pymrm.convect

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Convective-flux operators and TVD limiter functions.

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Public API¶

clam(normalized_c_c, normalized_x_c, normalized_x_d)¶

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Compute the CLAM TVD correction in normalized-variable space.

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construct_convflux_bc(shape, x_f, x_c = None, bc = (None, None), v = 1.0, axis = 0, shapes_d = (None, None), format = 'csc')¶

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Construct boundary-face upwind 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 for a * dc/dn + b * c = d with n the outward normal; {"outflow": True} marks a pure-outflow boundary.

• v (float or array_like, optional) Face velocity field.

• axis (int, optional) Convection axis.

• shapes_d (tuple[tuple | None, tuple | None], optional) Optional source-vector shapes for inhomogeneous boundary terms; d is then a coefficient on the external vector.

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

Returns¶

• tuple (conv_matrix_bc, conv_bc) when shapes_d is not supplied, or (conv_matrix_left, conv_bc_left, conv_matrix_right, conv_bc_right) otherwise.

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construct_convflux_upwind(shape, x_f, x_c = None, bc = (None, None), v = 1.0, axis = 0, shapes_d = (None, None), format = 'csc')¶

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Construct a first-order upwind convective-flux operator.

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. If omitted, arithmetic midpoints are used.

• bc (tuple[dict | None, dict | None], optional) Left and right boundary-condition dictionaries with keys a, b, and d for a * dc/dn + b * c = d with n the outward normal (at the left end dc/dn = -dc/dx). {"outflow": True} marks a pure-outflow boundary: the face value is the adjacent cell value (a stirred volume’s exit). It is meant for faces where material leaves; if flow enters there, the face still carries the adjacent cell value.

• v (float or array_like, optional) Face velocity field. Scalars and broadcastable arrays are accepted.

• axis (int, optional) Convection axis.

• shapes_d (tuple[tuple | None, tuple | None], optional) Optional source-vector shapes for boundary inhomogeneities. With shapes_d the dictionary’s d is a coefficient on that external vector (use d = 1 to pass the values through the vector).

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

Returns¶

• tuple Without shapes_d: (conv_matrix, conv_bc). With shapes_d: (conv_matrix, conv_bc_left, conv_bc_right).

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construct_convflux_upwind_int(shape, v = 1.0, axis = 0, format = 'csc')¶

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Construct the internal-face upwind advection operator.

Parameters¶

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

• v (float or array_like, optional) Face velocity field.

• axis (int, optional) Convection axis.

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

Returns¶

• scipy.sparse.csc_array or scipy.sparse.csr_array Sparse matrix mapping cell-centered values to interior face fluxes.

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minmod(normalized_c_c, normalized_x_c, normalized_x_d)¶

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Compute the Minmod TVD correction in normalized-variable space.

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muscl(normalized_c_c, normalized_x_c, normalized_x_d)¶

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Compute the MUSCL TVD correction in normalized-variable space.

Uniform grid: 2 c_c up to 1/4, c_c + 1/4 up to 3/4, then 1.

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osher(normalized_c_c, normalized_x_c, normalized_x_d)¶

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Compute the Osher TVD correction in normalized-variable space.

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smart(normalized_c_c, normalized_x_c, normalized_x_d)¶

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Compute the SMART TVD correction in normalized-variable space.

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stoic(normalized_c_c, normalized_x_c, normalized_x_d)¶

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Compute the STOIC TVD correction in normalized-variable space.

Piecewise: the SMART line c_f = k c_c up to its intersection with the central-difference line, then central differencing up to c_c = x_c, then QUICK, then c_f = 1. On a uniform grid (x_c = 1/2, x_d = 3/4) this is 3 c_c, (1 + c_c)/2, 3/8 + 3 c_c/4 and 1, with breaks at 1/5, 1/2 and 5/6.

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upwind(normalized_c_c, normalized_x_c, normalized_x_d)¶

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Return zero correction (first-order upwind limiter).

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vanleer(normalized_c_c, normalized_x_c, normalized_x_d)¶

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Compute the van-Leer TVD correction in normalized-variable space.

The curve is the parabola through (0, 0), (x_c, x_d) and (1, 1). It rises above c_f = 1 when x_d - x_c > x_c (1 - x_c), for example next to a boundary where the upstream point is a face half a cell away (x_c = 1/3, x_d = 2/3); the correction is capped at 1 - c_c to stay bounded. The cap acts only above c_c = x_c and does not reduce the order.

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