# Recent Posts

# Rigid Walled Room Revisited - Part 2

In the Rigid Walled Room Revisited - Part 1 episode we seen how to setup an eigen system problem with ElmerFEM by making use of the Wave Equation solver. In this episode we will review the simulation results and check the agreement with the analytical solutions in the Acoustic Modes of a Rectangular Room episode.
Project Files All the files used for this project are available at the repositories below:

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# Rigid Walled Room Revisited - Part 1

We covered the rigid walled rectangular room previously in the Rigid Walled Room episode. In that episode we solved for the steady state field in a rectangular rigid walled room as driven by a source placed somewhere in the room. This allowed us to see how the steady state field is sustained by a modal superposition, the purer the lower the driving frequency (assuming that this driving frequency matched an eigenfrequency of the room).

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# Mesh Order and Accuracy

In the Dealing with Convergence Issues we made use of first order meshes in order to ease convergence of our simulation at high frequency. However, the accuracy of FEM solutions is higher the higher the order of the mesh, so doing so will come at the expenses of accuracy. Still, we argued that the accuracy is mostly controlled by the mesh size, so as long as we have at least ten elements per wavelength the solution should be reasonably accurate.

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# Dealing with Convergence Issues

In the Home Studio - Part 1 episode we faced convergence issues when dealing with the highest driving frequency for our room (400 Hz). This meant that we could not quite trust the solution, and so we discarded it. In this episode we will look at what to do in this cases, and how to reach convergence. Rather that dealing with the issues in abstract and general terms (which would require writing an entire book about it) we will use the Home Studio - Part 1 episode to introduce the problem and figure out how to deal with it practically.

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# Home Studio - Part 1

In the Rigid Walled Room episode we seen how to model a rectangular room with rigid walls. We driven the room at the modal frequencies and compared the solution field with the theoretical modal shapes, finding that the results matched single modal shapes real well until, at a frequency high enough, the contribution of multiple modes (in addition to that related to the driving modal frequency) became important. In this episode we will look at making the model more realistic.

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# Intro to ParaView

In the previous episodes we often made use of the ParaView postprocessor to visualise our solution field from the ElmerFEM solver. ParaView can do all sorts of cool visualisations and animations, as well as providing the way of doing quantitative analysis. It is by far the best option to visualise and postprocess results from ElmerFEM. It also allows to export data in various formats, such as CSV, that allow us to do any additional kind of postprocessing or verification, by either using Julia, Python or any other language, or even spreadsheet software if you fancy that (for whatever reason…).

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# Rigid Walled Room

In the Acoustic Modes of a Rectangular Room episode we explored the analytical model of a rigid walled room with some Julia code. We focused on finding the resonance frequencies (or eigenfrequencies) of the room and calculating the related modal patterns (eigenfunctions). Now that, thanks to The Pulsating Sphere episode, we know how to setup Helmholtz problems with ElmerFEM we can approach the problem with the FEM method. In this episode we will solve for the modal superposition in a rectangular rigid walled room and use the results from the Acoustic Modes of a Rectangular Room episode to check the accuracy.

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# ElmerFEM Model and Solver Parameters

In the previous episodes we solved a few equations with ElmerFEM. We did some choices when we setup the solver parameters. What those parameters do, and how should we set them? This is perhaps the trickiest part in FEM (beside making the mesh right). In this episode we will step back and look at those solver options more closely. This post is really not meant to be an exhaustive explanation. For that, refer to the ElmerFEM documentation.

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# The Pulsating Sphere

In this episode we will build a model of a pulsating sphere source. The pulsating sphere source is an ideal source which forms the base for the development of point sources. In essence, a point source is a pulsating sphere in the limit of $a$, the radius of the sphere, approaching 0. For this reason, although abstract, the pulsating sphere is a very powerful theoretical tool that enables the study of point sources which in turn, through integration and wave propagation principles, enable to study of any arbitrary acoustic field source.

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# Refining the Metal Bar Model

In the last episode we seen that our model solution for the modes of vibration of a metal bar wasn’t looking particularly good for the highest mode. In fact, when we clipped into the bar, we seen few bubbles of discontinuity in the displacement field that are not expected for linearly elastic homogeneous and isotropic bodies. To understand this we have to step back a little and think about FEM some more.

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# Elastic Modes of a Metal Bar

In the last episode we examined the analytical solution of the acoustic modes of a rectangular room and we are now ready to take steps into moving in the world of FEM modelling. ElmerFEM is a powerful package, but it is not extremely user friendly. So, it is best to have a gentle introduction to it first before dwelling into the intricacies of FEM modelling of acoustic fields. One of the simplest problems to solve with ElmerFEM is that of the elastic vibration modes of solid.

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# Acoustic Modes of a Rectangular Room

In this episode we will look at how to make a simple Julia model of one of the simplest systems in acoustics, a rectangular room with rigid walls, assuming adiabatic wave propagation. Even if this system is among the simplest in acoustics it is actually already very complicated. As such, we will focus only on the modes, one part of the problem, without attempting impulse response simulation or other fancy things like that, for now.

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# The FEM Pipeline

In the previous article an overview of the open source ecosystem for scientific and technical computing was presented. In this article the focus will be on FEM. We will first look at how we build a FEM problem, and then select among the packages we listed the software that is best suited for implementing FEM studies.
The Basic Pipeline basic_pipeline The diagram above shows the process of creating a FEM study in its simplest form.

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# FEM in a Nutshell

In the previous episodes we seen that physical systems are described by PDEs. However, PDEs are seldom solved analytically, unless for certain simple cases, the reason being that finding the solution of a PDE on a complex, realistic, domain with realistic boundary and initial conditions is extremely complicated, or downright impossible, even when the PDE is known to have analytical solutions from theoretical considerations. For this reason, numerical methods have arisen in order to handle these problems.

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# What is Acoustic Modelling

Welcome to the first actual episode of the series about acoustic modelling with open source software. We will first try to understand what modelling acoustics means. In reality it doesn’t mean just one thing, as many phenomena of acoustic wave production and propagation can be modelled and simulated in various different ways, with higher or lower degree of accuracy. However, the core of the modelling problem resides in partial differential equations.

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# Setting Up an Ubuntu Modelling Environment

In the first episode of this series the open source ecosystem for the modelling of acoustics was covered. As we will see in the next episodes, we will make extensive use of FEM, at least initially, to model acoustic phenomena. This episode focus on building a simple simulation workstation based around ElmerFEM, a powerful multiphysics FEM suite with excellent acoustics capabilities.
Why an Ubuntu Based Workstation? Ubuntu Linux is a very convenient operating system for this purpose as all the needed packages are straightforward to install, especially ElmerFEM and Salome, which can be quite complicated to get up and running in other distributions.

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# Modelling Acoustics With Open Source Software

One of the backbones of the scientific paradigms is the repeatability of results. Ideally, all software used for scientific research should be open source, so to allow complete repeatability of data analysis and models. And in fact, a lot of this software is indeed open source, and a lot of this software can be used to model acoustic phenomena.
What follows below is a panoramic overview of the scientific open source software ecosystem.

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