arXiv subjects

Marek Behr

Publications and source records attributed to Marek Behr.

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

A Practical Computational Hemolysis Model Incorporating Biophysical Properties of the Red Blood Cell Membrane

Purpose: Hemolysis is a key issue in the design of blood-handling medical devices. Computational prediction of this phenomenon is challenging due to the complex multiscale nature of blood. As a result, conventional approaches often fail to predict hemolysis accurately, commonly showing deviations of multiple orders of magnitude compared to experimental data. More accurate models are typically computationally expensive and thus impractical for real-world applications. This work aims to fill this gap by presenting accurate yet simple and efficient computational hemolysis models. Methods: Hemolysis modeling relies on two key components: a red blood cell model and a hemoglobin release model. In this work, we compare three red blood cell models: a common stress-based model (Bludszuweit), a simple strain-based model based on the Kelvin-Voigt constitutive law, and a more complex tensor-based model (TTM). Further, we compare two hemoglobin release models: the widely used power-law approach and a biophysical pore formation model. Results: We evaluate these models in two benchmark cases: the FDA blood pump and the FDA nozzle. In both benchmarks, the simple strain-based model combined with the pore formation model achieves absolute predictions of hemolysis within the standard deviation of experimental measurements. In contrast, stress-based power law models deviate by several orders of magnitude. Conclusion: The strain-based pore modeling approach takes into account the biophysical properties of red blood cell membranes, in particular their viscoelastic deformation behavior and hemoglobin release through membrane pores. This leads to significantly improved hemolysis predictions in a framework that can easily be integrated into common CFD workflows.

physics.flu-dyn↗

arXiv2025

Quantifying data needs in surrogate modeling for flow fields in two-dimensional stirred tanks with physics-informed neural networks

Stirred tanks are vital in chemical and biotechnological processes, particularly as bioreactors. Although computational fluid dynamics (CFD) is widely used to model the flow in stirred tanks, its high computational cost$-$especially in multi-query scenarios for process design and optimization$-$drives the need for efficient data-driven surrogate models. However, acquiring sufficiently large datasets can be costly. Physics-informed neural networks (PINNs) offer a promising solution to reduce data requirements while maintaining accuracy by embedding underlying physics into neural network (NN) training. This study quantifies the data requirements of vanilla PINNs for developing surrogate models of a flow field in a 2D stirred tank. We compare these requirements with classical supervised neural networks and boundary-informed neural networks (BINNs). Our findings demonstrate that surrogate models can achieve prediction errors around 3% across Reynolds numbers from 50 to 5000 using as few as six datapoints. Moreover, employing an approximation of the velocity profile in place of real data labels leads to prediction errors of around 2.5%. These results indicate that even with limited or approximate datasets, PINNs can be effectively trained to deliver high accuracy comparable to high-fidelity data.

cs.CE↗

arXiv2024

An Ising Machine Formulation for Design Updates in Topology Optimization of Flow Channels

Topology optimization is an essential tool in computational engineering, for example, to improve the design and efficiency of flow channels. At the same time, Ising machines, including digital or quantum annealers, have been used as efficient solvers for combinatorial optimization problems. Beyond combinatorial optimization, recent works have demonstrated applicability to other engineering tasks by tailoring corresponding problem formulations. In this study, we present a novel Ising machine formulation for computing design updates during topology optimization with the goal of minimizing dissipation energy in flow channels. We explore the potential of this approach to improve the efficiency and performance of the optimization process. To this end, we conduct experiments to study the impact of various factors within the novel formulation. Additionally, we compare it to a classical method using the number of optimization steps and the final values of the objective function as indicators of the time intensity of the optimization and the performance of the resulting designs, respectively. Our findings show that the proposed update strategy can accelerate the topology optimization process while producing comparable designs. However, it tends to be less exploratory, which may lead to lower performance of the designs. These results highlight the potential of incorporating Ising formulations for optimization tasks but also show their limitations when used to compute design updates in an iterative optimization process. In conclusion, this work provides an efficient alternative for design updates in topology optimization and enhances the understanding of integrating Ising machine formulations in engineering optimization.

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↗

arXiv2024

In silico reproduction of the pathophysiology of in-stent restenosis

The occurrence of in-stent restenosis following percutaneous coronary intervention highlights the need for the creation of computational tools that can extract pathophysiological insights and optimize interventional procedures on a patient-specific basis. In light of this, a comprehensive framework encompassing multiple physical phenomena is introduced in this work. This framework effectively captures the intricate interplay of chemical, mechanical, and biological factors. In addition, computational approaches for the extraction of hemodynamic indicators that modulate the severity of the restenotic process are devised. Thus, this marks a significant stride towards facilitating computer-assisted clinical methodologies.

physics.bio-ph↗

arXiv2024

Eulerian Formulation of the Tensor-Based Morphology Equations for Strain-Based Blood Damage Modeling

The development of blood-handling medical devices, such as ventricular assist devices, requires the analysis of their biocompatibility. Among other aspects, this includes hemolysis, i.e., red blood cell damage. For this purpose, computational fluid dynamics (CFD) methods are employed to predict blood flow in prototypes. The most basic hemolysis models directly estimate red blood cell damage from fluid stress in the resulting flow field. More advanced models explicitly resolve cell deformation. On the downside, these models are typically written in a Lagrangian formulation, i.e., they require pathline tracking. We present a new Eulerian description of cell deformation, enabling the evaluation of the solution across the whole domain. The resulting hemolysis model can be applied to any converged CFD simulation due to one-way coupling with the fluid velocity field. We discuss the efficient numerical treatment of the model equations in a stabilized finite element context. We verify the model by comparison to the original Lagrangian formulation in selected benchmark flows. Two more complex test cases demonstrate the method's capabilities in real-world applications. The results highlight the advantages over previous hemolysis models. In conclusion, the model holds great potential for the design process of future generations of medical devices.

physics.flu-dyn↗

arXiv2024

A Model Hierarchy for Predicting the Flow in Stirred Tanks with Physics-Informed Neural Networks

This paper explores the potential of Physics-Informed Neural Networks (PINNs) to serve as Reduced Order Models (ROMs) for simulating the flow field within stirred tank reactors (STRs). We solve the two-dimensional stationary Navier-Stokes equations within a geometrically intricate domain and explore methodologies that allow us to integrate additional physical insights into the model. These approaches include imposing the Dirichlet boundary conditions (BCs) strongly and employing domain decomposition (DD), with both overlapping and non-overlapping subdomains. We adapt the Extended Physics-Informed Neural Network (XPINN) approach to solve different sets of equations in distinct subdomains based on the diverse flow characteristics present in each region. Our exploration results in a hierarchy of models spanning various levels of complexity, where the best models exhibit l1 prediction errors of less than 1% for both pressure and velocity. To illustrate the reproducibility of our approach, we track the errors over repeated independent training runs of the best identified model and show its reliability. Subsequently, by incorporating the stirring rate as a parametric input, we develop a fast-to-evaluate model of the flow capable of interpolating across a wide range of Reynolds numbers. Although we exclusively restrict ourselves to STRs in this work, we conclude that the steps taken to obtain the presented model hierarchy can be transferred to other applications.

cs.CE↗

arXiv2024

In-silico Analysis of Hemodynamic Indicators in Idealized Stented Coronary Arteries for Varying Stent Indentation

In this work, we investigate the effects of stent indentation on hemodynamic indicators in stented coronary arteries. Our aim is to assess in-silico risk factors for in-stent restenosis (ISR) and thrombosis after stent implantation. The proposed model is applied to an idealized artery with Xience V stent for four indentation percentages and three mesh refinements. We analyze the patterns of hemodynamic indicators arising from different stent indentations and propose an empirical frequency analysis of time-averaged WSS (TAWSS), oscillatory shear index (OSI), and relative residence time (RRT). We observe that higher indentations display higher frequency of critically low TAWSS and non-physiological OSI and RRT. Furthermore, an appropriate mesh refinement is needed for accurate representation of hemodynamics in the stent vicinity. The results provide physics-based evidence for the correlation between high indentation and ISR.

physics.med-ph↗

arXiv2023

Exploring the Influence of Parametrized Pulsatility on Left Ventricular Washout under LVAD Support: A Computational Study Using Reduced-Order Models

Medical therapy for patients with severe heart disease often relies on left ventricular assist devices (LVADs). It is an ongoing topic of research how complications like stagnation and thrombosis can be prevented by using artificial pulsatility. We study a parametric pulse profile and its effect on the left ventricular washout using a computational flow model. Based on finite element simulations, we construct reduced-order models to reduce the computational costs for evaluating the parametrized problem. We observe that a pulsatile flow rate improves the washout compared to a constant flow rate. In particular, we find that short, intense pulses wash out the left ventricle best, whereas the time between subsequent pulses plays no significant role.

physics.flu-dyn↗

arXiv2023

Computational modeling of in-stent restenosis: Pharmacokinetic and pharmacodynamic evaluation

Persistence of the pathology of in-stent restenosis even with the advent of drug-eluting stents warrants the development of highly resolved in silico models. These computational models assist in gaining insights into the transient biochemical and cellular mechanisms involved and thereby optimize the stent implantation parameters. Within this work, an already established fully-coupled Lagrangian finite element framework for modeling the restenotic growth is enhanced with the incorporation of endothelium-mediated effects and pharmacological influences of rapamycin-based drugs embedded in the polymeric layers of the current generation drug-eluting stents. The continuum mechanical description of growth is further justified in the context of thermodynamic consistency. Qualitative inferences are drawn from the model developed herein regarding the efficacy of the level of drug embedment within the struts as well as the release profiles adopted. The framework is then intended to serve as a tool for clinicians to tune the interventional procedures patient-specifically.

cs.CE↗

arXiv2022

Simplex space-time meshes in engineering applications with moving domains

This paper highlights how unstructured space-time meshes can be used in production engineering applications with moving domains. Unstructured space-time elements can connect different spatial meshes at the bottom and top level of the space-time domain and deal with complicated domain movements/rotations that the standard arbitrary Lagrangian-Eulerian techniques can not resolve without remeshing. We use a space-time finite element discretization, by means of 4D simplex space-time elements, referred to as pentatopes by Behr [2008], which leads to entirely unstructured grids with varying levels of refinement both in space and in time. Furthermore, we use stabilization techniques, and the stabilization parameter is defined based on the contravariant metric tensor, as shown in the work of Pauli and Behr [2017]. Its definition was extended in 4D by von Danwitz et al. [2019], allowing us to deal with complex anisotropic simplex meshes in the space-time domain.

cs.CE↗

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

A multiphysics modeling approach for in-stent restenosis: Theoretical aspects and finite element implementation

Development of in silico models are intrinsic in understanding disease progression in soft biological tissues. Within this work, we propose a fully-coupled Lagrangian finite element framework which replicates the process of in-stent restenosis observed post stent implantation in a coronary artery. Coupled advection-reaction-diffusion reactions are set up that track the evolution of the concentrations of the platelet-derived growth factor, the transforming growth factor-$β$, the extracellular matrix, and the density of the smooth muscle cells. A continuum mechanical description of growth incorporating the evolution of arterial wall constituents is developed, and a suitable finite element implementation discussed. Qualitative validation of the computational model are presented by emulating a stented artery. Patient-specific data can be integrated into the model to predict the risk of restenosis and thereby assist in tuning of stent implantation parameters to mitigate the risk.

cs.CE↗

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↗

arXiv2021

Stabilized finite element methods for a fully-implicit logarithmic reformulation of the Oldroyd-B constitutive law

Logarithmic conformation reformulations for viscoelastic constitutive laws have alleviated the high Weissenberg number problem, and the exploration of highly elastic flows became possible. However, stabilized formulations for logarithmic conformation reformulations in the context of finite element methods have not yet been widely studied. We present stabilized formulations for the logarithmic reformulation of the Oldroyd-B model by Saramito (2014) based on the Variational Multiscale framework and Galerkin/Least-Squares method. The reformulation allows the use of Newton's method due to its fully-implicit nature for solving the steady-state problem directly. The proposed stabilization methods cure instabilities of convection and compatibility while preserving a three-field problem. The spatial accuracy of the formulations is assessed with the four-roll periodic box, revealing comparable accuracy between the methods. The formulations are validated with benchmark flows past a cylinder and through a 4:1 contraction. We found an excellent agreement to benchmark results in the literature. The algebraic sub-grid scale method is highly robust, indicated by the high limiting Weissenberg numbers in the benchmark flows.

cs.CE↗

arXiv2021

Numerical Design of Distributive Mixing Elements

This paper presents a novel shape-optimization technique for the design of mixing elements in single-screw extruders. Extruders enable the continuous production of constant-cross-section profiles. Equipped with one or several screw-shaped rotors, extruders transport polymer particles towards the outlet. Due to shear heating, melting is induced and a melt stream is created, which can be further processed. While many variants of multi-screw extruders exist, a significant share of all extrusion machines is made up of single-screw extruders due to their comparatively low operating costs and complexity. While the reduced complexity yields economic benefits, single-screw extruders' mixing capabilities, i.e., their ability to produce a melt with a homogeneous material and temperature distribution, suffer compared to multi-screw extruders. To compensate for this shortcoming, so-called mixing elements are added to the screw to enhance mixing by recurring flow reorientations. In view of the largely unintuitive flow characteristics of polymer melts, we present an optimization framework that allows designing these mixing elements numerically based on finite-element simulations of the melt flow. To reduce the computational demand required by shape optimization of a complete mixing section, we only focus on the shape optimization of a single mixing element. This paper presents advances in three aspects of numerical design: (1) A combination of free-form deformation and surface splines is presented, allowing to parameterize the mixing element's shape by very few variables. (2) The combination of this concept with a linear-elasticity-based mesh update method to deform the computational domain without the need for remeshing is demonstrated. (3) A simple yet robust and sensitive objective formulation to assess distributive mixing in laminar flows based on a measure for the interfacial area is proposed.

math.NA↗