Proper Orthogonal Decomposition-based Model-Order Reduction for Smoothed Particle Hydrodynamics Simulation

TL;DR

This paper introduces a POD-based model-order reduction method for mesh-free SPH simulations, demonstrating significant error reduction and efficiency improvements in complex welding process modeling.

Contribution

It presents the first application of POD-MOR to SPH simulations, showing its feasibility and effectiveness in reducing computational errors and accelerating simulations.

Findings

POD-MOR significantly reduces computational error at the same degrees of freedom.

The acceleration technique via linearization maintains small errors.

Effective in predictive SPH simulations with varying parameters.

Abstract

In this paper, we present a projection-based model-order reduction (MOR) technique for smoothed particle hydrodynamics (SPH) simulations, which is a mesh-free approach within the Lagrangian framework. Our approach utilizes the proper orthogonal decomposition (POD) technique to generate a subspace basis for the reduction process. The main objective of this study is to conduct an initial exploration of the feasibility of employing POD-based MOR (POD-MOR) in SPH simulations and to quantify the associated POD error. To illustrate the effectiveness of this approach, we consider the friction stir spot welding problem, which involves the coupling of flow equations and heat equation. Our findings reveal that, with the same degrees of freedom, POD-MOR significantly reduces computational error compared to the uniform reduction of particle numbers in SPH simulations. Additionally, the acceleration technique of POD-MOR for SPH simulation via linearization and freezing coefficients has been shown to be effective while keeping the error small. We have also showed the effectiveness of POD-MOR in predictive settings in SPH simulations with different parameter values.