atl_eqn_nvrstk_module Module

Compressible Navier-Stokes equations for viscous flows.

The flow field is represented in terms of the conservative variables density, momentum and energy. The Navier-Stokes equations require the definitions of the inviscous Euler equations, as described in atl_eqn_euler_module and in addition the following parameters:

• Dynamic viscosity mu
• Thermal conductivity therm_cond
• Internal penalization (for the diffusive term implementation in DG)

Optionally you can also provide a visc_limit to adaptively switch off the computation of the viscous terms if their estimated magnitude falls below this limit for an element. If visc_limit is 0 (the default) no adaptivity will be considered.

The following equation names are implementing the Navier-Stokes equations and require the settings described above.

• navier_stokes (3D)
• navier_stokes_2d (2D)
• filtered_navier_stokes (3D) with turbulence modelling
• filtered_navier_stokes_2d (2D) with turbulence modelling

A complete example for the configuration of the Navier-Stokes equations is given below:

  equation = {
    name      = 'navier_stokes',
    isen_coef = 1.4,
    r         = 287,
    material = {
      characteristic = 0.0,
      relax_velocity = {0.0, 0.0, 0.0},
      relax_temperature = 0.0
    },
    -- Viscous parameters
    therm_cond = 0.5,
    mu         = 2.0,
    ip_param   = 4,
    visc_limit = 0
  }
  equation["cv"] = equation["r"] / (equation["isen_coef"] - 1.0)

The settings for isen_coef, r, material and cv are inherited from the Euler equations, see atl_eqn_euler_module. Please note, that there are more parameters that may be set as described in atl_eqn_euler_module