arXiv subjects

Stefan Schoder

Publications and source records attributed to Stefan Schoder.

At least 19 recordsLinked to original sources

arXiv2026

Generalised Perturbed Convective Wave Theory

The theory of the perturbed convective wave equation for compressible flows (cPCWE) is generalised to spatially varying mean-density fields. The resulting equation is an exact scalar reformulation of the acoustic perturbation equations and describes sound generation and propagation in moving inhomogeneous media using a single unknown. The intermediate variables of the associated workflow, in which a Helmholtz decomposition problem, a Poisson equation and the cPCWE are solved successively, are related to the vortical, entropy and acoustic modes of Kovasznay, providing a physical interpretation of each processing step. The quantitative accuracy is assessed against fully compressible direct numerical simulations (DNS) of two-dimensional isothermal mixing layer and Lighthill's analogy computed in the same framework at Mach numbers between M=0.2 and M=0.4, based on the velocity difference across the layer and the ambient speed of sound. Over this range of Mach numbers, the radiated power spans several orders of magnitude. For M>=0.25, the sound power levels obtained using the three methods agree within 0.9dB, and within 0.5dB for M>=0.3. At M=0.2, where the acoustic fluctuations are weakest relative to the hydrodynamic ones, Lighthill's analogy over-predicts the radiated power by 2.8dB. In contrast, the cPCWE deviates from the DNS reference by only -1.2dB. This closer agreement is because the cPCWE source term is confined to the vortex-pairing region, while convection and refraction are represented by its convective wave operator. Beyond reproducing the far-field sound, the cPCWE resolves the acoustic field within the shear zone itself, where the DNS' fields are masked by vortical fluctuations.

physics.flu-dyn↗

arXiv2026

Convergence of finite element right-hand-side computation from finite difference data

This work presents two integration methods for field transfer in computational aeroacoustics and in coupled field problems, using the finite element method to solve the acoustic field. Firstly, a high-order Gaussian quadrature computes the finite element right-hand side. In contrast, the (flow) field provided by the finite difference mesh is mapped by higher-order B-Splines or a Lagrangian function. Secondly, the cut-cell or supermesh integration with geometric clipping. For each method, the accuracy, performance characteristics, and computational complexity are analyzed. As a reference, the trapezoidal integration rule was computed from the finite difference results. The high-order quadrature converges as the B-Spline interpolation order increases, and the finite difference results and mesh resolutions are consistent. The supermesh approach eliminates interpolation and approximation errors at the grid-to-mesh level and improves accuracy. This behaviour is universal for smooth or strongly oscillating field quantities, which will be shown in a comparative study between the Lighthill-like source term and the source term of the perturbed convective wave equation for subsonic flows.

math.NA↗

arXiv2025

Super-Resolution of Elliptic PDE Solutions Using Least Squares Support Vector Regression

A hybrid computational approach that integrates the finite element method (FEM) with least squares support vector regression (LSSVR) is introduced to solve partial differential equations. The method combines FEM's ability to provide the nodal solutions and LSSVR with higher-order Legendre polynomial kernels to deliver a closed-form analytical solution for interpolation between the nodes. The hybrid approach implements element-wise enhancement (super-resolution) of a given numerical solution, resulting in high resolution accuracy, while maintaining consistency with FEM nodal values at element boundaries. It can adapt any low-order FEM code to obtain high-order resolution by leveraging localized kernel refinement and parallel computation without additional implementation overhead. Therefore, effective inference/post-processing of the obtained super-resolved solution is possible. Evaluation results show that the hybrid FEM-LSSVR approach can achieve significantly higher accuracy compared to the base FEM solution. Comparable accuracy is a achieved when comparing the hybrid solution with a standalone FEM result with the same polynomial basis function order. The convergence studies were conducted for four elliptic boundary value problems to demonstrate the method's ability, accuracy, and reliability. Finally, the algorithm can be directly used as a plug-and-play method for super-resolving low-order numerical solvers and for super-resolution of expensive/under-resolved experimental data.

math.NA↗

arXiv2025

Convergence of physics-informed neural networks modeling time-harmonic wave fields

Studying physics-informed neural networks (PINNs) for modeling partial differential equations to solve the acoustic wave field has produced promising results for simple geometries in two-dimensional domains. One option is to compute the time-harmonic wave field using the Helmholtz equation. Compared to existing numerical models, the physics-informed neural networks forward problem has to overcome several topics related to the convergence of the optimization toward the "true" solution. The topics reach from considering the physical dimensionality (from 2D to 3D), the modeling of realistic sources (from a self-similar source to a realistic confined point source), the modeling of sound-hard (Neumann) boundary conditions, and the modeling of the full wave field by considering the complex solution quantities. Within this contribution, we study 3D room acoustic cases at low frequency, varying the source definition and the number of boundary condition sets and using a complex speed of sound model to account for some degree of absorption. We assess the convergence behavior by looking at the loss landscape of the PINN architecture, the $L^2$ error compared to a finite element reference simulation for each network architecture and configuration. The convergence studies showed that at least six training points per wavelength are necessary for accurate training and subsequent predictions of the PINN. The developments are part of an initiative aiming to model the low-frequency behavior of room acoustics, including absorbers.

cs.CE↗

arXiv2024

pyCFS-data: Data Processing Framework in Python for openCFS

Many numerical simulation tools have been developed and are on the market, but there is still a strong need for appropriate tools capable of simulating multi-field problems, especially in aeroacoustics. Therefore, openCFS provides an open-source framework for implementing partial differential equations using the finite element method. Since 2000, the software has been developed continuously. The result is openCFS (before 2020, known as CFS++ Coupled Field Simulations written in C++). In this paper, we present pyCFS-data, a data processing framework written in Python to provide a flexible and easy-to-use toolbox to access and manipulate, pre- and postprocess data generated by or for usage with openCFS.

cs.CE↗

arXiv2024

Flow-Acoustics: Theory and Benchmarking

The urgent need for transitioning to green energy solutions, particularly in the context of house heating and urban redensification, has brought the issue of fan noise aeroacoustics investigations to the forefront. As societies worldwide strive to mitigate climate change and reduce carbon emissions, adopting sustainable heating technologies such as air heat pumps has gained significant traction. In Germany, renowned for its commitment to environmental sustainability, the "TA L\"arm" regulations, derived from the "Bundes-Immissionsschutzgesetz," impose stringent limits on noise levels both inside and outside buildings across various applications. These regulations delineate permissible noise levels during daytime (6 AM to 10 PM) and nighttime (10 PM to 6 AM), with particular emphasis on protecting residential areas with low noise limits. Moreover, the noise limits prescribed for indoor environments are even more stringent. Given the necessity of maintaining acoustic comfort and quality of life, compliance with these regulations necessitates meticulous attention to noise generation sources, especially those associated with heating and ventilation systems. Consequently, understanding and mitigating fan noise through aeroacoustic investigations is essential to ensure the successful adoption and integration of green energy solutions in residential and urban settings. In the following, an experimental benchmark for a low-pressure rise axial fan (FAN-01) is presented, and several prediction methods of the sound pressure and sound power are evaluated.

physics.soc-ph↗

arXiv2024

Feasibility study on solving the Helmholtz equation in 3D with PINNs

Room acoustic simulations at low frequencies often face significant uncertainties of material parameters and boundary conditions due to absorbing material. We discuss the application of Physics-Informed Neural Networks (PINNs) to solve the (forward) Helmholtz equation in three dimensions (3D), employing mini-batch stochastic gradient descent with periodic resampling every 100 iterations for memory-efficient training. Addressing the computational challenges posed by the extension of PINNs from 2D to 3D for acoustics, DeepXDE is used for implementing the forward PINN. The proposed numerical method is benchmarked against an analytical solution of a standing wave field in 3D. The PINN results are also compared to the Finite Element Method (FEM) solutions for a 3D wave field computed with openCFS. The alignment between PINN-generated solutions and analytical/FEM solutions shows the feasibility of PINNs modeling 3D acoustic applications for future inverse problems, and validating the accuracy and reliability of the proposed approach. Compared to FEM, establishing the PINN model took few hours (similar to the setup of a FEM simulation), the training took 38h to 42.8h (which is longer than the solution of the FEM simulation, which took 17min-19min), and the inference took 0.05 seconds being more than 20,000 times faster than the FEM benchmark openCFS using the same number of degrees of freedomwhen producing the results. Thereby, the insight is gained that 3D acoustic wave simulations in the frequency domain are feasible for forward PINNs and can predict complex wave behaviors in real-world applications.

physics.comp-ph↗

arXiv2024

An approach using the null space to implement Dirichlet and constraint boundary conditions into FEM

A handy technique for the Finite Element Method (FEM) is presented that uses the null space for the implementation of Dirichlet and constraint boundary conditions. The focus of this method is to present an illustrative approach to modeling boundary constraints within FEM simulations for teaching. It presents a consistent way of including the boundary terms in the forcing and constructing the field solution after solving the algebraic system of equations.

math.NA↗

arXiv2024

METAMAT 01: A semi-analytic Solution for Benchmarking Wave Propagation Simulations of homogeneous Absorbers in 1D/3D and 2D

The development of acoustic simulation workflows in the time-domain description is essential for predicting the sound of aeroacoustic or other transient acoustic effects. A common practice for noise mitigation is using absorbers. The modeling of these acoustic absorbers is typically provided in the frequency domain. Several, methods established bridging this gap, investigating methods to model absorber in the time domain. Therefore, this short article, describes the analytic solution in time-domain for benchmarking absorber simulations with infinite 1D, 2D, and 3D domains. Connected to the analytic solution, a Matlab script is provided to easily obtain the reference solution. The reference codes are provided as benchmark solution in the EAA TCCA Benchmarking database as METAMAT 01.

cs.SD↗

arXiv2024

Aeroacoustics -- Theory and methods for analyzing flow-induced sound generation of technical and biological applications

Flow instabilities, wave propagation phenomena, and structural interaction are current topics of the field "Flow acoustics" also named "Aeroacoustics". Assuming the theory of classical mechanics, aeroacoustic applications are modeled by the conservation equations and suitable material models. In particular, the continuity equation, the Navier-Stokes equation, energy conservation, and the Navier equation are coupled. Depending on the field of application (e.g., slow flow speeds in relation to the speed of sound), further assumptions can simplify the calculation considerably. A systematic derivation of the models according to physical accuracy and calculation efficiency allows us to categorize a computational aeroacoustic model into a hierarchy of models in terms of accuracy, applicability and computational effort. In the simplest case, flow acoustics is described by analytical models in the form of scale models (class~1), like the eighth power law of Lighthill or the methods of VDI 2081 and VDI 3731 for technical sound emissions. Class~2 models (e.g. Sharland, K\"oltzsch, stochastic noise generation and radiation, random particle mesh method) allow empirical factors to be incorporated, which are based on experience (such as fan noise) and allow prediction of the sound. Class~3 models use a numerical decoupling of flow, acoustics, and structure. Thus, this class of models describe a pure forward coupling from the higher energy containing flow field to the sound field. Finally, to solve the full fluid-structure-acoustic interaction numerically, the field equations are solved in a coupled manner (class~4). The class~4 models are characterized by high computational effort and are physically most general but struggle with considerable numerical challenges.

physics.flu-dyn↗

arXiv2023

First qualitative observations on deep learning vision model YOLO and DETR for automated driving in Austria

This study investigates the application of single and two-stage 2D-object detection algorithms like You Only Look Once (YOLO), Real-Time DEtection TRansformer (RT-DETR) algorithm for automated object detection to enhance road safety for autonomous driving on Austrian roads. The YOLO algorithm is a state-of-the-art real-time object detection system known for its efficiency and accuracy. In the context of driving, its potential to rapidly identify and track objects is crucial for advanced driver assistance systems (ADAS) and autonomous vehicles. The research focuses on the unique challenges posed by the road conditions and traffic scenarios in Austria. The country's diverse landscape, varying weather conditions, and specific traffic regulations necessitate a tailored approach for reliable object detection. The study utilizes a selective dataset comprising images and videos captured on Austrian roads, encompassing urban, rural, and alpine environments.

cs.CV↗

arXiv2023

Offline coupling of segregated multi-physical simulations with consistent boundary conditions and source terms based on scattered data

This article presents the openCFS submodule scattered data reader for coupling multi-physical simulations performed in different simulation programs. For instance, by considering a forward-coupling of a surface vibration simulation (mechanical system) to an acoustic propagation simulation using time-dependent acoustic absorbing material as a noise mitigation measure. The nearest-neighbor search of the target and source points from the interpolation is performed using the FLANN or the CGAL library. In doing so, the coupled field (e.g., surface velocity) is interpolated from a source representation consisting of field values physically stored and organized in a file directory to a target representation being the quadrature points in the case of the finite element method. A test case of the functionality is presented in the "testsuite" module of the openCFS software called "Abc2dcsvt". This scattered data reader module was successfully applied in numerous studies on flow-induced sound generation. Within this short article, the functionality, and usability of this module are described.

cs.CE↗

arXiv2023

Dataset CYLinCF-01 creation pipeline: Circular cylinder in a cross flow, Mach Number 0.03 and Reynolds Number 200

This article presents an aeroacoustic workflow (pipeline) to generate a flow and acoustic dataset for studying flow-induced sound in the context of a cylinder in cross flow. The numerical simulations are performed using OpenFOAM (v9 or v10, or v2306) for the flow and openCFS for acoustics using the perturbed convective wave equation (PCWE) and the dilatation equation of Ribner. The workflow involves several steps, including the flow simulation, the acoustic simulation, and post-processing of the results in Python 3.9. The simulation steps are presented in all their details to verify your own segregated aeroacoustic solver. The analysis focuses on the acoustic characteristics of the flow, including sound pressure levels, frequency spectra, and directivity patterns. The results show good agreement with literature benchmarking datasets. The article concludes by discussing applications of the workflow for different cases that involve flow-induced sound generation.

physics.flu-dyn↗

arXiv2023

Implementation of an aeroacoustic simulation pipeline using openCFS-Acoustics and openCFS-Data applied to human phonation

The human phonation process be modeled using the Finite Element Method (FEM) which provides a detailed representation of the voice production process. A software implementation in C++ using FEM (openCFS) has been used to simulate the phonation process. The FEM model consists of a 3D mesh of the upper human airways. The simVoice model provides an accurate representation of the phonation process and was valid in several publications. In this article, we show how to set up the model using openCFS and openCFS-Data.

cs.SD↗

arXiv2023

A Validated Finite Element Model for Room Acoustic Treatments with Edge Absorbers

Porous acoustic absorbers have excellent properties in the low-frequency range when positioned in room edges, therefore they are a common method for reducing low-frequency reverberation. However, standard room acoustic simulation methods such as ray tracing and mirror sources are invalid for low frequencies in general which is a consequence of using geometrical methods, yielding a lack of simulation tools for these so-called edge absorbers. In this article, a validated finite element simulation model is presented, which is able to predict the effect of an edge absorber on the acoustic field. With this model, the interaction mechanisms between room and absorber can be studied by high-resolved acoustic field visualizations in both room and absorber. The finite element model is validated against transfer function data computed from impulse response measurements in a reverberation chamber in style of ISO 354. The absorber made of Basotect is modeled using the Johnson-Champoux-Allard-Lafarge model, which is fitted to impedance tube measurements using the four-microphone transfer matrix method. It is shown that the finite element simulation model is able to predict the influence of different edge absorber configurations on the measured transfer functions to a high degree of accuracy. The evaluated third-octave band error exhibits deviations of 3.25dB to 4.11dB computed from third-octave band averaged spectra.

physics.class-ph↗

arXiv2023

openCFS-Data: Implementation of the Stochastic Noise Generation and Radiation Model (SNGR)

Preliminary aeroacoustic investigations in competitive industries require rapid numerical simulation techniques to gain initial insight into the flow and acoustic field. Although there are capabilities to resolve virtually all turbulence length scales, these techniques are often impractical in early stages of component development. Therefore, the flow field is typically assessed by a Reynolds-averaged Navier Stokes Simulation. Building upon the results of that flow simulation, a stochastic approach to reconstruct the turbulent velocity fluctuations. In conjunction with a hybrid aeroacoustic workflow, this approach is useful in early stage virtual prototyping of aeroacoustic applications. In this working paper, we present the SNGR algorithm of CFS-Data, the open-source pre-post-processing part of openCFS, with a focus on the computation of aeroacoustic sources.

physics.flu-dyn↗

arXiv2023

openCFS-Data: Data Pre-Post-Processing Tool for openCFS

Many numerical simulation tools have been developed and are on the market, but there is still a strong need for appropriate tools capable to simulate multi-field problems, especially in aeroacoustics. Therefore, openCFS provides an open-source framework for implementing partial differential equations using the finite element method. Since 2000, the software has been developed continuously. The result of is openCFS (before 2020 known as CFS++ Coupled Field Simulations written in C++). In this paper, we present for the first time the CFS-Data, the open-source pre-post-processing part of openCFS with a focus on the aeroacoustic source computation (called filters).

math.NA↗

arXiv2023

Anisotropic Minimum Dissipation Subgrid-Scale Model in Hybrid Aeroacoustic simulations of Human Phonation

This article deals with large-eddy simulations of 3D incompressible laryngeal flow followed by acoustic simulations of human phonation of five cardinal english vowels /u, i, \textipa{A}, o, {\ae}/. The flow and aeroacoustic simulations were performed in OpenFOAM and in-house code openCFS, respectively. Given the large variety of scales in the flow and acoustics, the simulation is separated into two steps: (1) computing the flow in the larynx using the finite volume method on a fine 2.2M grid followed by (2) computing the sound sources separately and wave propagation to the radiation zone around the mouth using the finite element method on a coarse 33k acoustic grid. The numerical results showed that the anisotropic minimum dissipation model, which is not well known since it is not available in common CFD software, predicted stronger sound pressure levels at higher harmonics and especially at first two formants than the wall-adapting local eddy-viscosity model. We implemented the model as a new open library in OpenFOAM and deployed the model on turbulent flow in the larynx with positive impact on the quality of simulated vowels. Numerical simulations are in very good agreement with positions of formants from measurements.

physics.flu-dyn↗