autopdex.models.navier_stokes_incompressible_steady

autopdex.models.navier_stokes_incompressible_steady(dynamic_viscosity, density=1.0, incompressible_weighting=1.0, volume_load_fun=None)[source]

Constructs the steady-state incompressible Navier-Stokes equations.

Parameters:

  • dynamic_viscosity (float) – Dynamic viscosity of the fluid.

  • density (float, optional) – Density of the fluid. Default is 1.0.

  • incompressible_weighting (float, optional) – Weighting factor for the incompressibility constraint. Default is 1.0.

  • volume_load_fun (function, optional) – Function to compute volume load given spatial coordinates. Default is None.

Returns:

A function that evaluates the steady-state incompressible Navier-Stokes equations.

Return type:

function

Notes

  • The first equation is the constraint of a divergence-free flow field.

  • The remaining equations are the linear momentum balance.

  • The first field in the ansatz function is the pressure field, and the remaining fields are the velocity components.

  • The density and viscosity are assumed to be constant.

  • The volume load function, if provided, must be volume-specific.

  • This models works for DOFs as a jnp.ndarray.