Posts

# 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 more than 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 ($400$ $\text{Hz}$). 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 Elmer 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 Elmer. 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…).

Posts

# 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 Elmer 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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# Elmer Model and Solver Parameters

In the previous episodes we solved a few equations with Elmer. 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 Elmer 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.

Posts

# 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. Elmer 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 Elmer is that of the elastic vibration modes of solids.

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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.