UncertaintyModel

UncertaintyModel is the abstract base class for computing the uncertainty estimate for a given discretization level. Below is the description of the abstract base class followed by the concrete classes.

class cfdverify.discretization.UncertaintyModel(parent: DiscretizationError)

Abstract base class for uncertainty models

abstract uncertainty(key: str, index: int | None = None, **kwargs) → floating | Series

Uncertainty method

Parameters:

  • key (str) – Key of system response quantity of interest

  • index (int | None) – Index of discretization level of interest or None for all levels

Returns:

Uncertainty of requested values

Return type:

np.floating | pd.Series

class cfdverify.discretization.GCI(parent: DiscretizationError)

Bases: UncertaintyModel

Computes uncertainty using the Grid Convergence Index

uncertainty(key: str, index: int | None = None, fs: int | float = 1.25, normalize: bool = False) → floating | Series

Compute Grid Convergence Index (GCI) for requested values

The GCI method was proposed by Patrick Roache as a way to uniformly report discretization uncertainty in computational fluid dynamics simulation results in 1994. By default values are not normalized as suggested by Roache and the factor of safety is 1.25. Roache provided the equation

\[GCI_1 = \frac{Fs * |\epsilon_{21}|}{r_{21}^p - 1},\]

for estimating the uncertainty of the finer mesh for any two mesh pairs, and the equation

\[GCI_2 = r_{21}^p * \frac{Fs * |\epsilon_{21}|}{r_{21}^p - 1},\]

for the coarser mesh of any mesh pair. These equations use the absolute relative error measure \(|\epsilon_{21}|\) corrected for the distance to the infinitely fine mesh; this is equivalent to the absolute estimated error \(|\epsilon_{\mathrm{est}}|\) for exact fits. However, for regression fits of data they are not equivalent; therefore, this code implements the GCI uncertainty measure as

\[GCI = Fs * |\epsilon_{\mathrm{est}}|,\]

so that it is valid for both exact and regression fits.

Parameters:

  • key (str) – Key of system response quantity of interest

  • index (int | None) – Index of discretization level of interest or None for all levels

  • fs (int | float) – Factor of safety for computation. Defaults to 1.25

  • normalize (bool) – Whether output GCI value should be normalized or not

Returns:

gci – GCI of requested values

Return type:

np.floating | pd.Series

References

Patrick J. Roache, 1994, Perspective: A Method for Uniform Reporting of Grid Refinement Studies, Journal of Fluids Engineering, 116(3): 405-413. https://doi.org/10.1115/1.2910291.

class cfdverify.discretization.StudentsTDistribution(parent: DiscretizationError)

Bases: UncertaintyModel

Computes uncertainty using student’s t distribution

uncertainty(key: str, index: int | None = None, significance: float = 0.05) → floating | Series

Compute uncertainty using Student’s t distribution

Student’s t distribution is a generalization of the normal probability distribution with fatter tails to account for low sample counts from a population.

Parameters:

  • key (str) – Key of system response quantity of interest

  • index (int | None) – Not used for class but included for uniform interface

  • significance (float) – Double-sided significance for Student’s-t distribution

Returns:

u – Uncertainty of requested values using Student’s t distribution

Return type:

np.floating | pd.Series

class cfdverify.discretization.FactorOfSafety(parent: DiscretizationError)

Bases: UncertaintyModel

Computes uncertainty by a constant factor of safety

uncertainty(key: str, index: int | None = None, factor: int | float = 3) → floating | Series

Compute uncertainty as a constant factor of the error estimate

Parameters:

  • key (str) – Key of system response quantity of interest

  • index (int | None) – Index of discretization level of interest or None for all levels

  • factor (int | float) – Factor of safety to apply to error estimate

Returns:

Uncertainty of requested values using supplied factor of safety

Return type:

np.floating | pd.Series