We consider the initial and boundary value problem for isentropic gas dynamics by the vanishing viscosity method, where we consider the boundary condition m (momentum)=0, in particular. The difficult point is what boundary conditions we give the isentropic gas dynamics with the artifical viscosity (We call this equation (AV)). As you know, (AV) is the parabolic equation. So, we must give two boundary conditions. On the other hand, the limit equation, i.e. isentropic gas dynamics, is hyperbolic equation. So, the boundary
condition is only one, m=0.
You can use the same BC.s prescribed for the compressible NSE model, that is a non-reflecting type that depends on the sign of the characteristic curves.
There are some results using the Spectral VV method. Look at the work of Y. Maday also the work of Pasquetti.
Karamanos and Karniadakis have applied this method for LES.
- Badges
- Science topic