A wind gust is a short-term but strong phenomenon naturally appearing in the atmospheric boundary layer. Fluid-structure interaction investigations under wind gust conditions, ideally in a wind tunnel with controlled parameters, are essential for evaluating the safety of final designs for example in civil engineering. For this purpose, Wood et al. (J Wind Eng Ind Aerodyn 230:105170, 2022) developed a novel wind gust generator denoted the “Paddle”. Its basic principle relies on the partial dynamic blocking of the wind tunnel nozzle’s outlet by a vertically moving plate that penetrates the free-stream. The setup and the flow induced by the paddle were numerically simulated in Boulbrachene and Breuer (Phys Fluids 36:015146, 2024) by employing an immersed boundary method (IBM) relying on a direct forcing approach to mimic the motion of the paddle. This configuration restricted the undisturbed gust region in the test section of the wind tunnel as a result of the shear layer forming at the lower edge of the moving paddle. Moreover, it caused an undershoot of the gust velocity below the free-stream velocity as a result of high pressure losses associated with the paddle’s blockage effect. Wood and Breuer (Artificial wind gust generation based on an adaptive nozzle design. Berlin, pp 9-1–9-8, 2024) and Wood and Breuer (J Wind Eng Ind Aerodyn 261:106080, 2025) recently introduced an improved design that addresses the shortcomings of the paddle while maintaining the same underlying principle for generating the gust. The new setup features an adjustable nozzle with a fully rotatable upper contour to generate smoother wind gusts. In order to gain a comprehensive understanding of the evolving flow field during the movement of the nozzle’s upper boundary, large-eddy simulations of the process are conducted. This involves modeling the nozzle’s upper boundary as a moving immersed boundary using again the IBM with direct forcing but this time on a curvilinear Eulerian grid. The numerical methodology and its application to the movable nozzle case is presented in the present study. The predicted results are analyzed in detail and compared with available experimental measurement data (Wood and Breuer in Artificial wind gust generation based on an adaptive nozzle design. Berlin, pp 9-1–9-8, 2024) and (Wood and Breuer in J Wind Eng Ind Aerodyn 261:106080, 2025).
This study presents a high-order discontinuous Galerkin (DG) scheme for capturing the Richtmyer–Meshkov Instability (RMI) at polygonal gas interfaces. The two-dimensional, two-component compressible Euler equations are solved using an in-house explicit modal DG solver with third-order accuracy, employing scaled Legendre polynomials and a strong stability-preserving Runge–Kutta time integration method. The accuracy of solver is validated against experimental data for a shocked square light gas interface, demonstrating excellent agreement in interface evolution and characteristic scales. The study focuses on the interaction of shock waves with trapezoidal helium ( He ) and sulfur hexafluoride ( SF_6 ) gas interfaces surrounded by nitrogen. Results reveal that density gradients significantly influence the flow evolution, vorticity generation, and instability growth. For the He interface, weaker baroclinic torque leads to gradual vorticity development, moderate vortex roll-up, and a laminar-like evolution with coherent structures. In contrast, the SF_6 interface, with its higher density contrast, exhibits intense baroclinic vorticity generation, amplified Kelvin–Helmholtz instabilities, and strong vortex interactions, resulting in chaotic mixing and turbulent flow behavior. Spatially integrated fields of average vorticity, baroclinic vorticity, and enstrophy provide quantitative insights into the dynamics, showing a sharp increase in instability growth for SF_6 compared to He. The findings highlight the robustness of the high-order DG scheme in accurately capturing complex shock-interface interactions, instabilities, and flow structures.
This paper explores fluid-structure interaction (FSI) of two-phase flows involving a three-phase contact line using the extended Discontinuous Galerkin (XDG) method within the Euler-Euler framework. The fluid dynamics are governed by the incompressible Navier-Stokes equations, while the soft solid mechanics of the Kelvin-Voigt material are described using the Navier-Cauchy equations. Coupling conditions between the fluid and solid phases are established through continuity of velocity and stress at the interface, mirroring the conditions applied at the boundary between two fluid phases. At the three-phase contact line, the generalized Young’s equation is employed to maintain consistency. The spatial discretization of the governing equations is also introduced. A convergence study of FSI is presented, validated against an analytical solution, alongside several classical FSI test cases. Additionally, the paper showcases 2D and 3D simulations of a droplet interacting with a soft substrate at a three-phase contact line, highlighting the method’s capabilities and practical implications.
The structural integrity of engineering components is crucial in engineering design, because they are prone to damage due to repeated loading and unloading, particularly under low-cycle fatigue (LCF) conditions. This study presents a critical strain-based phase-field damage model (PFDM) for ductile fatigue. The model captures the accumulation of damage by relating the critical strain energy to fracture energy release rate. The PFDM formulation is integrated into Finite Element Method (FEM) software, enabling the simulation of damage phenomena under cyclic loading. The model considers the evolution of damage driven by energy-based criteria. A numerical example demonstrates the capability of the approach to predict fatigue-induced failure and validates the model’s functionality. This work underscores the importance of energy-based damage indicators for modeling fatigue in ductile materials and a possibility to use critical total strain energy as a material parameter.
Multi-phase flows occur in industrial applications such as sealing rings in internal combustion engines, electrolysis, foam casting, and many others. Simulation of these processes is a valuable tool to investigate relevant physical phenomena and perform design optimization in the early stages of component development. This is especially relevant when building multiple prototypes is more expensive than running multiple simulations. When the fluid domain deforms over time, additional challenges arise for modeling approaches and simulation software. Adaptive re-meshing can make simulations more efficient when facing a deforming fluid domain as well as moving inter-fluid boundaries typical in multi-phase flow. We investigate two versions of adaptive refinement for compressible/incompressible multi-phase flow with the level-set method using space-time finite elements [1] for a fixed domain benchmark problem and a newly introduced deforming domain test case. Both the accuracy and potential gains in performance are investigated. The two derived refinement schemes agree well with the rising bubble benchmark case and give reasonable results for the studied moving domain test case. Both approaches increase performance compared to uniform refinement for the investigated cases. A heuristic for estimating the relative performance of the two approaches is derived for assembly-heavy computations.
Optimizing the performance and durability of engineering components requires efficient tribological system simulation. Gaining insight into such systems can be done by elastohydrodynamic lubrication (EHL) simulation or experimental methods. The latter is often costly and time-consuming. EHL, however, represents an alternative by providing understanding by incorporating hydrodynamic behavior, deformation, and contact mechanics. However, these simulations can be computationally intensive. Machine learning, especially models like physics-informed neural networks (PINNs), offers a promising solution by directly embedding the governing physical laws into neural network models. By integrating partial differential equations (PDEs) into their framework, PINNs enable fast and reusable simulations, making them particularly useful for tribological research. This work applies PINNs to model the hyperelastic deformation of a pneumatic seal, using the Piola–Kirchhoff stress equilibrium as the governing law to capture finite deformations. The seal material is modeled as a Neo-Hookean solid. The developed PINN framework for deformation can integrate with a previously established PINN for hydrodynamic lubrication to achieve a complete, accelerated EHL simulation. Results confirm the capability of PINNs to model deformation with high accuracy and reduced computational effort, highlighting their potential as efficient tools for simulating complex tribological systems.
In multiphase simulations, accurately determining the interface between fluids is a significant challenge. This study focuses on the Volume of Fluid (VOF) method, which reconstructs fluid interfaces after solving the equations of motion. The primary goal is to achieve a smooth interface that ensures accurate volume flux approximations in Eulerian simulations while balancing computational efficiency and stability. This work investigates enhancements in the Piecewise Linear Interface Construction (PLIC) method, particularly addressing the computational burden of positioning reconstructed planes within polyhedral cells through efficient volume calculations. The new approach is integrated into OpenFOAM as a new freely available module and tested against benchmark cases to evaluate its performance. Results demonstrate improvements in computational efficiency, offering valuable insights for simulating complex two-phase flows relevant to numerous real world applications.
Adjoint evaluations are increasingly used in gradient-based aerodynamic shape optimization due to their cost-effectiveness. However, high-dimensional gradient based optimizations face the curse of dimensionality, leading to higher computational costs and slower convergence rates. This paper introduces a novel multi-level strategy to accelerate convergence. The approach structures the optimization into hierarchical levels, where each level corresponds to a sub-optimization within a reduced-dimensional active subspace. The subspace’s dimension gradually increases as the optimization progresses, with the final level addressing the full-dimensional space. This aims to guide the optimizer toward the correct optimum during early iterations while minimizing errors from dimension reduction in the later stages. The method was validated on a 13-dimensional analytical geometry parametrization problem, achieving a 19
We present a novel framework to model the effective material behavior of irregular cellular materials such as stochastic strut-based lattices. The essential modeling tool is a parametric physics-augmented neural network establishing a flexible relation between lattice design variables and the effective constitutive stiffness tensor. We derive and implement hard constraints, ensuring that relevant physical principles such as material symmetry and positive definiteness of the stiffness tensor are satisfied. Additionally, we address the generation of training data from computational homogenization and model suitable parametric representative volume elements. Finally, we incorporate our model into a multiscale topology optimization problem to compute functionally graded lattice structures with improved stiffness properties.
The decumulation of a defined contribution (DC) pension plan is well known to be one of the hardest problems in finance. We model this decumulation challenge as an optimal stochastic control problem. The control problem is solved, at each rebalancing date, by alternatively solving a linear partial-integro differential equation (PIDE) followed by an optimization step. We solve the PIDE by using a δ-monotone Fourier method, which ensures that monotonicity holds to O(δ). We allow for the use of leverage (i.e. borrowing to invest in stocks), as well as minimum constraints on bond holdings. We pay particular attention to minimizing wrap-around error, an issue which is endemic for Fourier methods and central to the effective use of these methods for optimal control problems. Rather unexpectedly, we find that restricting the portfolio equity fraction to a maximum of 50% does not reduce portfolio efficiency noticeably. This may be a useful strategy for risk-averse retirees.
This contribution investigates the computational complexity of simulating linear ordinary differential equations (ODEs) on digital computers. We provide an exact characterization of the complexity blowup for a class of ODEs of arbitrary order based on their algebraic properties, extending previous characterization of first order ODEs. Complexity blowup indeed arises in most ODEs (except for certain degenerate cases) and means that there exists a low complexity input signal, which can be generated on a Turing machine in polynomial time, leading to a corresponding high complexity output signal of the system in the sense that the computation time for determining an approximation up to n significant digits grows faster than any polynomial in n. Similarly, we derive an analogous blowup criterion for a subclass of first-order systems of linear ODEs. Finally, we discuss the implications for the simulation of analog systems governed by ODEs and exemplarily apply our framework to a simple model of neuronal dynamics-the leaky integrate-and-fire neuron-heavily employed in neuroscience.
We present an optimization-based formulation of the Red Light Green Light (RLGL) algorithm for computing stationary distributions of large Markov chains. This perspective clarifies the algorithm's behavior, establishes exponential convergence for a class of chains, and suggests practical scheduling strategies to accelerate convergence.
Efficient solutions of large-scale, ill-conditioned and indefinite algebraic equations are ubiquitously needed in numerous computational fields, including multiphysics simulations, machine learning, and data science. Because of their robustness and accuracy, direct solvers are crucial components in building a scalable solver toolchain. In this article, we will review recent advances of sparse direct solvers along two axes: 1) reducing communication and latency costs in both task- and data-parallel settings, and 2) reducing computational complexity via low-rank and other compression techniques such as hierarchical matrix algebra. In addition to algorithmic principles, we also illustrate the key parallelization challenges and best practices to deliver high speed and reliability on modern heterogeneous parallel machines.
We present an overview of randomized orthogonalization techniques that construct a well-conditioned basis whose sketch is orthonormal. Randomized orthogonalization has recently emerged as a powerful paradigm for reducing the computational and communication cost of state-of-the-art orthogonalization procedures on parallel architectures, while preserving, and in some cases improving, their numerical stability. This approach can be employed within Krylov subspace methods to mitigate the cost of orthogonalization, yielding a randomized Arnoldi relation. We review the main variants of the randomized Gram–Schmidt and Householder QR algorithms, and discuss their application to Krylov methods for the solution of large-scale linear algebra problems, such as linear systems of equations, eigenvalue problems, the evaluation of matrix functions, and matrix equations.
