arXiv subjects

Norbert Hosters

Publications and source records attributed to Norbert Hosters.

At least 19 recordsLinked to original sources

arXiv2026

Marking strategies for adaptive mesh refinement: An efficiency-focused benchmark study for steady solid and fluid mechanics problems

Adaptive mesh refinement (AMR) is indispensable for efficient finite element analyses. However, its performance depends not only on the refinement itself but also on strategy to mark elements for refinement and the way it is tuned. This work compares classical marking methods (maximum, D\"orfler bulk-chasing, quantile) with non-classical, statistically based approaches (z-score, Isolation Forest), all driven by the residual-based Kelly error estimator and tested on steady solid and fluid mechanics problems. The study finds quantile and z-score markings to be the most robust, D\"orfler effective for large bulk parameters, and maximum marking sensitive to irregular fields. Isolation Forest can rival top classical methods with a generous contamination level but may fail under aggressive settings. These results offer practical guidance for selecting marking strategies that balance refinement aggressiveness and computational cost in adaptive FEM workflows.

cs.CE↗

arXiv2026

Quantum Lattice Boltzmann with Denoising Collision Operators

The Lattice Boltzmann method (LBM) is a well-established mesoscopic approach for simulating fluid dynamics by evolving particle distribution functions on discrete lattices. While the LBM is highly parallelizable on classical hardware, its translation to quantum algorithms is impeded by the collision process, which is intrinsically nonlinear and irreversible. Several existing quantum formulations implement this process through repeated quantum tomography and state preparation at every timestep, leading to significant overheads. We introduce a quantum LBM based on a denoising-type collision operator that avoids tomography-based updates. The collision dynamics are reformulated as an orthogonal projection onto the linearized manifold of equilibrium distributions around a reference state. This geometric approach filters non-equilibrium components while preserving lattice symmetries and approximating nonlinear terms needed to recover hydrodynamic behavior. A complete pipeline is presented with efficient gate-level realizations, incorporating encoding of distributions, collision, streaming, boundary conditions, and measurement of physical quantities such as hydrodynamic forces. In addition, we outline an approach for implementing projector-based operators deterministically without postselection, paving the way to fully coherent multi-timestep LBM simulations. Numerical experiments for advection-diffusion and flow problems demonstrate that the method reproduces macroscopic behaviors with high accuracy, with performance depending on the choice of reference state.

quant-ph↗

arXiv2026

Adaptive Encoding Strategy for Quantum Annealing in Mixed-Variable Engineering Optimization

Mixed discrete-continuous optimization is central to engineering design, where discrete choices interact with continuous fields. These problems are difficult due to high-dimensional, complex search spaces. To tackle them, Quantum Annealing (QA) is promising, yet its native binary nature supports only discrete variables, making accurate and efficient encodings of continuous quantities a central challenge. Existing approaches either split the coupled problem, mapping discrete decisions to QA while solving continuous fields classically, or use fixed-bit-depth encodings. The former compromises QA's global search advantages; the latter can underrepresent dynamic range or inflate the number of binary variables. We show that simply increasing bit depth can even degrade performance on current QA hardware, underscoring the need for alternative encodings. In response, we introduce an adaptive encoding strategy for continuous variables in QA that enables efficient treatment of coupled mixed-variable problems. We propose an update strategy for the representable ranges of the continuous variables and demonstrate its utility by integrating it into the minimum complementary energy formulation for structural design optimization, which provides a single, coupled constrained problem. We apply a quadratic penalty method where we update the representation of the continuous variables while targeting the full original objective, preserving QA's global search capability. On a published benchmark, the size optimization of a composite rod, our adaptive encoding improves solution quality under a fixed binary variable budget, demonstrating a superior precision-resource trade-off. Since the framework generalizes beyond structural design, it offers practical guidance for encoding continuous variables for QA and indicates that adaptive representations can enhance precision on current hardware.

cs.CE↗

arXiv2024

Multiphase Flow Simulation of Blow-by and Fuel-in-Oil Dilution via the Piston Ring Pack Using the CFD Level-Set Method

Modern diesel engines temporarily use a very late post-injection in the combustion cycle to either generate heat for a diesel particulate filter regeneration or purge a lean NOx trap. In some configurations, unburned fuel is left at the cylinder walls and is transported via the piston rings toward the lower crankcase region, where fuel may dilute the oil. Reduced oil lubrication shortens the oil service intervals and increases friction. Beside diesel fuel, this problem may also occur for other types of liquid fuels such as alcohols and e-fuels. The exact transport mechanism of the unburned fuel via the piston ring pack grooves and cylinder wall is hard to measure experimentally, motivating numerical flow simulation in early design stages for an in-depth understanding of the involved processes. A new CFD simulation methodology has been developed to investigate the transient, compressible, multiphase flow around the piston ring pack, through the gap between piston and liner, and its impact on fuel or oil transport. The modern level-set approach is used for the multiphase physics, which directly captures the sharp interface between blow-by gas and fuel or oil. Transient blow-by and two-phase flow simulations have been extensively applied to a Ford 2.0L I4 diesel test engine. The results confirm the validity of the flow compressibility assumption and highlight the sensitivity of the fuel leakage regarding piston sealing ring movement and highly resolved meshes for the multiphase flow. Based on the simulation results, design recommendations for piston and piston ring geometry are provided to reduce the fuel transport toward the crankcase.

physics.flu-dyn↗

arXiv2023

On the number of subproblem iterations per coupling step in partitioned fluid-structure interaction simulations

In literature, the cost of a partitioned fluid-structure interaction scheme is typically assessed by the number of coupling iterations required per time step, while ignoring the internal iterations within the nonlinear subproblems. In this work, we demonstrate that these internal iterations have a significant influence on the computational cost of the coupled simulation. Particular attention is paid to how limiting the number of iterations within each solver call can shorten the overall run time, as it avoids polishing the subproblem solution using unconverged coupling data. Based on systematic parameter studies, we investigate the optimal number of subproblem iterations per coupling step. Lastly, this work proposes a new convergence criterion for coupled systems that is based on the residuals of the subproblems and therefore does not require any additional convergence tolerance for the coupling loop.

math.NA↗

arXiv2022

A Robin-Neumann Scheme with Quasi-Newton Acceleration for Partitioned Fluid-Structure Interaction

The Dirichlet-Neumann scheme is the most common partitioned algorithm for fluid-structure interaction (FSI) and offers high flexibility concerning the solvers employed for the two subproblems. Nevertheless, it is not without shortcomings: to begin with, the inherent added-mass effect often destabilizes the numerical solution severely. Moreover, the Dirichlet-Neumann scheme cannot be applied to FSI problems in which an incompressible fluid is fully enclosed by Dirichlet boundaries, as it is incapable of satisfying the volume constraint. In the last decade, interface quasi-Newton methods have proven to control the added-mass effect and substantially speed up convergence by adding a Newton-like update step to the Dirichlet-Neumann coupling. They are, however, without effect on the incompressibility dilemma. As an alternative, the Robin-Neumann scheme generalizes the fluid's boundary condition to a Robin condition by including the Cauchy stresses. While this modification in fact successfully tackles both drawbacks of the Dirichlet-Neumann approach, the price to be paid is a strong dependency on the Robin weighting parameter, with very limited a priori knowledge about good choices. This work proposes a strategy to merge these two ideas and benefit from their combined strengths. The resulting quasi-Newton-accelerated Robin-Neumann scheme is compared to both Robin- and Dirichlet-Neumann variants. The numerical tests demonstrate that it does not only provide faster convergence, but also massively reduces the influence of the Robin parameter, mitigating the main drawback of the Robin-Neumann algorithm.

cs.CE↗

arXiv2022

A Data-driven Reduced Order Modeling Approach Applied In Context Of Numerical Analysis And Optimization Of Plastic Profile Extrusion

In course of this work, we examine the process of plastic profile extrusion, where a polymer melt is shaped inside the so-called extrusion die and fixed in its shape by solidification in the downstream calibration unit. More precise, we focus on the development of a data-driven reduced order model (ROM) for the purpose of predicting temperature distributions within the extruded profiles inside the calibration unit. Therein, the ROM functions as a first step to our overall goal of prediction based process control in order to avoid undesired warpage and damages of the final product.

math.NA↗

arXiv2022

Time-Continuous and Time-Discontinuous Space-Time Finite Elements for Advection-Diffusion Problems

We construct four variants of space-time finite element discretizations based on linear tensor-product and simplex-type finite elements. The resulting discretizations are continuous in space, and continuous or discontinuous in time. In a first test run, all four methods are applied to a linear scalar advection-diffusion model problem. Then, the convergence properties of the time-discontinuous space-time finite element discretizations are studied in numerical experiments. Advection velocity and diffusion coefficient are varied, such that the parabolic case of pure diffusion (heat equation), as well as, the hyperbolic case of pure advection (transport equation) are included in the study. For each model parameter set, the L2 error at the final time is computed for spatial and temporal element lengths ranging over several orders of magnitude to allow for an individual evaluation of the methods' spatial, temporal, and spacetime accuracy. In the parabolic case, particular attention is paid to the influence of time-dependent boundary conditions. Key findings include a spatial accuracy of second order and a temporal accuracy between second and third order. The temporal accuracy tends towards third order depending on how advection-dominated the test case is, on the choice of the specific discretization method, and on the time-(in)dependence and treatment of the boundary conditions. Additionally, the potential of time-continuous simplex space-time finite elements for heat flux computations is demonstrated with a piston ring pack test case.

math.NA↗

arXiv2022

Numerical Prediction and Post-Test Numerical Analysis of the ASDMAD Wind Tunnel Tests in ETW

This paper presents numerical results in comparison with experimental data of nominally static aeroelastic polars of the second ASDMAD (Aero-Structural Dynamics Methods for Airplane Design) campaign conducted in the European Transonic Windtunnel. For the simulation the modular solver package SOFIA combined with the DLR solver TAU on the fluid side and the in-house solver FEAFA on the structural side is applied. First the experimental setup and the aeroelastic solver are introduced, followed by a detailed analysis of the results. Comparisons of pressure distributions and the global lift coefficients are presented for variations of angle of attack, Mach number and aerodynamic loading factor. Additionally, the paper contains preliminary investigations of dynamic results for excited vibration applying periodical inner force couples in the wing root area.

physics.flu-dyn↗

arXiv2022

Spline-Based Space-Time Finite Element Approach for Fluid-Structure Interaction Problems With a Focus on Fully Enclosed Domains

Non-Uniform Rational B-Spline (NURBS) surfaces are commonly used within Computer-Aided Design (CAD) tools to represent geometric objects. When using isogeometric analysis (IGA), it is possible to use such NURBS geometries for numerical analysis directly. Analyzing fluid flows, however, requires complex three-dimensional geometries to represent flow domains. Defining a parametrization of such volumetric domains using NURBS can be challenging and is still an ongoing topic in the IGA community. With the recently developed NURBS-enhanced finite element method (NEFEM), the favorable geometric characteristics of NURBS are used within a standard finite element method. This is achieved by enhancing the elements touching the boundary by using the NURBS geometry itself. In the current work, a new variation of NEFEM is introduced, which is suitable for three-dimensional space-time finite element formulations. The proposed method makes use of a new mapping which results in a non-Cartesian formulation suitable for fluid-structure interaction (FSI). This is demonstrated by combining the method with an IGA formulation in a strongly-coupled partitioned framework for solving FSI problems. The framework yields a fully spline-based representation of the fluid-structure interface through a single NURBS. The coupling conditions at the fluid-structure interface are enforced through a Robin-Neumann type coupling scheme. This scheme is particularly useful when considering incompressible fluids in fully Dirichlet-bounded and curved problems, as it satisfies the incompressibility constraint on the fluid for each step within the coupling procedure. The accuracy and performance of the introduced spline-based space-time finite element approach and its use within the proposed coupled FSI framework are demonstrated using a series of two- and three-dimensional benchmark problems.

cs.CE↗

arXiv2022

Investigation of Physics-Informed Deep Learning for the Prediction of Parametric, Three-Dimensional Flow Based on Boundary Data

The placement of temperature sensitive and safety-critical components is crucial in the automotive industry. It is therefore inevitable, even at the design stage of new vehicles that these components are assessed for potential safety issues. However, with increasing number of design proposals, risk assessment quickly becomes expensive. We therefore present a parameterized surrogate model for the prediction of three-dimensional flow fields in aerothermal vehicle simulations. The proposed physics-informed neural network (PINN) design is aimed at learning families of flow solutions according to a geometric variation. In scope of this work, we could show that our nondimensional, multivariate scheme can be efficiently trained to predict the velocity and pressure distribution for different design scenarios and geometric scales. The proposed algorithm is based on a parametric minibatch training which enables the utilization of large datasets necessary for the three-dimensional flow modeling. Further, we introduce a continuous resampling algorithm that allows to operate on one static dataset. Every feature of our methodology is tested individually and verified against conventional CFD simulations. Finally, we apply our proposed method in context of an exemplary real-world automotive application.

cs.LG↗

arXiv2021

The Performance Impact of Newton Iterations per Solver Call in Partitioned Fluid-Structure Interaction

The cost of a partitioned fluid-structure interaction scheme is typically assessed by the number of coupling iterations required per time step, while ignoring the Newton loops within the nonlinear sub-solvers. In this work, we discuss why these single-field iterations deserve more attention when evaluating the coupling's efficiency and how to find the optimal number of Newton steps per coupling iteration.

math.NA↗

arXiv2021

A novel approach to fluid-structure interaction simulations involving large translation and contact

In this work, we present a novel method for the mesh update in flow problems with moving boundaries, the phantom domain deformation mesh update method (PD-DMUM). The PD-DMUM is designed to avoid remeshing; even in the event of large, unidirectional displacements of boundaries. The method combines the concept of two mesh adaptation approaches: (1) The virtual ring shear-slip mesh updatemethod (VR-SSMUM); and (2) the elastic mesh update method (EMUM). As in the VR-SSMUM, the PD-DMUMextends the fluid domain by a phantom domain; the PD-DMUM can thus locally adapt the element density. Combined with the EMUM, the PD-DMUMallows the consideration of arbitrary boundary movements. In this work, we apply the PD-DMUM in two test cases. Within the first test case, we validate the PD-DMUM in a 2D Poiseuille flow on a moving background mesh. Subsequently the fluid-structure interaction (FSI) problem in the second test case serves as a proof of concept. More, we stress the advantages of the novel method with regard to conventional mesh update approaches.

math.NA↗

arXiv2020

Four-Dimensional Elastically Deformed Simplex Space-Time Meshes for Domains with Time Variant Topology

Thinking of the flow through biological or technical valves, there is a variety of applications in which the topology of a fluid domain changes over time. This topology change is characteristic for the physical behaviour, but poses a particular challenge in computer simulations. A way to overcome this challenge is to consider the space-time extent of the application as a contiguous computational domain. In this work, we obtain a boundary conforming discretization of the space-time domain with four-dimensional simplex elements (pentatopes). To facilitate the construction of pentatope meshes for complex geometries, the widely used elastic mesh update method is extended to four-dimensional meshes. In the resulting workflow, the topology change is elegantly included in the pentatope mesh and does not require any additional treatment during the simulation. The potential of simplex space-time meshes for domains with time variant topology is demonstrated in a valve simulation and a flow simulation inspired by a clamped artery.

math.NA↗

arXiv2020

SplineLib: A Modern Multi-Purpose C++ Spline Library

This paper provides the description of a novel, multi-purpose spline library. In accordance with the increasingly diverse modes of usage of splines, it is multi-purpose in the sense that it supports geometry representation, finite element analysis, and optimization. The library features reading and writing for various file formats and a wide range of spline manipulation algorithms. Further, a new efficient and objective-oriented algorithm for B-spline basis function evaluation is included. All features are available by a spline-type independent interface. The library is written in modern C++ with CMake as build system. This enables it for usage in typical scientific applications. It is provided as open-source library.

cs.MS↗

arXiv2020

A Multi-Vector Interface Quasi-Newton Method with Linear Complexity for Partitioned Fluid-Structure Interaction

In recent years, interface quasi-Newton methods have gained growing attention in the fluid-structure interaction community by significantly improving partitioned solution schemes: They not only help to control the inherent added-mass instability, but also prove to substantially speed up the coupling's convergence. In this work, we present a novel variant: The key idea is to build on the multi-vector Jacobian update scheme first presented by Bogaers et al. (2014) and avoid any explicit representation of the (inverse) Jacobian approximation, since it slows down the solution for large systems. Instead, all terms involving a quadratic complexity have been systematically eliminated. The result is a new multi-vector interface quasi-Newton variant whose computational cost scales linearly with the problem size.

cs.CE↗

arXiv2019

Space-Time NURBS-Enhanced Finite Elements for Solving the Compressible Navier-Stokes Equations

This article considers the NURBS-Enhanced Finite Element Method (NEFEM) applied to the compressible Navier-Stokes equations. NEFEM, in contrast to conventional finite element formulations, utilizes a NURBS-based computational domain representation. Such representations are typically available from Computer-Aided-Design tools. Within the NEFEM, the NURBS boundary definition is utilized only for elements that are touching the domain boundaries. The remaining interior of the domain is discretized using standard finite elements. Contrary to isogeometric analysis, no volume splines are necessary. The key technical features of NEFEM will be discussed in detail, followed by a set of numerical examples that are used to compare NEFEM against conventional finite element methods with the focus on compressible flow.

math.NA↗

arXiv2019

Simplex space-time meshes in thermally coupled two-phase flow simulations of mold filling

The quality of plastic parts produced through injection molding depends on many factors. Especially during the filling stage, defects such as weld lines, burrs, or insufficient filling can occur. Numerical methods need to be employed to improve product quality by means of predicting and simulating the injection molding process. In the current work, a highly viscous incompressible non-isothermal two-phase flow is simulated, which takes place during the cavity filling. The injected melt exhibits a shear-thinning behavior, which is described by the Carreau-WLF model. Besides that, a novel discretization method is used in the context of 4D simplex space-time grids [2]. This method allows for local temporal refinement in the vicinity of, e.g., the evolving front of the melt [10]. Utilizing such an adaptive refinement can lead to locally improved numerical accuracy while maintaining the highest possible computational efficiency in the remaining of the domain. For demonstration purposes, a set of 2D and 3D benchmark cases, that involve the filling of various cavities with a distributor, are presented.

cs.CE↗