Non-Reflective Boundary Conditions for the Wave Equation

[NeoDevin]

I wasn't completely sure where to put this (programming or Diff.E.'s), so if there's a better place, maybe the mentors could move it for me.

I'm doing some numerical simulations involving the (2-D) wave equation, and was wondering if anyone could tell me (or give a reference to a paper which would tell me) how to implement a boundary condition which will prevent reflections?

For now I'm just doing a straightforward centered difference, I may implement a higher order method later, depending how much time I have.

 

[NeoDevin]

Anybody? Could we move this to the programming forum and try there?
THanks

 

[minger]

What is the particular problem of interest, and why do you wish to use non-reflective BCs? I've typically used Thompson-style boundary conditions as they seem the most "physical." Are you having problems with reflecting waves growing and ruining the solution?

If so, you might just want to stretch the grid away from the area of interest. The old way of doing things is that if the waves don't make it to the boundary (by way of damping), then you don't have to worry about the boundaries ;).

 

[Nphung78]

What is the particular problem of interest, and why do you wish to use non-reflective BCs? I've typically used Thompson-style boundary conditions as they seem the most "physical." Are you having problems with reflecting waves growing and ruining the solution?

If so, you might just want to stretch the grid away from the area of interest. The old way of doing things is that if the waves don't make it to the boundary (by way of damping), then you don't have to worry about the boundaries ;).

Yes, you are so right minger. I am also extending the computational domain as your idea...
However, since I need to compute on a large domain in a proper computed time, so I have to learn how to make my code better with PML boundary condition...

I've heard about PML, but it's not easy for me to implement it into my code...

Anyone can help us out? How should I start with coding PML?

Thank you so much !

 

[LudusRex]

I can provide some information about non-reflective boundary conditions for the wave equation. These boundary conditions are important in numerical simulations to ensure that the results accurately represent the behavior of waves in real-world scenarios.

One approach to implementing non-reflective boundary conditions is to use perfectly matched layers (PMLs). These are artificial layers that are added to the boundaries of the simulation domain and are designed to absorb outgoing waves, preventing them from reflecting back into the domain. PMLs are commonly used in finite-difference time-domain (FDTD) simulations and have been shown to be effective in reducing reflections.

Another approach is to use absorbing boundary conditions (ABCs), which are based on the idea of artificially adding a layer of material with high attenuation at the boundaries of the simulation domain. This layer will absorb the outgoing waves and prevent them from reflecting back into the domain. ABCs have been used in various numerical methods, such as finite element methods (FEMs) and boundary element methods (BEMs).

There are also other techniques for implementing non-reflective boundary conditions, such as the perfectly matched absorbing layer (PMAL) method and the transparent boundary condition (TBC) method. These methods have been developed to address specific challenges in different types of numerical simulations.

I recommend consulting literature on the specific numerical method you are using, as well as papers that discuss non-reflective boundary conditions for the wave equation. This will provide you with a better understanding of the different techniques and their effectiveness in different scenarios. Additionally, there are also software packages available that can help implement non-reflective boundary conditions in your simulations.

In summary, non-reflective boundary conditions are crucial in accurately simulating wave behavior and there are various techniques available for implementing them. It is important to carefully select the appropriate method for your specific simulation and to validate the results to ensure accuracy.