fullseye

potential_flow_joukowski — MATH `complex` op

データ種: なし → cimage(引数だけで決まる op —— 画像やデータの入力を取らない)
呼び出し: import fullseye as fs; fs.ledger.potential_flow_joukowski(alpha_deg=5.0, speed=1.0, chord_b=1.0, centre_offset=(-0.09+0.09j), centre=0j, half_width=3.0, shape=(256, 256)) (実装を直接呼ぶなら import mathops; mathops.potential_flow_joukowski(alpha_deg=5.0, speed=1.0, chord_b=1.0, centre_offset=(-0.09+0.09j), centre=0j, half_width=3.0, shape=(256, 256))、台帳から引くなら opsmath.get("potential_flow_joukowski"))

使い方

Inviscid flow past a Joukowski aerofoil, as a complex velocity field.

Returns the complex velocity w(z) = dW/dz = u - i*v sampled over a window of the physical plane. Inside the solid body the field is set to exactly 0 (there is no flow there), so field == 0 is the body mask and nothing is silently nan.

The construction is the classical one: flow past a circle of radius a = |chord_b - centre_offset| centred at centre_offset, plus the circulation the Kutta condition demands, pushed through the Joukowski map z = zeta + chord_b**2 / zeta. The window is inverted back to the circle plane by choosing, of the two preimages, the one outside the circle.

★What makes this checkable rather than merely plotted:

The field is holomorphic outside the body, so this family’s own cplx_cr_residual must read ~0 on it — an existing operator is the oracle, and it is not the formula used to build the field.
The Kutta condition is the whole point: dW/dzeta vanishes at the trailing edge exactly where dz/dzeta does, so the velocity there stays finite. Perturb the circulation by any amount and the trailing-edge velocity diverges — the gate has a control group.
Re(closed integral of w dz) around the body is the circulation, and it is path independent (Cauchy) — a big rectangle and a small one must agree.
Far from the body w -> speed * exp(-i*alpha), decaying like 1/|z|.
The zeroed region is the aerofoil, whose area the shoelace formula on cplx_joukowski of the circle gives independently.

Parameters

alpha_deg : float Angle of attack in degrees. speed : float > 0 Free-stream speed. chord_b : float > 0 Half the flat-plate chord; the map is zeta + chord_b**2/zeta. centre_offset : complex Circle centre. Negative real part thickens, positive imaginary part cambers. The default is a thin cambered section. centre, half_width, shape : The window in the physical plane, as in :func:cplx_plane_grid.

Raises ValueError: speed <= 0; non-finite angle; a circle that does not enclose -chord_b (the image would fold over itself) or whose centre is at or beyond +chord_b; degenerate window.

HALCON: no operator.

ファミリ共通の入力契約(fail-closed)

mathops の全 op は入力を検証してから計算する(黙って通さない):

complex 入力は ValueError — float64 への強制変換は虚部を黙って捨てる(numpy は ComplexWarning だけ出して「もっともらしく間違った」実数を返す)。.real/.imag/abs() を明示するか、複素対応の complexops を使う。
masked array(masked 要素あり)は ValueError — マスクを剥がして下の生値を使う暗黙変換を拒否。埋める/落とすを明示する。
NaN/Inf は全入力で ValueError(件数を明示して拒否 — 結果全体に伝播するため)。
形状は厳格: 1-D と 2-D を暗黙昇格・ブロードキャストしない(vector 枠に matrix、matrix 枠に vector は ValueError。reshape を明示する)。
サイズ上限: 行列を取る op と stat_histogram の bins は mathops.MAX_ELEMENTS(2^26 ≈ 6700 万要素)超で ValueError。

詳しい使い方ガイド

math_metrology ファミリガイド

参考(サンプルデータ・文献)

サンプルデータカタログ(DL URL / ライセンス) — 2-D は skimage.data(BSD/public)+ 合成、3-D は実データ源(Stanford/PDS 等)の DL URL。
演算子の来歴・参考文献 — この op 族の元になった研究/手法の出典。
アルゴリズムの正典(著者・年)と用途は上記ファミリ使い方ガイドに記載。

実行できる例(この op を実際に呼ぶ検証済みサンプル)

poc_complex_plane_fields — py -3.11 examples/poc_complex_plane_fields.py

型が繋がる次の op(`cimage` を入力に取れる)

cplx_cr_residual · cplx_domain_colour · mandelbrot_interior

同カテゴリ(`complex`)

cplx_contour_circle · cplx_poly_eval · cplx_contour_integral · cplx_winding_number · cplx_cauchy_value · cplx_argument_principle · cplx_laurent_coeffs · cplx_joukowski

Provenance: mathops.py — MATH operator registry. この per-op ノートは tools/opdocs.py md が自動生成(手編集しない)。

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