The contribution of this paper is the introduction of a probabilistic VFM based on Bayesian neural networks. Uncertainty in the model and measurements is described, and the paper shows how to perform approximate Bayesian inference using variational inference. The method is studied by modeling on a large and heterogeneous dataset, consisting of 60 wells across five different oil and gas assets. The predictive performance is analyzed on historical and future test data, where an average error of 4%–6% and 8%–13% is achieved for the 50% best performing models, respectively. Variational inference appears to provide more robust predictions than the reference approach on future data. Prediction performance and uncertainty calibration is explored in detail and discussed in light of four data challenges. The findings motivate the development of alternative strategies to improve the robustness of data-driven VFMs.

Development of virtual fan flow and acoustic performance testers based on RANS solvers and acoustic analogy

As the potential of computational resources dramatically increases, the so-called computer-aided engineering readily replaces experiment-based engineering in related industrial fields. In this study, the virtual fan flow and acoustic performance testers are developed using the RANS solvers and the acoustic analogy. Two types of forward-curved centrifugal fans are selected for numerical and experimental investigations into its flow and acoustic performances. First, to experimentally evaluate the performances of the centrifugal fan units, their P-Q curves and sound power levels are measured using a fan flow performance tester and a semi-anechoic chamber, respectively. Second, the virtual fan flow and acoustic performance testers are constructed using the RANS solvers and the acoustic analogy based on the FW-H equation and CFD method. The validity of the current virtual methods is confirmed by comparing the prediction results with the measured ones. During the validation, the effects of the wall functions, y+ distribution, and turbulence models on predicted flow performance accuracy are closely examined. The effects of the integral surfaces used for the computation of the FW-H equations are also assessed on the predicted spectral levels of sound pressure.

Dynamic Evolution and Spatial Convergence of the Virtual Cultivated Land Flow Intensity in China.

Exploring the flow intensity of virtual cultivated land is the key to improving the ecological compensation and food security policy. This study aimed to analyze the dynamic evolution, spatial convergence, and its affecting factors of the virtual cultivated land flow intensity. The spatial convergence model was used in this study. The results showed that, during 2000–2018, the growth rate of the surplus state of virtual cultivated land at the national level is less than that of the deficit state of virtual cultivated land in China. Moreover, the number of deficit provinces of virtual cultivated land flow intensity is increasing. The absolute β-convergence characteristics of the virtual cultivated land flow intensity are significant at the national, northeast, central, and western regions. Additionally, the conditional β-convergence exists at the national and four regional levels. Meanwhile, cultivated land resource endowment, population scale, regional economic development level, and agricultural mechanization level play an important role in the convergence process of inter-regional virtual cultivated land flow intensity. However, the influence degree of different control variables on different regional virtual cultivated land flow intensity is not consistent. Therefore, policymakers should pay attention to cultivated land resources’ spatial transfer mechanism when making regional cultivated land ecological compensation policies to coordinate the interesting relationship between the deficit area and surplus area of virtual cultivated land. Therefore, it is necessary to take the virtual cultivated land flow intensity as the reference index and use the combination of market guidance and government control to stimulus the stakeholders to protect cultivated land by taking different measures.