Compressible fluid

Neko supports compressible flow simulations via the compressible solver. To enable compressible flow, set "scheme": "compressible" in the fluid configuration. This solver integrates the compressible Navier-Stokes equations using a Runge-Kutta time integration scheme with artificial viscosity for stability.

The compressible solver accepts the following parameters:

Name	Description	Admissible values	Default value
gamma	Ratio of specific heats for ideal gas	Positive reals	1.4
mu	Constant physical dynamic viscosity	Non-negative real	0.0
kappa	Constant physical thermal conductivity	Non-negative real	0.0

The compressible solver uses variable time-stepping controlled by the CFL number. Set variable_timestep to true and specify target_cfl in the time control object.

Constant physical viscosity and thermal conductivity can be specified as mu and kappa in the fluid section of the case file. Alternatively, they can be set via the material_properties user interface in the user file, which also allows spatially or temporally varying values. When a user material-properties routine is provided, it takes precedence over the constant JSON values. Stabilization uses the existing Laplacian artificial viscosity, computed as the minimum of entropy-based and low-order viscosities. When fluid_mu or fluid_kappa are nonzero, the solver also applies the compressible Navier-Stokes viscous stress flux and conductive energy flux. If neither property is provided, both default to zero and no physical viscous flux is added. See the user file documentation for details on implementing material_properties.

Example configuration:

{
  "fluid": {
    "scheme": "compressible",
    "gamma": 1.4,
    "viscous_regularization":{
        "type": "artificial_viscosity",
        "reg_coeff_name": "entropy_viscosity"
    },
    "initial_condition": {
      "type": "user"
    },
    "boundary_conditions": [
      {
        "type": "velocity_value",
        "zone_indices": [1],
        "value": [3, 0, 0]
      },
      {
        "type": "density_value",
        "zone_indices": [1],
        "value": 1.4
      },
      {
        "type": "pressure_value",
        "zone_indices": [1],
        "value": 1
      }
    ],
    "output_control": "nsamples",
    "output_value": 20
  },
  "simulation_components": [
    {
      "type": "artificial_viscosity_model",
      "model": "entropy_viscosity",
      "field_name": "entropy_viscosity"
    }
  ]
}

Compressible boundary conditions

The compressible solver supports the following boundary conditions:

Boundary Condition	Description
velocity_value	Dirichlet condition for velocity (inflow)
density_value	Dirichlet condition for density
pressure_value	Dirichlet condition for pressure
no_slip	Zero velocity wall
slip	A slip wall
symmetry	Symmetry plane
outflow	Pressure outlet (zero gradient)
normal_outflow	Normal outflow condition

For examples of compressible flow setups, see the euler_1d_sod, euler_2d_forward_facing_step, and euler_tgv examples.

Viscous regularization

Users can use the viscous regularization object to enhance the smoothness or the numerical stability of the solution via a diffusion term. For example, artificial viscosity can be set up by this object to perform shock capturing. Note that some regularization techniques do not have a diffusive mathematical form, for example gradient jump penalty and high-pass filter relaxation terms, and they are included in the source terms instead. The viscous regularization can be set up with the following options:

• type, the viscous regularization type.
  • artificial_viscosity, the standard second-order diffusion term, \(\frac{\partial}{\partial x}\left(\mu_\mathrm{artificial}\frac{\partial u}{\partial x}\right)\).
• reg_coeff_name, name of the \(\mu_\mathrm{artificial}\) field, usually computed by a simulation component.

Viscous regularization is currently supported by the compressible fluid solver. Artificial viscosity requires both the regularization object that consumes the coefficient and a simulation component that computes it. The reg_coeff_name and field_name values must match:

{
  "fluid": {
    "scheme": "compressible",
    "viscous_regularization": {
      "type": "artificial_viscosity",
      "reg_coeff_name": "entropy_viscosity"
    }
  },
  "simulation_components": [
    {
      "type": "artificial_viscosity_model",
      "model": "entropy_viscosity",
      "field_name": "entropy_viscosity"
    }
  ]
}