# Kernel-smoothed proper orthogonal decomposition (KSPOD)-based emulation for prediction of spatiotemporally evolving flow dynamics

## TL;DR

This paper introduces a kernel-smoothed POD (KSPOD) method that significantly accelerates the prediction of complex flow dynamics, enabling rapid design exploration with high accuracy compared to traditional high-fidelity simulations.

## Contribution

The study develops a novel KSPOD-based surrogate model that improves upon previous CPOD methods by incorporating kernel smoothing and kriging, greatly enhancing prediction efficiency and fidelity.

## Key findings

- KSPOD model accurately captures spatiotemporal flow dynamics.
- Prediction speed is 42,000 times faster than high-fidelity simulations.
- Model effectively supports rapid design exploration.

## Abstract

This interdisciplinary study, which combines machine learning, statistical methodologies, high-fidelity simulations, and flow physics, demonstrates a new process for building an efficient surrogate model for predicting spatiotemporally evolving flow dynamics. In our previous work, a common-grid proper-orthogonal-decomposition (CPOD) technique was developed to establish a physics-based surrogate (emulation) model for prediction of mean flowfields and design exploration over a wide parameter space. The CPOD technique is substantially improved upon here using a kernel-smoothed POD (KSPOD) technique, which leverages kriging-based weighted functions from the design matrix. The resultant emulation model is then trained using a dataset obtained through high-fidelity simulations. As an example, the flow evolution in a swirl injector is considered for a wide range of design parameters and operating conditions. The KSPOD-based emulation model performs well, and can faithfully capture the spatiotemporal flow dynamics. The model enables effective design surveys utilizing high-fidelity simulation data, achieving a turnaround time for evaluating new design points that is 42,000 times faster than the original simulation.

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Source: https://tomesphere.com/paper/1802.08812