2D Navier-Stokes Equations

The 2D Navier-Stokes equations represent instationary, viscous, compressible flows in two spatial dimensions. It is configured by setting the name in the equation table to navier_stokes_2d.

Here is an example for the equation table of this equation system:

  equation = {
    name      = 'navier_stokes_2d',
    isen_coef = 1.4,
    r         = 287,
    -- Viscous parameters
    therm_cond = 0.5,
    mu         = 1.e-5,
    ip_param   = 8/3,
    material = {
      characteristic = 0.0,
      relax_velocity = {0.0, 0.0},
      relax_temperature = 0.0
    }
  }

Note: you have to use the modg_2d scheme to compute this equation system (scheme.spatial.name = 'modg_2d').

The following example setups are available:

• constant state: represents the simplest possible setup with a constant state and periodic boundary conditions. It mainly serves as a check to ensure there is nothing fundamentally flawed in the implementation.

• shear hat: provides a small example with extreme viscosity and an initial hat velocity profile in y direction (linear y-velocity profile left and right of the x-axis). It serves as a check on the treatment of viscous effects in the scheme.

• viscous vortex: provides a 2D vortex setup with additional source terms that yield a known analytical solution to the system.