GaPFlow.models.viscous

GaPFlow.models.viscous#

Viscous stress tensor components.

This module contains functions that calculate the (generalized) Newtonian stress tensor components at the walls of the bottom and top surface, and averaged across the gap.

Functions

stress_avg(q, h, U, V, eta, zeta, Ls[, dqx, ...])

Gap-averaged viscous stress tensor (normal and in-plane shear components).

stress_bottom(q, h, U, V, eta, zeta, Ls[, ...])

Viscous stress tensor at the bottom wall.

stress_top(q, h, U, V, eta, zeta, Ls[, dqx, ...])

Viscous stress tensor at the top wall.
GaPFlow.models.viscous.stress_avg(q, h, U, V, eta, zeta, Ls, dqx=None, dqy=None, slip='top')#

Gap-averaged viscous stress tensor (normal and in-plane shear components).

Parameters:

  • q (numpy.ndarray) – Height-averaged variables field. First index is mass density, 2nd and 3rd mass flux in x and y direction, respectively.

  • h (numpy.ndarray) – Gap height field. First index is actual height, 2nd and 3rd heihgt gradients in x and y direction, respectively.

  • U (float) – Lower wall velocity in x direction.

  • V (float) – Upper wall velocity in y direction.

  • eta (float) – Dynamic shear viscosity

  • zeta (float) – Dynamic bulk viscosity

  • Ls (float) – Slip length

  • dqx (numpy.ndarray, optional) – Gradient (x) field of the height-averaged variables. First index is mass density, 2nd and 3rd mass flux in x and y direction, respectively. (the default is None, which falls back to zero)

  • dqy (numpy.ndarray, optional) – Gradient (x) field of the height-averaged variables. First index is mass density, 2nd and 3rd mass flux in x and y direction, respectively. (the default is None, which falls back to zero)

  • slip (str, optional) – Slipping walls keyword, either “both”, “top”, or “bottom”. (the default is ‘top’, which means no slip bottom wall)

Returns:

Gap-averaged viscous stress tensor components

Return type:

numpy.ndarray

GaPFlow.models.viscous.stress_bottom(q, h, U, V, eta, zeta, Ls, dqx=None, dqy=None, slip='top')#

Viscous stress tensor at the bottom wall.

Parameters:

  • q (numpy.ndarray) – Height-averaged variables field. First index is mass density, 2nd and 3rd mass flux in x and y direction, respectively.

  • h (numpy.ndarray) – Gap height field. First index is actual height, 2nd and 3rd heihgt gradients in x and y direction, respectively.

  • U (float) – Lower wall velocity in x direction.

  • V (float) – Upper wall velocity in y direction.

  • eta (float) – Dynamic shear viscosity

  • zeta (float) – Dynamic bulk viscosity

  • Ls (float) – Slip length

  • dqx (numpy.ndarray, optional) – Gradient (x) field of the height-averaged variables. First index is mass density, 2nd and 3rd mass flux in x and y direction, respectively. (the default is None, which falls back to zero)

  • dqy (numpy.ndarray, optional) – Gradient (x) field of the height-averaged variables. First index is mass density, 2nd and 3rd mass flux in x and y direction, respectively. (the default is None, which falls back to zero)

  • slip (str, optional) – Slipping walls keyword, either “both”, “top”, or “bottom”. (the default is ‘top’, which means no slip bottom wall)

Returns:

Viscous stress tensor components

Return type:

numpy.ndarray

GaPFlow.models.viscous.stress_top(q, h, U, V, eta, zeta, Ls, dqx=None, dqy=None, slip='top')#

Viscous stress tensor at the top wall.

Parameters:

  • q (numpy.ndarray) – Height-averaged variables field. First index is mass density, 2nd and 3rd mass flux in x and y direction, respectively.

  • h (numpy.ndarray) – Gap height field. First index is actual height, 2nd and 3rd heihgt gradients in x and y direction, respectively.

  • U (float) – Lower wall velocity in x direction.

  • V (float) – Upper wall velocity in y direction.

  • eta (float) – Dynamic shear viscosity

  • zeta (float) – Dynamic bulk viscosity

  • Ls (float) – Slip length

  • dqx (numpy.ndarray, optional) – Gradient (x) field of the height-averaged variables. First index is mass density, 2nd and 3rd mass flux in x and y direction, respectively. (the default is None, which falls back to zero)

  • dqy (numpy.ndarray, optional) – Gradient (x) field of the height-averaged variables. First index is mass density, 2nd and 3rd mass flux in x and y direction, respectively. (the default is None, which falls back to zero)

  • slip (str, optional) – Slipping walls keyword, either “both”, “top”, or “bottom”. (the default is ‘top’, which means no slip bottom wall)

Returns:

Viscous stress tensor components

Return type:

numpy.ndarray