This study predicts pollutant propagation using numerical simulation and machine learning methods downstream the Ural River and into the Caspian Sea as a result of an accidental oil spill near the Ural River estuary near Atyrau, Kazakhstan. A CFD model based on the Reynolds-averaged Navier-Stokes equations, coupled with concentration and temperature equations, was developed to simulate the hydrodynamic behavior of the oil product selected as a pollutant. The simulation domain covers the northeastern part of the Caspian Sea. The direct computation CFD model was numerically solved using the SIMPLE algorithm, which relates pressures and velocities. To reduce the computation time, the Bi-LSTM neural network was used to predict the value of pollutant concentrations at specific locations. The Bi-LSTM model was trained based on the data from the direct computations performed using the CFD model at specific control points of the computational domain. The results show that the BiLSTM architecture effectively predicts pollutant values, although improvements are needed for the models at some points with higher error levels and noise. The results demonstrate the effectiveness of combining CFD calculations and machine learning methods to reduce the computation time in predicting and monitoring the spread of oil spills. The use of this approach in the future will lead to the fact that it will be possible to carry out operational calculations using machine learning methods using less computing resources compared to direct calculations.

The study of conjugate convection plays a key role in heat transfer systems such as collectors, heat exchangers, electrical cooling, and thermal insulation. In this paper, we investigated conjugate natural convection in a square inclined cavity with a heat-conducting baffle using computational fluid dynamics and machine learning. The effect of inclination angles on conjugate natural convection was examined, ranging from 0 to 330°. The goal of the study was to improve the accuracy and efficiency of predicting temperature changes in the computational domain. To achieve this goal, three regression models were developed and tested: gradient boosting, random forest, and decision tree. The Computational fluid dynamics (CFD) model solved the Navier-Stokes governing equations using the control volume method. Analysis of the results showed that the gradient boosting model demonstrated the best performance, with high values of the coefficient of determination (best case 0.988) and minimal prediction errors. The random forest model also demonstrated good results, although slightly inferior to the gradient boosting model. The tree model demonstrated the least effective solution among all the models considered, but still achieved acceptable accuracy. It should be noted that the gradient boosting model yielded an R2 of 0.987, a Mean Squared Error (MSE) of 0.033, a Mean Absolute Error (MAE) of 0.13, and a Mean Absolute Percentage Error (MAPE) of 0.00044. Thus, the obtained error values are the lowest compared to other machine learning models. The obtained results confirm the potential of machine learning methods for quickly obtaining solutions to fluid dynamics and heat transfer modeling problems.

This study performs computational modeling of air pollution and dispersion around the isolated cubic model of a building with different barrier heights. A system of Reynolds averaged Navier–Stokes (RANS) equation was applied to solve the problem, and different turbulent models have been used to close the equations. To validate the system of equation and numerical algorithm, the test problem has been solved numerically. The received computational data were matched with measurement results and computational data of other authors. The main problem specifying the pollutant release process behind an obstacle with a barrier was solved after validation the system of equations and the numerical algorithm. For modeling, the Re-Normalisation Group k – ε (RNG k – ε) turbulence model was used. It was determined that by using solid barriers height of 0.1D, the pollution reduces 1.5 times compared to case without the barriers. The received results can be used in the construction of protective barriers near the carriageways for maximum protection of residential buildings. Since building a barrier with the optimal height to protect nearby residential buildings can save a lot of funds.

Urban air pollution poses a serious threat to public health, particularly in areas with heavy traffic, such as street canyons. This paper numerically investigates the effect of noise barriers of varying heights (0.1H, 0.2H, 0.3H, where H is the building height) on the dispersion of a passive pollutant (ethylene) in a street canyon model. The simulation is based on the Reynolds-averaged Navier-Stokes (RANS) equations and the SST k-w turbulent model. The numerical model is verified by comparison with published experimental data and large eddy simulation (LES) results. Spatiotemporal distributions of pollutant concentrations are analyzed. The results show that a barrier of medium height (0.2H) forms a stable recirculation zone, acting as a "trap" for pollutants with maximum concentrations. A low barrier (0.1H) has a negligible effect, while a high barrier (0.3H) effectively screens the leeward zone but promotes pollutant accumulation on the windward side. A conclusion is drawn about the dual effect of barriers and the need to consider aerodynamic effects in their design.

This study examines the influence of the thermophysical properties of various partition materials on heat transfer processes in a cavity filled with liquid. To achieve this goal, both direct computational fluid dynamics (CFD) and machine learning (ML) methods were applied. Direct CFD simulations were performed to obtain a detailed understanding of the temperature distribution within the cavity for different septum materials. Subsequently, machine learning methods were applied to create regression models capable of predicting changes in the temperature value inside the cavity based on different septum materials. The best results were achieved using third-degree polynomial regression, achieving a coefficient of determination (R 2) of 0.816. This indicates that the model is well adapted to the data and is able to explain the variability of the target variable. Additionally, random forest regression models were examined, but their results were slightly less accurate compared to polynomial regression. The study demonstrates that integrating machine learning techniques into computational fluid dynamics can significantly improve the analysis and prediction of thermal processes.

This study presents a 3D numerical model for assessing the breakthrough of dam flows with a mud-stone flow, as well as obstacles of various shapes and heights that have partial collapse. The proposed model was developed using the VOF method in a combination of the Newtonian, non-Newtonian model for liquid and sediment, and the DPM and MPM models for describing the motion of particles with different sizes. To verify the reliability and efficiency of the model, the calculated data were compared with experiments and numerical data. This paper presents an inhomogeneous terrain with a trapezoidal shape and series of cylindrical obstacles that represent a system of protection against mudflow. This design taraps large particles, reducing downstream hazards. Thus, using the proposed approach, it can be assumed that only a stream of sediment and particles of small diameters, which significantly reduce the threat of the structure and the settlement destruction, will reach the residential unit.

In this paper, we investigate the behavior of different viscosity models under conditions of conjugate natural convection in a square cavity divided by a heat-conducting partition with a changing inclination angle and differential heating of the side walls. Numerical modeling is performed using the finite volume method for a fluid with a viscosity similar to the properties of blood. The main parameters of the study were the cavity inclination angle (0 degrees, 30 degrees, 45 degrees, 60 degrees, and 90 degrees) and the choice of the viscosity model of the non-Newtonian fluid. The results showed that inclination angles of 30 degrees and 60 degrees contribute to the enhancement of convection flows. Among the studied non-Newtonian viscosity models and the power law model demonstrated the highest flow velocity, whereas for the Herschel-Bulkley model, heat transfer due to conduction prevailed, with minimal mixing process.

Natural dams are the result of the actions of natural forces: landslides, mudflows, avalanches, collapses, earthquakes. The behavior of natural dams in the process of destruction is highly unpredictable and endangers the lives of citizens and urban infrastructure. For this reason, it is important to assess the stability and strength of the formed structure immediately after its formation. However, the complex terrain and various geomorphological conditions in the area of potential disaster often make it difficult to conduct such field experiments. In the present study, a numerical method was proposed for simulating the failure of a natural earth dam, which was previously tested for reliability and accuracy. The proposed mathematical model is developed using the VOF method to simulate three-phase flow in combination of Newtonian, non-Newtonian model for air, liquid and sediment. To approximate reality process for the sedimentary phase was described using a non-Newtonian model. After verification, the model was used for an in-depth study of the destruction process of a natural earth-type dam. The results demonstrate the erosion behavior of the earth dam corresponding to the hydrological and morphological conditions, so by the end of 21.1 s the loss is more than 35

Fractional derivatives, due to their nonlocality, can describe complex processes where historical data is important for future calculations. At the same time, this property brings difficulties in numerical simulations. This paper presents a new discrete operator for approximating the fractional derivative based on the Grünwald–Letnikov definition, the “short memory principle,” memorization and analytical assumptions. This operator significantly reduces the number of operations in the calculation process when solving boundary value problems by saving the calculated data and transforming it for further use with adjustable accuracy. The results obtained showed that the use of this technique on specific problems reduced the execution time from 1262 s to 19 s, which is more than 66 times less than the standard method. It should be taken into account that the use of the modified method showed a worse result compared to the analytical method and amounted to 0.011

Studying air quality in urban conditions is an important problem today, as it directly affects human health. In this paper, we study a busy residential area of Almaty, which consists of several educational buildings located on both sides of the road from the roadway. The impact of a barrier with different heights having a slope at the top of the barrier to improve air quality was assessed using numerical modeling. In numerical modeling, special attention was paid to different weather conditions. To identify effective barriers to improve air quality, several options were considered: no barrier, the presence of barriers 2 and 4 m high with an additional slope of 30° at the top of the barrier, the presence of barriers 2 and 4 m high with an additional slope of 45° at the top of the barrier. To take into account different weather conditions that depend on time, the period from 9 am to 9 pm (43,200 s) was used. According to the results obtained, the most effective barrier height was chosen to be 4 m with a slope of 30°. The choice of the barrier height with the optimal slope was made for the process of changing the concentration distribution with a real change in wind direction, wind force, ambient temperature, road surface temperature and relative air humidity, which changes over time. The obtained results showed that taking into account the relative humidity and ambient temperature, which change over time, significantly affects the distribution of concentrations in a residential area.

This paper compares the finite difference and finite volume methods for solving time-fractional diffusion equations. These methods are widely known for diffusion equations with integer order, but their effectiveness for time-fractional diffusion equations has not been sufficiently studied. The definition of the Grunwald-Letnikov fractional derivative is used to approximate the equation. An explicit difference scheme for the finite difference method is obtained and a stability condition for the fractional time order difference scheme is derived, which is also a generalisation for parabolic and hyperbolic type equations, which was previously unknown for schemes with a fractional time order. An explicit discrete form for solving subdiffusion equations in two-dimensional space with fractional time order by the finite volume method is presented. Numerical results show that the finite difference method demonstrates high accuracy, while the finite volume method is better suited for complex geometries. These findings provide insights for future developments in anomalous diffusion modeling.

Investigating the dynamics of intranasal spray represents an important aspect in the field of improving drug delivery for more effective treatment of nasal diseases. In this paper, a numerical simulation of the nasal spray nebulization process was carried out using the VOF-to-DPM model. This model allows us to describe the breakdown of a liquid flow in air into tiny droplets. The study also took into account the influence of breathing velocity and frequency on the spread of particles in the upper respiratory tract. To study the inertial motion of particles, a numerical model was developed for modeling the hydrodynamics of the respiratory air flow and the transfer of drops in the nasal cavity. This model makes it possible to describe a spray stream as a continuous flow of liquid in an air stream, which then turns into discrete droplets. The model also took into account various aspects of the behavior of droplets upon impact with the wall of the nasal cavity, including rebound, disintegration, adhesion and spreading. The results showed little effect of air flow rate on wall film mass distribution, droplet size, and particle spray atomization characteristics. A new approach using the VOF-to-DPM model is proposed to numerically simulate the process of liquid spray atomization in the human nasal cavity.

This paper examines the application of PINN models to solving a two-dimensional cylinder flow problem with limited data. Using data obtained by direct numerical simulation, a surrogate PINN model was developed and trained. The model utilizes the governing equations of fluid dynamics and heat transfer, enabling it to accurately predict flow parameters such as velocity components, pressure, and temperature. The direct computational flow model was numerically solved using the SIMPLE algorithm, which couples pressures and velocities. The results showed that the PINN model, which does not contain initial and boundary conditions from direct numerical simulation, is capable of reproducing complex dynamic processes such as the formation of a K & aacute;rm & aacute;n vortex street behind a cylinder. However, limitations were identified due to the lack of initial and boundary conditions, which led to increased errors at the boundaries of the computational domain. For example, from the data obtained using the PINN model, a very small absolute difference in error for the velocity and temperature components between the reference data and the predicted values can be noted. Thus, for the horizontal velocity component, the maximum relative error was no more than 2.5%. For the temperature component, the relative error was no more than 0.02%. However, the relative error for pressure was 60%-75%. The main reason for this large error is the lack of a reference pressure value or initial pressure conditions in the loss function. The results show that the PINN surrogate model with eight hidden layers of 200 neurons successfully copes with the task of modeling complex unsteady flow. The integration of physical laws made it possible to achieve relatively satisfactory accuracy using only 10,000 data points.

The confluence of rivers is a very common phenomenon; a large number of works have been devoted to its study. Quite often, confluent rivers are characterized by significantly different water compositions. If the flow velocity in the confluence zone is sufficiently low, then the formation of stratification of water masses is possible, which significantly affects the nature of the hydrodynamics of the phenomenon under consideration. In this case, as a rule, only one factor determining density stratification is considered. In this work, the influence of two factors: temperature and water salinity on the formation of density stratification of water masses is considered using an example of the confluence of the Sylva and Chusovaya Rivers, which are backed up by the Kama hydroelectric station. The influence of these two factors on the formation of layered structures is shown. Based on a combined set of field observations and computational experiments, the possibility of the formation of three-layer structure is shown where water masses with increased mineralization occupy the central part of the flow in depth. The novelty of the study is associated with a situation in which an equal contribution of two independent factors is realized: temperature and water salinity, which leads to a more complex distribution pattern of the consumer properties of water by depth.

This paper presents a numerical simulation of blood flow in a patient-specific pulmonary artery geometry to study the effect of pulmonary hypertension and associated pathologies such as stenosis and aneurysm on hemodynamics. Six models were investigated: healthy artery, artery with pulmonary hypertension, stenosis, aneurysm, pulmonary hypertension with stenosis, and pulmonary hypertension with aneurysm. Pulsatile blood flow was modeled using a physiologically accurate velocity waveform corresponding to normal and hypertensive conditions. The Carreau rheological model was applied to account for the non-Newtonian behavior of blood, with the flow assumed to be laminar and incompressible. The governing Navier-Stokes equations were discretized using the finite volume method. The analysis focused on the evaluation of pressure distributions, velocity profiles, and wall shear stress. The results showed significant differences between normal and pathological conditions, with pulmonary hypertension leading to increased pressure and wall shear stress, especially in areas of stenosis and bifurcations. Aneurysms caused localized decreases in flow velocity, while stenosis led to increases in velocity and wall shear stress.

This paper investigates the effect of barriers of different heights on the distribution of pollutant concentrations in a confined space using numerical simulation and machine learning models. The analysis showed that barriers significantly change the dynamics of pollutant distribution, forming localization and turbulence zones. Three barrier heights were studied: 0.1H, 0.2H, and 0.3H, and their effect was compared with no barrier. Error metrics (MAE, MAPE, and R2) demonstrated that machine learning models cope well with predicting concentrations for low barriers, but with an increase in their height, the accuracy of the models decreases due to the complexity of aerodynamic processes. The results of the study show that the barrier height has a significant impact on the accuracy of predictions, especially at points with high sensitivity to changes in air flows. The greatest error is observed at a barrier height of 0.2H, while for a barrier of 0.3H, an improvement in the stability of predictions was observed in some cases. The findings highlight the importance of considering the architecture of urban spaces and aerodynamic characteristics by designing protective structures and predictive models. The study demonstrates the applicability of machine learning to the analysis of complex aerodynamic processes, as well as the need for further improvement of models to operate in complex conditions.