💻 computer science

Building Acoustics 01: Finite Element Model of an Building Acoustics Test Facility to Predict the Sound Transmission Loss Based on DIN EN ISO 10140

This paper presents a finite element model of a building acoustics test facility, developed using SALOME and the in-house code elPaSo, to predict sound transmission loss for various wall configurations in accordance with DIN EN ISO 10140, demonstrating good agreement with theoretical profiles for insulated double-leaf walls.

Original authors: Sebastian Schmidt, Sabine C. Langer

Published 2026-05-20

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CC BY 4.0

Original authors: Sebastian Schmidt, Sabine C. Langer

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine you are an architect trying to design a super-quiet building. Usually, to see if your walls work, you have to build a real, full-sized room, hire a band to play loud music on one side, and measure how much noise leaks through to the other side. This is expensive, takes a long time, and you can't easily change the materials once the walls are built.

This paper is about building a digital twin of a sound-testing lab. Instead of building a physical room, the researchers created a virtual one inside a computer to predict how well different walls block noise.

Here is the story of how they did it, broken down into simple parts:

1. The Goal: A Virtual Sound Lab

The researchers wanted to create a "virtual prototype" of a building acoustics test facility. Think of this like a flight simulator, but for sound. They wanted to test how well single walls (like a single sheet of drywall) and double walls (two sheets with a gap in between) stop sound from passing through, following strict international rules called DIN EN ISO 10140.

2. The Tool: The "Pixelator" and the "Solver"

To make this simulation work, they used two main tools:

SALOME (The Architect): This software drew the blueprints and chopped the virtual rooms and walls into millions of tiny puzzle pieces (called a "mesh"). Imagine taking a loaf of bread and slicing it into tiny cubes so you can study how sound moves through each crumb.
elPaSo (The Calculator): This is a custom-made computer program written by the researchers themselves. It takes all those tiny puzzle pieces and does the heavy math to figure out how sound waves bounce, vibrate, and get absorbed.

3. The Challenge: The "Pixel Density" Problem

Sound waves are tricky. High-pitched sounds (like a whistle) have very short wavelengths, meaning they need tiny puzzle pieces to be seen correctly by the computer. Low-pitched sounds (like a bass drum) have long wavelengths and need bigger pieces.

The Problem: If you make the puzzle pieces small enough to catch the high-pitched sounds, the computer has to solve billions of equations, which takes forever.
The Solution: The researchers used a clever trick called "domain-specific discretization." Imagine looking at a map: you use a very detailed, zoomed-in view for the busy city center (where the complex sounds are) and a zoomed-out, simpler view for the quiet countryside. They made the puzzle pieces tiny only where they needed to be (like inside the insulation material) and larger where they could get away with it. This saved them a massive amount of computer time.

4. The Test Drive: Checking the Engine

Before trusting their custom calculator (elPaSo), they had to prove it worked. They built a tiny, scaled-down version of the sound lab and ran the simulation. Then, they compared their results against a famous, expensive commercial software called COMSOL.

The Result: Their custom calculator matched the expensive software almost perfectly. It was like proving their homemade car engine ran just as smoothly as a Ferrari's before they tried to drive it across the country.

5. The Experiments: Testing the Walls

Once the engine was verified, they ran the simulation on a full-sized virtual test facility. They tested three scenarios:

A Single Wall: Just one layer of plasterboard.
A Double Wall (Empty): Two layers with an air gap in between.
A Double Wall (Insulated): Two layers with a gap filled with glass wool (insulation).

They measured the Sound Transmission Loss (STL), which is basically a score of how many decibels of noise the wall blocks.

6. The Findings

The Insulated Wall: This was the star of the show. The computer simulation showed that the double wall with insulation blocked sound very effectively, matching the theoretical "textbook" predictions perfectly. It acted like a great noise barrier.
The Empty Walls: The single wall and the empty double wall showed some agreement with theory, but not as perfectly as the insulated one. The researchers noted that to get a clearer picture, they would need to test a wider range of frequencies (like testing more musical notes).

Summary

In short, the researchers successfully built a virtual sound lab that can predict how well walls block noise without needing to build a physical one. They proved their custom software works by comparing it to industry standards and showed that adding insulation to a double-wall setup creates a highly effective sound barrier, just as physics theory suggests.

They also made their data and model available to the public, essentially handing the "blueprints" of this virtual lab to other scientists so they can run their own experiments without starting from scratch.

Technical Summary: Finite Element Model of a Building Acoustics Test Facility for Sound Transmission Loss Prediction

Problem Statement
Accurate estimation of Sound Transmission Loss (STL) is critical for quantifying noise pollution and designing buildings with effective acoustic protection. While STL can be measured in-situ or in dedicated test facilities adhering to DIN EN ISO 10140, experimental setups are costly, time-consuming, and exhibit variability between facilities. Furthermore, during early design phases, material parameters and construction details are often not fully specified, making physical prototyping difficult. While numerical methods like Statistical Energy Analysis (SEA) exist, they lack the spatial resolution required for complex constructions. Finite Element Methods (FEM) offer wave-resolving capabilities but face challenges in large-scale geometries due to the computational resources required to resolve decreasing wavelengths at higher frequencies. Existing literature often limits FEM applications to small-scale or downscaled test facilities, or restricts frequency ranges, limiting their utility for full-scale, broadband acoustic prediction.

Methodology
This study presents a full-scale, virtual prototype of a building acoustics test facility designed to predict STL for single-leaf and double-leaf walls (with and without insulation) in accordance with DIN EN ISO 10140. The simulation chain utilizes SALOME 9.14 for geometry and mesh generation and the in-house research code elPaSo (elementary Parallel Solver) for matrix assembly and solving.

Physical Modeling:
- Acoustic Fluids: The source room, receiving room, and air-filled gaps are modeled using the Helmholtz equation. Damping is introduced via a complex bulk modulus to achieve specific reverberation times (e.g., $T=1.5$ s) or atmospheric propagation loss.
- Porous Insulation: Glass wool insulation is modeled as an equivalent fluid using the Johnson-Champoux-Allard (JCA) model. To account for frame inertia at low frequencies, a "limp frame" assumption is applied, modifying the effective density while retaining the Helmholtz formulation.
- Structure: Walls are modeled as 2D plane shells using Mindlin plate theory (for bending) and membrane theory (for in-plane motion). This allows for the modeling of thick walls and includes shear effects. Structural damping is defined via a complex Young's modulus.
- Coupling: Strong fluid-structure coupling is implemented using Nitsche-type coupling conditions on non-conforming meshes. This approach allows different domains to be discretized with element lengths specific to their respective wave speeds and frequencies, avoiding the computational bottleneck of conforming meshes.
Verification and Validation:
- Verification: The elPaSo solver was verified against the commercial software COMSOL 6.3 using a small-scale test facility (1 Hz to 1000 Hz). Four configurations were tested (single-leaf, double-leaf with/without insulation). Results showed visual consistency and low average relative errors ( $\epsilon_{r,ave} \approx 0.0$ to $0.01$), confirming the accuracy of the element and coupling formulations.
- Mesh Convergence: A convergence study on the large-scale facility (100 Hz to 300 Hz) compared sampling rates of 7, 10, 13, and 16 nodes per wavelength. Using the Frequency Response Assurance Criterion (FRAC), 13 nodes per wavelength was identified as the optimal sampling rate to balance accuracy and computational cost.
Simulation Strategy:
- A frequency- and domain-specific discretisation approach was employed. Instead of a single mesh resolving up to the maximum frequency (715 Hz), four separate meshes were created for frequency bands [1–300], [300–500], [500–650], and [650–715] Hz. This significantly reduced solution times compared to a single high-resolution mesh.
- The model adheres to DIN EN ISO 10140-5 dimensions (Source Room: 60 $m^3$ , Receiving Room: 54 $m^3$ ) and defines specific source and microphone positions to ensure a diffuse sound field.

Key Contributions

Full-Scale Virtual Prototype: The creation of a full-scale building acoustics test facility model compliant with DIN EN ISO 10140, capable of predicting STL for single- and double-leaf walls.
Open-Source Benchmark: The dataset, including geometry, mesh, and simulation parameters, has been published on Zenodo as a benchmark for the EAA Computational Acoustics community.
Efficient Solver Implementation: Demonstration of the elPaSo code's capability to handle large-scale vibroacoustic problems using non-conforming meshes and domain-specific discretisation, achieving solution times feasible on commercial workstations (approx. 14–24 hours for the full frequency range).
Validation of Equivalent Fluid Approaches: Successful application of the limp frame equivalent fluid model for glass wool insulation within a full-scale FEM framework.

Results

Verification: The elPaSo solver produced results consistent with COMSOL across all test cases, validating the implementation of the Helmholtz equation, Mindlin plate theory, and fluid-structure coupling.
Single-Leaf Wall: The numerically derived STL showed declines corresponding to the first nine eigenfrequencies of the wall. The profile followed Berger's mass impedance law in the mid-frequency range, though the coincidence frequency ( $f_c \approx 662$ Hz) was near the upper limit of the simulated range (630 Hz), preventing a full observation of the post-coincidence behavior.
Double-Leaf Wall (No Insulation): The STL profile exhibited a resonance decline at $f_0 \approx 84.92$ Hz. Following the resonance, the STL increased, but the expected 12 dB/octave slope was not fully realized within the 630 Hz limit; a 6 dB/octave increase (consistent with mass law) was observed instead.
Double-Leaf Wall (With Insulation): The inclusion of glass wool insulation shifted the resonance frequency lower ( $f_0 \approx 73.26$ Hz). Crucially, the STL profile after the resonance showed a clear 12 dB/octave increase, aligning well with theoretical predictions found in literature.

Significance and Claims
The authors claim that this work provides a validated, open-source dataset for a full-scale building acoustics test facility, enabling the prediction of STL without reliance on repeated physical experiments. The study demonstrates that while full-scale FEM is computationally demanding, it is feasible on standard workstations when utilizing non-conforming meshes and frequency-specific discretisation.

The paper modestly concludes that while the double-leaf wall with insulation showed good agreement with theoretical profiles, the single-leaf and uninsulated double-leaf walls showed only partial agreement within the limited frequency range (8 Hz to 630 Hz). The authors state that more justified comparisons with theoretical profiles require investigations in a wider frequency range. The work is presented as a foundation for future virtual prototyping of entire buildings in acoustic-oriented design processes, with potential for further efficiency gains through High-Performance Computing (HPC) and surrogate modeling.