Reduced order models for Lagrangian hydrodynamics

Abstract

As a mathematical model of high-speed flow and shock wave propagation in a complex multimaterial setting, Lagrangian hydrodynamics is characterized by moving meshes, advection-dominated solutions, and moving shock fronts with sharp gradients. These challenges hinder the existing projection-based model reduction schemes from being practical. We develop several variations of projection-based reduced order model techniques for Lagrangian hydrodynamics by introducing three different reduced bases for position, velocity, and energy fields. A time-windowing approach is also developed to address the challenge imposed by the advection-dominated solutions. Lagrangian hydrodynamics is formulated as a nonlinear problem, which requires a proper hyper-reduction technique. Therefore, we apply the over-sampling DEIM and SNS approaches to reduce the complexity due to the nonlinear terms. Finally, we also present both a posteriori and a priori error bounds associated with our reduced order model. We compare the performance of the spatial and time-windowing reduced order modeling approaches in terms of accuracy and speed-up with respect to the corresponding full order model for several numerical examples, namely Sedov blast, Gresho vortices, Taylor-Green vortices, and triple-point problems.

arXiv comment42 pages, 7 figure, 8 tables

References in corpus (23)

• The GNAT method for nonlinear model reduction: effective implementation and application to computational fluid dynamics and turbulent flows
• A New Selection Operator for the Discrete Empirical Interpolation Method -- improved a priori error bound and extensions
• On the need for a nonlinear subscale turbulence term in POD models as exemplified for a high Reynolds number flow over an Ahmed body
• POD/DEIM Nonlinear model order reduction of an ADI implicit shallow water equations model
• Adaptive $h$-refinement for reduced-order models
• Extreme learning machine for reduced order modeling of turbulent geophysical flows
• Conservative model reduction for finite-volume models
• Data-Driven Variational Multiscale Reduced Order Models
• Lagrangian Dynamic Mode Decomposition for Construction of Reduced-Order Models of Advection-Dominated Phenomena
• Generating Random Earthquake Events for PTHA
• Component-wise reduced order model lattice-type structure design
• Domain-decomposition least-squares Petrov-Galerkin (DD-LSPG) nonlinear model reduction
• Non-Markovian Closure Models for Large Eddy Simulations using the Mori-Zwanzig Formalism
• POD/DEIM Reduced-Order Modeling of Time-Fractional Partial Differential Equations with Applications in Parameter Identification
• Lagrangian basis method for dimensionality reduction of convection dominated nonlinear flows
• Efficient space-time reduced order model for linear dynamical systems in Python using less than 120 lines of code
• Accelerating design optimization using reduced order models
• Efficient nonlinear manifold reduced order model
• On the comparison of LES data-driven reduced order approaches for hydroacoustic analysis
• Manifold Approximations via Transported Subspaces: Model reduction for transport-dominated problems
• VisIt: Experiences with Sustainable Software
• Depth separation for reduced deep networks in nonlinear model reduction: Distilling shock waves in nonlinear hyperbolic problems
• Windowed space-time least-squares Petrov-Galerkin method for nonlinear model order reduction

Cited by in corpus (8)

• LaSDI: Parametric Latent Space Dynamics Identification
• Non-intrusive reduced order modeling of natural convection in porous media using convolutional autoencoders: comparison with linear subspace techniques
• Domain-decomposition least-squares Petrov-Galerkin (DD-LSPG) nonlinear model reduction
• Parametric Dynamic Mode Decomposition for Reduced Order Modeling
• gLaSDI: Parametric Physics-informed Greedy Latent Space Dynamics Identification
• S-OPT: A Points Selection Algorithm for Hyper-Reduction in Reduced Order Models
• Continuous conditional generative adversarial networks for data-driven solutions of poroelasticity with heterogeneous material properties
• Reduced order modeling for flow and transport problems with Barlow Twins self-supervised learning