2026 Abstracts Spring meeting

Revisiting the role of reorthogonalisation in the solution of least-squares problems

Large-scale least squares problems arise in many areas of scientific computing, including inverse problems, data assimilation, machine learning and PDE-constrained optimisation. Krylov subspace methods allow users to solve these problems using only matrix-vector products, and are hence suitable for high-dimensional problems. Although in exact arithmetic Krylov subspace methods generate mutually orthonormal basis vectors, this behaviour breaks down in finite precision, leading to delayed convergence. In this talk I will present some memory-efficient strategies for partial reorthogonalisation that can provide substantial acceleration at a significantly reduced cost compared to full reorthogonalisation, and demonstrate our results on a number of illustrative examples.

Evolution and Future of CFD Development at NLR

NLR’s CFD system ENFLOW has, since its emergence in the late-1980s vector-supercomputing era, developed from a tool for transonic aerodynamic analysis into a broader CFD environment supporting aeroelasticity, aeroacoustic applications, and design optimization. Over the same period, the target problems have shown increasing physical and geometric complexity, while CFD workflows have remained partly a craft, relying on expert, tailor-made grids and case-specific choices. The talk will review key algorithmic and computational developments over the past decades, and discuss how future needs, including richer multi-physics, greater automation, and adaptation to modern GPU-accelerated HPC systems, are likely to shape the next generation of ENFLOW.

Mathematical Models for the Mechanics of Soft Tissues: From Linear Elasticity to Morpho-Visco-Poroelasticity

Biological tissues are often subjected to forces. In many cases, such as tumor growth or skin contraction, it is crucially important to model the state of tissues that are exposed to forces in order to improve or optimize therapies for different pathologies. The simplest models use linear elasticity as a constitutive law. This linearity enables the use of the superposition principle and the use of fundamental solutions to analyze the influence of multiple points of action of forces. A clear illustration of this principle is the immersed interface method. In this presentation, we discuss this principle in terms of convergence properties using the singularity removal principle.

However, in real-life tissues, the use of linear elasticity is too restrictive due to the presence of moisture and the porous structure of biological tissues. Furthermore, in various biomedical cases, the microstructure of the tissue changes due to cellular activity. For this reason, we construct and use a model that consists of elasticity, porosity and microstructural changes. The mathematical framework is referred to as morpho-visco-poroelasticity. This framework is original and for this reason, we analyze this framework in terms of stability around equilibria. Since numerical solutions can be characterized by spurious oscillations, we provide conditions for monotonicity by mathematical analysis. Furthermore, we propose a numerical stabilization method to avoid spurious oscillations on forehand.

Level set-based topology optimization for flow problems

Many engineering systems rely on moving fluid to achieve specific functions. Such flow devices can reach increased performance when their geometry is
optimized. Originally introduced for structural design, topology optimization has now been successfully applied to flow problems. To design flow devices, accurately resolving the geometry of and the physics around fluid/solid interfaces is crucial. With these challenges in mind, this talk will explore the use of the level set method to represent the geometry of the fluid devices and its combination with an immersed boundary technique to predict the physics responses in flow problems. Design domains are immersed in a background mesh and approximations are extended by a generalized Heaviside enrichment strategy. The ability of immersed methods to accurately resolve flows is demonstrated with benchmark examples considering different geometry configurations, flow regimes, and coupled physics. The proposed level set-based topology optimization framework is illustrated with the design of fluid devices for minimum pressure loss, minimum dissipated energy, target flow distribution, or maximum heat transfer.

A deep dive into shallow water models

The Shallow Water Equations (SWE) are a well-known tool for the simulation of free-surface flows. They reduce the 3D velocity setting of the incompressible Navier-Stokes equations to the correspinding depth-averaged horizontal velocities. While efficient, this approach does not take into account velocity profiles varying in vertical direction and it is therefore limited in accuracy and applicability.
In this talk, we introduce the Shallow Water Moment Equations (SWME), which first parametrize the velocity profile using a polynomial expansion and then derive evolution equations for the coefficients using higher-order depth-averaging. We show the explicit equations, discuss properties like hyperbolicity, steady states or entropy, and present numerical results which highlight the advantages of this new way of simulating free-surface flows.

Reduced Subgrid Scale Terms for Turbulent Flows

Turbulent flows span a wide range of spatial and temporal scales, presenting a major computational bottleneck. Large eddy simulations (LES) address this challenge through coarse graining, where the effects of unresolved motions appear as an unclosed subgrid-scale (SGS) term in the coarse-grained equations.

Recent efforts in computational fluid dynamics have explored numerous data-driven approaches to model the SGS term, typically aiming to reproduce the full coarse-grained flow field, a high-dimensional and computationally demanding task.

Many practical LES applications focus on a limited set of Quantities of Interest (QoIs), such as average energy or enstrophy. By shifting the focus to these specific metrics, we reformulate SGS modeling as a low-dimensional learning problem. Our approach represents unresolved dynamics through a minimal set of scalar time series, significantly reducing complexity while enhancing model interpretability.

We introduce the Tau-Orthogonal (TO) method, which captures QoI-state dependence and temporal correlations using regularized least-squares regression combined with a multivariate Gaussian residual model. This yields a simple yet effective stochastic time-series prediction model. The resulting stochastic time-series model accurately reproduces long-term QoI distributions and maintains robust performance across hyperparameter settings. Despite being trained solely on QoI trajectories, the TO method effectively captures fundamental flow features, including kinetic energy spectra and coherent structures.

Symplectic model reduction of general nonlinear port-Hamiltonian systems

This work proposes a structure-preserving model order reduction (MOR) method for general nonlinear port-Hamiltonian (pH) systems based on a symplectic projection.
Consider a high-dimensional pH system which is defined by a Dirac structure, a Hamiltonian, and a resistive map; its simulation is computationally expensive. To reduce the computational cost, a structure-preserving MOR method is required to approximate the original system with a low-dimensional pH system. In recent decades, lots of structure preserving MOR methods for pH systems have been proposed. However, most existing algorithms can only be applied to a special type of pH systems where the resistive map is linear with respect to the effort (the gradient of the Hamiltonian).
The main novelty of this work is that a symplectic-like projection is applied to general pH systems, which preserves the Dirac structure and the Hamiltonian. Meanwhile, a reduced-order resistive map is built based on an approximation map we construct.
Consequentially, the resulting reduced-order model (ROM) is again a pH system. In the numerical example, we test the proposed algorithm with a pH system given by a nonlinear circuit where the resistive relation is a nonlinear map with respect to the effort. The results show that both the state and output error of the resulting ROMs decrease as the reduced-order increases.