arXiv subjects

Henrik Rosenberger

Publications and source records attributed to Henrik Rosenberger.

4 recordsLinked to original sources

arXiv2026

Stable self-adaptive timestepping for Reduced Order Models for incompressible flows

This work introduces RedEigCD, the first self-adaptive timestepping technique specifically tailored for reduced-order models (ROMs) of the incompressible Navier-Stokes equations. Building upon linear stability concepts, the method adapts the timestep by directly bounding the stability function of the employed time integration scheme using exact spectral information of matrices related to the reduced operators. Unlike traditional error-based adaptive methods, RedEigCD relies on the eigenbounds of the convective and diffusive ROM operators, whose computation is feasible at reduced scale and fully preserves the online efficiency of the ROM. A central theoretical contribution of this work is the proof, based on the combined theorems of Bendixson and Rao, that, under linearized assumptions, the maximum stable timestep for projection-based ROMs is shown to be larger than or equal to that of their corresponding full-order models (FOMs). Numerical experiments for both periodic and non-homogeneous boundary conditions demonstrate that RedEigCD yields stable timestep increases up to a factor 40 compared to the FOM, without compromising accuracy. The methodology thus establishes a new link between linear stability theory and reduced-order modeling, offering a systematic path towards efficient, self-regulating ROM integration in incompressible flow simulations.

math.NA↗

arXiv2026

Exact operator inference with minimal data

This work introduces a novel method to generate snapshot data for operator inference that guarantees the exact reconstruction of intrusive projection-based reduced-order models (ROMs). To ensure exact reconstruction, the operator inference least squares matrix must have full rank, without regularization. Existing works have achieved this full rank using heuristic strategies to generate snapshot data and a-posteriori checks on full rank, but without a guarantee of success. Our novel snapshot data generation method provides this guarantee thanks to two key ingredients: first we identify ROM states that induce full rank, then we generate snapshots corresponding to exactly these states by simulating multiple trajectories for only a single time step. This way, the number of required snapshots is minimal and orders of magnitude lower than typically reported with existing methods. The method avoids non-Markovian terms and does not require re-projection. Since the number of snapshots is minimal, the least squares problem simplifies to a linear system that is numerically more stable. In addition, because the inferred operators are exact, properties of the intrusive ROM operators such as symmetry or skew-symmetry are preserved. Numerical results for differential equations involving 2nd, 3rd and 8th order polynomials demonstrate that the novel snapshot data generation method leads to exact reconstruction of the intrusive reduced order models.

math.NA↗

arXiv2024

A pressure-free long-time stable reduced-order model for two-dimensional Rayleigh-Bénard convection

The present work presents a stable POD-Galerkin based reduced-order model (ROM) for two-dimensional Rayleigh-Bénard convection in a square geometry for three Rayleigh numbers: $10^4$ (steady state), $3\times 10^5$ (periodic), and $6 \times 10^6$ (chaotic). Stability is obtained through a particular (staggered-grid) full-order model (FOM) discretization that leads to a ROM that is pressure-free and has skew-symmetric (energy-conserving) convective terms. This yields long-time stable solutions without requiring stabilizing mechanisms, even outside the training data range. The ROM's stability is validated for the different test cases by investigating the Nusselt and Reynolds number time series and the mean and variance of the vertical temperature profile. In general, these quantities converge to the FOM when increasing the number of modes, and turn out to be a good measure of accuracy. However, for the chaotic case, convergence with increasing numbers of modes is relatively difficult and a high number of modes is required to resolve the low-energy structures that are important for the global dynamics.

physics.flu-dyn↗

arXiv2022

No pressure? Energy-consistent ROMs for the incompressible Navier-Stokes equations with time-dependent boundary conditions

This work presents a novel reduced-order model (ROM) for the incompressible Navier-Stokes equations with time-dependent boundary conditions. This ROM is velocity-only, i.e. the simulation of the velocity does not require the computation of the pressure, and preserves the structure of the kinetic energy evolution. The key ingredient of the novel ROM is a decomposition of the velocity into a field with homogeneous boundary conditions and a lifting function that satisfies the mass equation with the prescribed inhomogeneous boundary conditions. This decomposition is inspired by the Helmholtz-Hodge decomposition and exhibits orthogonality of the two components. This orthogonality is crucial to preserve the structure of the kinetic energy evolution. To make the evaluation of the lifting function efficient, we propose a novel method that involves an explicit approximation of the boundary conditions with POD modes, while preserving the orthogonality of the velocity decomposition and thus the structure of the kinetic energy evolution. We show that the proposed velocity-only ROM is equivalent to a velocity-pressure ROM, i.e., a ROM that simulates both velocity and pressure. This equivalence can be generalized to other existing velocity-pressure ROMs and reveals valuable insights in their behaviour. Numerical experiments on test cases with inflow-outflow boundary conditions confirm the correctness and efficiency of the new ROM, and the equivalence with the velocity-pressure formulation.

math.NA↗