pymrm.operators

Back to modules overview

Sparse gradient and divergence operators for finite-volume discretisation.

View module source on GitHub

Public API¶

construct_div(shape, x_f, nu = 0, axis = 0, format = 'csc')¶

Open dedicated reference page

Construct a divergence matrix that maps face fluxes to cell balances.

Parameters¶

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

• x_f (array_like) Face coordinates along axis.

• nu (int or callable, optional) Geometry descriptor. 0 gives Cartesian, 1 cylindrical, 2 spherical, and a callable nu(x) enables custom metrics.

• axis (int, optional) Axis for flux divergence.

• format ({‘csc’, ‘csr’}, optional) Sparse format of the returned operator.

Returns¶

• scipy.sparse.csc_array or scipy.sparse.csr_array Divergence operator.

View source on GitHub

construct_grad(shape, x_f, x_c = None, bc = (None, None), axis = 0, shapes_d = (None, None), format = 'csc')¶

Open dedicated reference page

Construct the full gradient operator including boundary contributions.

Parameters¶

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

• x_f (array_like) Face coordinates along axis.

• x_c (array_like, optional) Cell-center coordinates along axis. If omitted, they are generated as arithmetic midpoints.

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

• axis (int, optional) Differentiation axis.

• shapes_d (tuple[tuple | None, tuple | None], optional) Optional output shapes for inhomogeneous boundary source vectors.

• format ({‘csc’, ‘csr’}, optional) Sparse format used for returned operator matrices.

Returns¶

• tuple Without shapes_d: (grad_matrix, grad_bc). With shapes_d: (grad_matrix, grad_bc_left, grad_bc_right).

View source on GitHub

construct_grad_bc(shape, x_f, x_c = None, bc = (None, None), axis = 0, shapes_d = (None, None), format = 'csc')¶

Open dedicated reference page

Construct boundary-face gradient corrections and source terms.

Parameters¶

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

• x_f (array_like) Face coordinates along axis.

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

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

• axis (int, optional) Differentiation axis.

• shapes_d (tuple[tuple | None, tuple | None], optional) Optional source-vector shapes for left/right boundary contributions.

• format ({‘csc’, ‘csr’}, optional) Sparse format for returned operator matrices.

Returns¶

• tuple (grad_matrix_bc, grad_bc) when shapes_d is not supplied, or (grad_matrix_left, grad_bc_left, grad_matrix_right, grad_bc_right) otherwise.

View source on GitHub

construct_grad_int(shape, x_f, x_c = None, axis = 0, format = 'csc')¶

Open dedicated reference page

Construct the interior-face gradient operator.

Parameters¶

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

• x_f (array_like) Face coordinates along axis.

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

• axis (int, optional) Differentiation axis.

• format ({‘csc’, ‘csr’}, optional) Output sparse format.

Returns¶

• scipy.sparse.csc_array or scipy.sparse.csr_array Matrix that maps cell-centered values to face-normal gradients.

View source on GitHub