I'm doing work on a finite volume 1D Euler solver (quasi-1D using source terms for area variation). The method calculates the fluxes at the cell boundaries, then when updating the conservation variables it calculates the flux between two cell boundaries by using a Riemann solver (Roe or Lax-Friedrich).

I'm new to this and am having great difficulty implementing boundary conditions (right now just subsonic in, subsonic out). I want to using characteristics - this is the most common way it is (or used to be) done, isn't it?

The problem is I don't have any good notes or resources on this. Does anyone know somewhere I can find good notes on this online? I guess a book reference would be helpful too.

Thanks

Charlie,

For a subsonic inlet 2 characteristics enter the flow domain. Therefore you can specify 2 physical boundary conditions (stagnation temperature T0 and pressure P0) at a subsonic inlet. 1 characteristic ( an acoustic wave )can leave the domain therefore 1 numerical boundary condition must be calculated from the interior. I extrapolate the pressure from the interior, then knowing this and the stagnation pressure I can calculate mach number from the isentropic flow equations and hence all other flow variables.

For a subsonic outlet 1 characteristic ( an acoustic wave )can travel upstream and enter the flow domain. Therefore I specify one physical boundary condition (exit or static pressure). 2 characteristics leave the flow domain. Therefore two numerical boundary conditions must be calculated from the interior. You could extrapolate RO and ROU from the interior.

If you're looking for reading material, I'd recommend " Computational Fluid Dynamics, The Basics With Applications" by Anderson, you can buy this on Amazon.

Hope this helps.

Simon.

My goal is to calculate the fluxes at the boundaries using the boundary conditions, then use a Riemann solver that takes the two values of flux at each boundary and finds the appropriate flux. I understand in subsonic there is 1 characteristic out the inlet and 2 characteristics

If I'm understanding you correctly, all I have to do is use the total pressure and total temperature (for the inlet) for the left face at the boundary, then extrapolate a variable from the right face of the boundary (since everything's already calculated there)? How do I extrapolate - just use the same value of the variable since they're the same location? When the person I was working with told me to use characteristics, they jotted down some brief notes, like

dW/dt + A dW/dx = 0, where W are the Riemann variables and A is the vector of eigenvalues (u, u+a, u-a).

The problem was that I have no idea how to use this to determine the boundary fluxes.

If it matters, I'm comparing the results of this nozzle to the analytical solution to determine the accuracy of the scheme, so spatial accuracy is very important.

Thanks

Oops, disregard that last sentence in the first paragraph of my previous post. It doesn't make any sense and I forgot to proofread.

Thanks in advance