PROPER ORTHOGONAL DECOMPOSITION TECHNIQUE FOR DIMENSIONAL REDUCTION FOR NUMERICAL SNAPSHOT MATRIX

Abstract

Computational fluid dynamics (CFD) simulations generate huge datasets with many variables such as Velocity and Pressure at nodes, elements, and time steps. It is challenging and expensive to analysis large datasets and storage, developing applications over the large datasets required additional computational resources and storage volume. To addresses this problem, we have employed data reduction technique for the reduction of the complexity and utilize its computational resources. Reduced Order Modelling emerged technique leading dimensional reduction yet preserving dominant features, patterns and discarding less significant features. Focusing on developing the Reduced Order Models (ROM) for data compression, we implemented Proper Orthogonal Decomposition (POD) technique for dimensionality reduction. Proper Orthogonal Decomposition (POD) is widely used for building efficient Reduced Order Model (ROM) in CFD simulations, enabling effective dimensionality reduction while preserving key flow characteristics. POD extracts the high-energy structures from the flow field, representing dominant patterns through POD modes that contributes to the overall dynamics. Dimensional reduction is achieved by truncating lower-energy modes based on rank, retaining only the most significant features. In this paper we conducted numerical simulation flow over the convex shape object cantered in the flow path, with parametric velocity ranging 25 -300 m/s and density 900 - 2000 kg/m2 of the water. The solution matrix is extracted and total volume was 8.83 MB. After computing POD modes and captured five most energetic modes (Rank = 5) and truncated other modes. The resulting ROM took 4.42 MB achieving a data volume saving of 4.41 MB (8.83 - 4.42 MB). when compared with volume consumptions over the single full numerical simulation (482 MB) to ROM (4.2 MB) is 477.8 MB and percentage occupation for the ROM is only 0.87% which is less than 1% of the original size of full simulation. This study also explores effective techniques for generating and truncating POD-based ROM. It also demonstrates the use of EZyRB-based ROM combined with Radial Basis Function (RBF) interpolation is applied to the POD coefficients using EZyRB library allows fast reconstruction of flow fields without running Full Order Model (FOM) to predict system responses for new parameter values, density 1232 kg/m2 and velocity 152 m/s we successfully reconstructed the flow field using ROM without conducting FOM. These new parameter values were projecting onto the original spatial domain for the visualization and comparing results with Ansys Fluent FOM. Highlighting the efficiency and effectiveness of ROM in parametric interpolation with lower dimensions and provides an intuitive approach for developing digital models that accurately represent physical systems with significantly reduced the computational volume and resources.