Bekdaulet Khudaibergen

The object of this study is steady two-dimensional incompressible viscous flow in L-shaped channels with different bend angles. The problem to be solved is to determine how the bend angle affects the flow pattern and hydraulic losses. Two geometries are compared: channels with 45° and 90° bends. The computations are carried out for Re = 500, 1000, and 2000. The flow is described by the stationary Navier-Stokes equations, which are solved by the finite element method. Newton's method is used to solve the nonlinear system. The comparison is performed under the same boundary conditions and computational parameters. The results are analyzed using velocity and pressure fields, stream-function distributions, pressure drop, loss coefficient, and Euler number. The calculations show that the 90° bend causes a stronger change in the flow after the corner than the 45° bend. In the 90° channel, the direction of motion changes more sharply. Therefore, the velocity field downstream of the bend is more distorted, the gradients are higher, and recirculation zones become more visible as Re increases. In the 45° channel, the turn is smoother, so the velocity and pressure fields change more regularly. The integral characteristics confirm this result. For all Re considered, the 90° bend gives a larger pressure drop than the 45° bend. The loss coefficient and Euler number vary with Re, but the 90° geometry remains less favorable. This is explained by stronger rearrangement of the flow caused by the sharper turn. The influence of the bend angle is shown both by field plots and by pressure-loss indicators. The results may be used in design of ducts, cooling channels, and pipelines when pressure losses in curved parts should be reduced

This study presents an integrated approach for predicting the spatial distribution of gold, copper, and lithium concentrations using machine learning, geostatistical methods, and multivariate geospatial data. The problem is formulated as a spatially dependent multivariate regression task, distinguishing it from traditional classification-based mineral prospectivity approaches. A unified database was developed, incorporating geochemical indicators, geomorphometric terrain parameters, remote sensing data, and spatial coordinates. Correlation analysis with an adaptive threshold was applied to optimize the feature set and improve model robustness. The results show that linear methods are limited in capturing nonlinear relationships, while ensemble methods provide significantly higher predictive accuracy. In some cases, geostatistical methods achieve the best performance, emphasizing the importance of spatial structure. Feature importance analysis indicates that gold prediction is primarily driven by geochemical indicators, spatial coordinates, and terrain characteristics. Results for copper and lithium confirm the general applicability of the proposed approach. Overall, the study demonstrates the effectiveness of combining machine learning and geostatistics for modeling geochemical processes.