013. Видання НаУКМА

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Browsing 013. Видання НаУКМА by Author "Avramenko, Olha"

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    Deviation of the interface between two liquid half-spaces with surface tension: multiscale approach
    (2024) Avramenko, Olha
    This paper investigates the deviation of the interface between two semi-infinite liquid media under the influence of surface tension and gravity using a multiscale analysis. The initial-boundary value problem is formulated based on key dimensionless parameters, such as the density ratio and the surface tension coefficient, to describe the generation and propagation of wave packets along the interface. A weakly nonlinear model is employed to examine initial deviations of the interface, enabling the derivation of integral solutions for both linear and nonlinear approximations. The linear approximation captures the fundamental structure of forward and backward waves, while nonlinear corrections account for higherorder effects derived through multiscale expansions. These corrections describe the evolution of the wave packet envelope, highlighting the interplay between dispersion, nonlinearity, and surface tension. Integral expressions are provided for both linear and nonlinear solutions, including those illustrating the role of even and odd initial deviations of the interface. Comparisons between linear and nonlinear approximations emphasize their interconnectedness. The linear model defines the primary wave dynamics, while the nonlinear terms contribute higher harmonics, refining the solutions and facilitating stability analysis. The results reveal significant contributions from higher-order harmonics in determining the dynamics of the interface. Furthermore, the study explores the conditions under which the nonlinear envelope remains stable, including constraints on initial amplitudes to prevent instability. This research opens new perspectives for further analysis of stability and wave dynamics at fluid interfaces using symbolic computations. Potential applications include the study of wave behavior under various geometric configurations and fluid properties. The findings contribute to advancing hydrodynamic wave modeling and establish a foundation for future research in this field.
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    PINN-based machine learning for modeling internal waves insemi-infinite fluids
    (2025) Avramenko, Olha; Kompan, Serhii; Sarana, Maksym
    This study investigates the application of Physics-Informed Neural Networks (PINNs) for modelingwave processes at the interface between two incompressible fluids of differing densities. As a first step,the linear formulation of the problem is considered, which admits an analytical solution based on aspectral method involving Fourier decomposition of the initial perturbation. This solution serves as abenchmark for testing and validating the accuracy of the PINN predictions.The implementation is carried out in Python using specialized libraries such as TensorFlow, NumPy,SciPy, and Matplotlib, which provide both efficient deep learning frameworks and tools for solving mathe-matical physics problems numerically. The approach integrates artificial intelligence with domain-specificknowledge in hydrodynamics, enabling the construction of interpretable and physically consistent mod-els. Particular attention is given to the organization of the computational experiment, automation ofvisualizations, and storage of intermediate results for further analysis. The PINN model includes a lossfunction that encodes the governing equations and boundary conditions, and the training is conductedon randomly sampled points across the spatio-temporal domain. The influence of network architectureand training parameters on solution accuracy is examined. Visualization of loss function evolutionand predicted wave profiles provides insight into convergence behavior and physical plausibility of thesolutions.A comparative analysis between the PINN-based and analytical solutions across different time in-stances is presented, revealing phase shifts and amplitude deviations. The model demonstrates goodagreement at early times and a gradual accumulation of errors as time progresses—an expected featureof this class of methods. The results confirm the feasibility of applying the PINN framework to linearhydrodynamic problems, laying the groundwork for future extensions to weakly and strongly nonlinearregimes, including studies of wave stability and nonlinear wave dynamics.