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[10726559]

Good afternoon, Mr. Ketch, I am a master student in fluid mechanics, now I am trying to use Pyclaw and specify boundary conditions by myself for shock tube type problems. However, the pressure value of the current time step on the boundary needs to be determined through the values of pressure and self-defined quantities in the previous time steps, I would like to ask that if there are some ways to extract and use them from the previous numerical results? Thank you very much!

[mandli]

How many time steps do you need?

[10726559]

• From t=0 (initial beginning time) to the current time step t=tn, or from the first time when the first pressure wave arriving at the boundary(if there exists time trigger in Pyclaw to help me identify it), I need to define the current pressure value on the boundary according to these waves in the boundary condition definition part, I don't know if there are some functions can achieve this. Thank you!

[mandli]

How are these boundary conditions dependent on the solution internal to the domain?

[10726559]

The quantities(density, velocity, pressure, etc.) of the last cell in the inner domain are known at the current time step, and the pressure on the ghost cell is just set to the ambient pressure; two Riemann invariants are used to connect the values of the last cell and the boundary, as well as those of the boundary and the adjacent ghost cell; under a certain assumption, the normalized Riemann invariant for the right-traveling wave can connect the incident pressure waves with ambient pressure, and it is known from the internal solution. Therefore, the strength of each incident pressure wave element at different time steps can be calculated; Then the pressure on the boundary at different time steps will be affected jointly by these previous pressure waves elements according to acoustic response theory, so I would like to extract and use the previous numerical results to define the current pressure on the boundary, afterwards Riemann invariants are used to determine the velocities on the boundary and ghost cell.

[mandli]

It sounds like all you need then is the previous time step's value of the pressure.  We do this often with Riemann based FV methods.  I am not sure why you would anything but the immediately available values in the cells though, especially given that this is a hyperbolic PDE.  These are easily available unless there is some sort of history you are looking for. Kyle

…

On Feb 24, 2023 at 10:39 AM -0500, Chen Liu ***@***.***>, wrote: The quantities(density, velocity, pressure, etc.) of the last cell in the inner domain are known at the current time step, and the pressure on the ghost cell is just set to the ambient pressure; two Riemann invariants are used to connect the values of the last cell and the boundary, as well as those of the boundary and the adjacent ghost cell; under a certain assumption, the normalized Riemann invariant for the right-traveling wave can connect the incident pressure waves with ambient pressure, and it is known from the internal solution. Therefore, the strength of each incident pressure wave element at different time steps can be calculated; Then the pressure on the boundary at different time steps will be affected jointly by these previous pressure waves elements according to acoustic response theory, so I would like to extract and use the previous numerical results to define the current pressure on the boundary, afterwards Riemann invariants are used to determine the velocities on the boundary and ghost cell. — Reply to this email directly, view it on GitHub, or unsubscribe. You are receiving this because you commented.Message ID: ***@***.***>

[10726559]

Thank you very much, Mr. Mandli. I am considering a partially reflective boundary on which incident pressure waves at different times will act on it. I will look up the state.problem_data dictionary and guage in Pyclaw document mentioned by Mr. Ketch.

[ketch]

In general, if you need values from times earlier than the previous step, you could use the state.problem_data dictionary to keep track of them, or put a guage at the boundary.

[10726559]

Thank you very much, Mr. Ketch. It can be helpful for me. I will look at it.