discrete1.utils.manufactured module
Functions for manufactured solutions.
Provides solutions for given steady state and time-dependent problems. Includes functions to calculate the order of accuracy.
- discrete1.utils.manufactured.order_accuracy(error1, error2, ratio)[source]
Calculate order of accuracy.
Finding the order of accuracy between errors on different grids where error2 is the refined grid.
- Parameters:
error1 (
float) – Error between an approximate solution and the reference solution on the same grid.error2 (
float) – Error between an approximate solution and the reference solution on a more refined grid.ratio (
float) – Ratio between the spatial cell width of the error1 grid and the error2 grid (delta x1 / delta x2).
- Returns:
Order of accuracy.
- Return type:
float
- discrete1.utils.manufactured.solution_ss_03(x, angle_x)[source]
One material, angular dependent, with source.
- discrete1.utils.manufactured.solution_ss_04(x, angle_x)[source]
Two materials, angular independent.
- discrete1.utils.manufactured.solution_td_01(x, angle_x, edges_t)[source]
One material, time dependent, angular independent.
- discrete1.utils.manufactured.solution_td_02(x, angle_x, edges_t)[source]
One material, time dependent, angular dependent.
- discrete1.utils.manufactured.spatial_error(approx, reference, ndims=1)[source]
Calculate the spatial error between approximate and reference solutions.
- Parameters:
approx (
numpy.ndarray) – Approximate flux.reference (
numpy.ndarray) – Reference flux.ndims (
int) – Number of spatial dimensions for flux (1 or 2).
- Returns:
L2 error normalized for the number of spatial cells.
- Return type:
float
- discrete1.utils.manufactured.wynn_epsilon(lst, rank)[source]
Perform Wynn Epsilon Convergence Algorithm.
- Parameters:
lst (
list) – List of float type. Values for convergence.rank (
int) – Rank of system.
- Returns:
2D array with float type of shape (2 * rank + 2, 2 * rank + 2). Diagonal is convergence.
- Return type:
numpy.ndarray