Mondaic - Full Waveform Solutions

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Salvus has a number of built-in tools for layered meshes and cubed sphere meshes, among others. However, there may be some instances where it becomes necessary to construct a mesh within an external meshing software, which can then be imported into your Salvus project.

Within this tutorial series, we will review the following points:

Important considerations to be aware of when constructing discretizations in third-party meshing tools
How to import external meshes from the Exodus .e file format
Performing some basic quality control operations on the imported mesh
Use the mesh in a forward simulation

The built-in meshing tools in Salvus are designed to produce simulation-ready spectral-element meshes. This means that the meshes are constructed in such a way that they will perform well when used in a wave simulation. However, when constructing meshes manually using third-party tools, it is up to the user to ensure the mesh satisfies a variety of criteria:

For more details on best-practices for constructing meshes for use within Salvus, please see the knowledge base article here.

The approximate element size required to accurately resolve the wavelengths in a particular region of the domain can be obtained using

\Delta x = \frac{v_\text{min}}{f_\text{max} \times n_\text{EPW}},

where

v_\text{min}

is the minimum speed of sound in that region of the domain,

f_\text{max}

is the maximum frequency in the source wavelet, and

n_\text{EPW}

are the number of elements per wavelength needed to accurately resolve the waves. As is discussed in this knowledge base article, around 2.0 elements per wavelength tends to yield excellent results for order 4 simulation (default in Salvus).

The processes for meshing the domains in the accompanying 2D and 3D examples can be skipped by simply using the .e files that are enclosed with the tutorial.

The meshing steps outlined in these tutorials are intended to serve as illustrative examples for how one could go about constructing hexahedral meshes in an external software tool, which will be subsequently imported into the Salvus project later in the tutorial. While these instructions specifically use Coreform Cubit, these steps are equally transferrable to other third-party hexahedral meshing software.

Coreform Cubit is an external meshing software that allows for the generation of complex quadrilateral and hexahedral meshes. There are two accompanying tutorials that describe how one can construct and use these types of external meshes in both 2D and 3D.

The first tutorial from this series involves meshing a circular inclusion that is embedded within a rectangular domain. While this geometry is relatively simple, it illustrates how one can go about generating domains with multiple distinct materials in 2D.

Building off of the approaches showcased in the 2D tutorial, this notebook provides an analogous workflow for a 3D domain that consists of a hemisphere embedded within a cuboid. While this 3D mesh is considerably more complex than that used in the 2D example, the procedure of importing and preparing the mesh for use within Salvus are nearly identical between the 2D and 3D cases.