Date of Defense
10-4-2026 10:00 AM
Location
Microsoft Teams
Document Type
Thesis Defense
Degree Name
Master of Science in Mechanical Engineering (MSME)
College
COE
Department
Mechanical and Aerospace Engineering
First Advisor
Dr. Mohamed M. Kamra
Keywords
Machine learning, volume of fluid (VOF) method, interface orientation, multiphase flow, Cartesian mesh.
Abstract
Accurate estimation of interface orientation is crucial for ensuring both the accuracy and robustness of Volume of Fluid (VOF) schemes in multiphase flow simulations, especially when using non-uniform Cartesian meshes. Conventional gradient reconstruction approaches, such as least-squares (LSQ) methods, often suffer from significant errors and strong oscillations on highly stretched grids. This thesis proposes a grid-transferable, learning-based methodology that predicts interface unit normal vectors directly from the local volume-fraction field on non-uniform structured Cartesian grids by means of a compact feedforward neural network.
The methodology extends earlier work originally developed for uniform grids, which is first reproduced to assess how performance deteriorates in the presence of grid non-uniformity. A new model is then trained on a synthetically generated dataset consisting of radially symmetric, star-shaped interfaces with analytically prescribed normals, sampled on non-uniform grids exhibiting cell aspect ratios up to 1000. Furthermore, specialized models trained on limited aspect-ratio intervals are used to systematically investigate sensitivity to grid stretching. In addition to global accuracy measures, a detailed error analysis is performed to characterize error trends, spatial patterns, and statistical properties over a broad spectrum of grid configurations.
Performance evaluation using the mean angular error indicates improvements of more than 78.3% compared with standard LSQ reconstructions, along with a pronounced decrease in oscillatory behavior. Examination of the error distribution shows a significant contraction of the error tail and enhanced robustness on strongly anisotropic meshes. Correlation analyses additionally characterize how prediction error relates to local grid descriptors, such as cell aspect ratio, stretching gradients, and stencil anisotropy, thereby clarifying the mechanisms that control model performance. Grid-convergence studies verify second-order accuracy for the learned predictor, in clear contrast to the poor and inconsistent convergence exhibited by LSQ-based approaches.
The proposed approach generalizes well to unseen grid configurations, including varying stretching rates, resolutions, and irregular quadratic grids, while preserving high accuracy on uniform meshes excluded from training. Detailed error diagnostics underscore the importance of embedding local geometric grid information in the input representation and demonstrate a robust, scalable, easily integrable basis for improving interface-normal prediction in VOF solvers on challenging non-uniform Cartesian grids.
Included in
DEVELOPMENT OF A NOVEL CFD APPROACH FOR PREDICTING MULTIPHASE FLOW ENHANCED BY MACHINE LEARNING
Microsoft Teams
Accurate estimation of interface orientation is crucial for ensuring both the accuracy and robustness of Volume of Fluid (VOF) schemes in multiphase flow simulations, especially when using non-uniform Cartesian meshes. Conventional gradient reconstruction approaches, such as least-squares (LSQ) methods, often suffer from significant errors and strong oscillations on highly stretched grids. This thesis proposes a grid-transferable, learning-based methodology that predicts interface unit normal vectors directly from the local volume-fraction field on non-uniform structured Cartesian grids by means of a compact feedforward neural network.
The methodology extends earlier work originally developed for uniform grids, which is first reproduced to assess how performance deteriorates in the presence of grid non-uniformity. A new model is then trained on a synthetically generated dataset consisting of radially symmetric, star-shaped interfaces with analytically prescribed normals, sampled on non-uniform grids exhibiting cell aspect ratios up to 1000. Furthermore, specialized models trained on limited aspect-ratio intervals are used to systematically investigate sensitivity to grid stretching. In addition to global accuracy measures, a detailed error analysis is performed to characterize error trends, spatial patterns, and statistical properties over a broad spectrum of grid configurations.
Performance evaluation using the mean angular error indicates improvements of more than 78.3% compared with standard LSQ reconstructions, along with a pronounced decrease in oscillatory behavior. Examination of the error distribution shows a significant contraction of the error tail and enhanced robustness on strongly anisotropic meshes. Correlation analyses additionally characterize how prediction error relates to local grid descriptors, such as cell aspect ratio, stretching gradients, and stencil anisotropy, thereby clarifying the mechanisms that control model performance. Grid-convergence studies verify second-order accuracy for the learned predictor, in clear contrast to the poor and inconsistent convergence exhibited by LSQ-based approaches.
The proposed approach generalizes well to unseen grid configurations, including varying stretching rates, resolutions, and irregular quadratic grids, while preserving high accuracy on uniform meshes excluded from training. Detailed error diagnostics underscore the importance of embedding local geometric grid information in the input representation and demonstrate a robust, scalable, easily integrable basis for improving interface-normal prediction in VOF solvers on challenging non-uniform Cartesian grids.