Revealing Low-Dimensional Structure in 2D Richtmyer-Meshkov Instabilities via Parametric Reduced-Order Modeling
This work addresses the problem of controlling RMI-induced mixing in high-speed engineering tasks, offering a practical modeling approach with potential for downstream applications, though it is incremental in applying existing methods to a specific domain.
The paper tackled efficient modeling of the Richtmyer-Meshkov instability (RMI) for engineering applications like Inertial Confinement Fusion, by introducing a reduced-order model based on the LaSDI algorithm that reveals the RMI exhibits low-dimensional linear dynamics after a nonlinear transformation.
Efficient modeling of the Richtmyer-Meshkov instability (RMI) is essential to many engineering tasks, including high-speed combustion and drive and capsule geometry optimization in Inertial Confinement Fusion (ICF). In the latter, RMI causes the ablator and fuel to mix, introducing cold spots into the fuel and lowering performance; controlling RMI is thus a core ICF design concern. In this work, we introduce a reduced-order model for two-dimensional RMI based on the Latent Space Dynamics Identification (LaSDI) algorithm. We demonstrate the efficacy of the proposed methodology in efficiently parametrizing the solution space over a high-dimensional parameter vector consisting of material EOS parameters and initial conditions known to affect RMI growth rates. Using only late-time partial observations of the dynamics, we use our framework to not only provide a highly efficient dynamic surrogate model, but to reveal that the RMI exhibits the structure of a surprisingly low-dimensional and linear dynamical system, into the nonlinear growth regime, after a suitable nonlinear transformation is applied to the material interface, which we approximate as a trained autoencoder. Our use of practical observables and fundamental parameters suggests that such ROMs may be useful for downstream engineering tasks which confront the RMI, while the low-dimensional representation suggests a new direction for theoretical work.