https://github.com/ashxsong/hyperbolic-models-in-elasticity
2025 Modeling and Simulation with PDEs Undergraduate Summer School at Texas A&M University
Science Score: 26.0%
This score indicates how likely this project is to be science-related based on various indicators:
-
○CITATION.cff file
-
✓codemeta.json file
Found codemeta.json file -
✓.zenodo.json file
Found .zenodo.json file -
○DOI references
-
○Academic publication links
-
○Academic email domains
-
○Institutional organization owner
-
○JOSS paper metadata
-
○Scientific vocabulary similarity
Low similarity (7.1%) to scientific vocabulary
Repository
2025 Modeling and Simulation with PDEs Undergraduate Summer School at Texas A&M University
Basic Info
Statistics
- Stars: 1
- Watchers: 0
- Forks: 0
- Open Issues: 0
- Releases: 0
Metadata Files
README.md
Hyperbolic Models in Elasticity
Note: This is a sample of the work completed at the 2025 Modeling and Simulation with PDEs Undergraduate Summer School at Texas A&M University. The visualizations in the file are animated when they are run, even though they appear static on GitHub.
This code computes the solutions to certain partial differential equations involved in the deformation of solid objects under externally acting forces. In particular, assuming the deformation is small, the 1-dimensional balance of momentum equation in $t$ and $x$ becomes
$$\partialt^2 u - c^2 \partialx^2 u = 0,$$
which is simply the 1-dimensional wave equation. First, the 1-dimensional wave equation can be rewritten as the following system of first-order partial differential equations:
$$\partialt u + \partialx v = 0,$$
$$\partialt v + c^2 \partialx u = 0.$$
The forward Euler time-stepping scheme with central differences for the interior and one-sided differences for the endpoints can be implemented to solve this. Additionally, reflecting boundaries can be included by setting $v = 0$ after every time step.
Next, a stabilization term can be added to get that
$$\partialt u + \partialx v - \epsilon \Delta u = 0,$$
$$\partialt v + c^2 \partialx u - \epsilon \Delta v = 0,$$
where $\epsilon = c\text{stable} h^2$ and $c\text{stable}$ is a real number chosen between 1 and 32.
Now, we consider the 1-dimensional nonlinear balance of momentum equation in $t$ and $x$, which is
$$\partialt^2 u - c^2 \partialx \left\{(1 + \partialx u)\left(\partialx u + \frac{1}{2} (\partial_x u)^2\right)\right\} = 0.$$
This equation can be rewritten as the following system of first-order partial differential equations:
$$\partialt u + \partialx v = 0,$$
$$\partialt v + c^2 (1 + \partialx u)\left(\partialx u + \frac{1}{2}(\partialx u)^2\right) = 0.$$
We also simulate an elastic string subject to gravity in both the linear and nonlinear cases.
Owner
- Login: ashxsong
- Kind: user
- Repositories: 1
- Profile: https://github.com/ashxsong
GitHub Events
Total
- Push event: 6
Last Year
- Push event: 6