trixi-framework
Is Trixi.jl suitable for simulation of acoustic wave through inhomogeneous media ?
Sorry for this probably dumb question, but I wonder if Trixi.jl is suitable for simulation of acoustic wave through (3D) inhomogeneous media (in time domain) ? I have seen the keywork acoustic on a slide in a video presentation of Trixi.jl, but I was not able to find example for it.
What are the governing equations? Acoustic perturbation, (non)linear Euler, how does inhomogeneous media translate into physical modeling?
I would like to solve this kind of equation
$\frac{1}{\rho c^2} \frac{\partial^2}{\partial t^2}u-\nabla \cdot (\frac{1}{\rho}\nabla u) =s $
like in https://arxiv.org/pdf/2003.09812.pdf
That should be possible - however, you need to implement this equation yourself which involves rewriting this as a two-dimensional system with only first order temporal derivatives.
That should be possible - however, you need to implement this equation yourself which involves rewriting this as a two-dimensional system with only first order temporal derivatives.
Exactly! Once rewritten, you should be able to discretize the equations with Trixi.jl. Furthermore:
- If $\rho$ and $c$ are to vary in space, you need to implement them as additional state variables, and set the physical flux (
flux) and the numerical fluxes for them to zero. We did something similar for, e.g., the acoustic perturbation equations. - If $\rho$ and $c$ are to vary in time, you need to provide a custom
rhs!function as described in this tutorial that updates the values appropriately in each Runge-Kutta stage.
Feel free to ping us in case of further questions.
