Expansion wave

The expansion wave is a test case adopted in the 1st Int1st International Workshop on High-Order CFD Methods, held in Nashville, Tennessee, on January 7–8, 2012.

It consists is the supersonic expansion of a circular wave in a square 2D domain.

The initial conditions of radial velocity are assigned, along with the conservative variables, which are transformed into primitive ones for the Gales computations.

The initial velocity is defined as:

The initial distribution of sound velocity is thus:

Under the assumption of uniform entropy, density can be written as:

And every property and primitive variable can be computed by means of the perfect gas law:

Supersonic (Ma = 2) outflow boundary conditions are assigned, that is, free outflow.

The time step is 0.01 s, with a grid of element size 0.05 m for a [-2,2]X[-2,2] domain.

The stabilization parameters are the tau 2001 and the 1998 discontinuity capturing.

The fluid properties are defined in file props.txt, the initial and boundary conditions are specified in the fluid_ic_bc.hpp file, the set up of the simulation is set in the setup.txt file, and the mesh is defined in the mesh.geo file.

Results

The evolution of velocity, pressure, temperature and density is shown below

Velocity

Pressure

Temperature

Density