pymrm.interpolate

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Interpolation utilities between cell-centered and staggered grids.

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Public API¶

compute_boundary_values(cell_centered_values, x_f, x_c = None, bc = None, axis = 0, bound_id = None)¶

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Compute boundary values and boundary-normal gradients.

Parameters¶

• cell_centered_values (numpy.ndarray) Cell-centered solution values.

• x_f (array_like) Face coordinates along axis.

• x_c (array_like, optional) Cell-center coordinates.

• bc (dict or tuple[dict | None, dict | None], optional) Boundary-condition data. For a single boundary query (bound_id set), a single dictionary is accepted. For both boundaries, pass a two-element tuple.

• axis (int, optional) Axis normal to the boundary.

• bound_id ({0, 1} or None, optional) Boundary selector. None returns both boundaries.

Returns¶

• tuple If bound_id is None: (value_left, grad_left, value_right, grad_right). Otherwise: (value, grad) for the requested boundary.

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construct_boundary_value_matrices(shape, x_f, x_c = None, bc = None, axis = 0, bound_id = 0, shape_d = None, format = 'csc')¶

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Build matrices that evaluate boundary values from cell-centered unknowns.

Parameters¶

• shape (tuple[int, ...]) Cell-centered field shape.

• x_f (array_like) Face coordinates along axis.

• x_c (array_like, optional) Cell-center coordinates near the selected boundary.

• bc (dict, optional) Boundary-condition dictionary with keys a, b, and d.

• axis (int, optional) Boundary-normal axis.

• bound_id ({0, 1}, optional) 0 for the lower/left boundary, 1 for upper/right.

• shape_d (tuple[int, ...], optional) Shape of external inhomogeneous source unknowns.

• format ({‘csc’, ‘csr’}, optional) Sparse format for the homogeneous matrix.

Returns¶

• tuple (matrix, mat_bc) where matrix maps cell-centered values to boundary values and mat_bc maps inhomogeneous boundary terms.

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create_staggered_array(array, shape, axis, x_f = None, x_c = None)¶

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Create a face/staggered field from scalar, centered, or staggered input.

Parameters¶

• array (array_like) Input values. May be scalar, centered, or already staggered.

• shape (tuple[int, ...] or int) Target centered-field shape.

• axis (int) Staggering axis.

• x_f, x_c (array_like, optional) Face and center coordinates used when centered input must be interpolated to faces.

Returns¶

• numpy.ndarray Broadcasted/interpolated array with staggered shape.

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interp_cntr_to_stagg(cell_centered_values, x_f, x_c = None, axis = 0)¶

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Interpolate cell-centered values to face/staggered locations.

Parameters¶

• cell_centered_values (numpy.ndarray) Values defined at cell centers.

• x_f (array_like) Face coordinates along axis.

• x_c (array_like, optional) Cell-center coordinates. If omitted, midpoint locations are used.

• axis (int, optional) Interpolation axis.

Returns¶

• numpy.ndarray Staggered values with one additional element along axis.

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interp_cntr_to_stagg_tvd(cell_centered_values, x_f, x_c = None, bc = None, v = 0, tvd_limiter = None, axis = 0)¶

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Perform TVD interpolation from cell centers to faces.

Parameters¶

• cell_centered_values (numpy.ndarray) Cell-centered values.

• x_f (array_like) Face coordinates along axis.

• x_c (array_like, optional) Cell-center coordinates. If omitted, midpoint locations are used.

• bc (tuple[dict | None, dict | None], optional) Left and right boundary-condition dictionaries with keys a, b, and d.

• v (float or array_like, optional) Face velocity used to determine upwind/downwind directions.

• tvd_limiter (callable, optional) Limiter function with signature phi(c_norm, x_norm_c, x_norm_d). If None, the routine returns linear upwind interpolation without TVD correction.

• axis (int, optional) Interpolation axis.

Returns¶

• tuple[numpy.ndarray, numpy.ndarray] Interpolated staggered values and TVD correction term.

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interp_stagg_to_cntr(staggered_values, x_f, x_c = None, axis = 0)¶

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Interpolate face/staggered values to cell centers.

Parameters¶

• staggered_values (numpy.ndarray) Values defined on staggered (face) locations.

• x_f (array_like) Face coordinates along axis.

• x_c (array_like, optional) Cell-center coordinates. If omitted, midpoint interpolation is used.

• axis (int, optional) Interpolation axis.

Returns¶

• numpy.ndarray Cell-centered values with one fewer element along axis.

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