Prandtl Meyer Shock problem

Shockwave :

It is characterized by an abrupt, nearly discontinuous change in pressure, temperature and density of the medium, when a wave moves faster than the local speed of sound in a fluid.

Based on characterization it can be of many types. For example

based on angle: Normal shock, Oblique shocks, Bow shocks.

For this problem and mostly for most shock-problems: Neumann Boundary conditions are used.

Neumann Boundary conditions: specifies the derivative of a variable at a boundary. It is used rather than the actual value when a certain rate of change in value needs to be imposed for a variable.

These boundary conditions work well for shock probletms, because taking the case of blunt shock problem, some part of the domain has subsonic region whereas other part has supersonic region. Hence the mathematical behaviour of euler equations changes. To counteract this problem, an unsteady analysis is conducted, introducing time variable. This converts the mathematical behaviour to only hyperbolic. Hence Neumann boundary conditions are used.

In this case we will analyze the results based on SGS variation using Converge :

1. SGS 0.05

Initial grid:

Final Grid:

Velocity and Temperature:

2. SGS 0.1

Velocity and Temperature:

2. SGS 0.01

Velocity and Temperature:

One can easily analyze that with decrease in subgrid scaling, grid becomes sensetive to calculated variables variation and hence, the grid size decreases for major part of domain and also becomes more finer.