Added 2D source elements and a comparison to thin 3D rectangles.

numerical/models/rectangle/rectangle_2d_vs_3d.py

+import matplotlib.pyplot as plt
+import matplotlib as mpl
+import numpy as np
+import math
+
+import numerical.bem as bem
+import numerical.util.gen_utils as gen
+import numerical.potential_flow.element_utils as eu
+from numerical.potential_flow.elements import Source3D, Source2D
+
+
+def get_rectangle_jet_vel_2d(x, z, length, k=25, m_0=1):
+    elements = []
+    for i in range(-k, k + 1):
+        s_x = i * length + x + (2 * x - length) * ((-1) ** i - 1) / 2
+        if i != 0:
+            elements.append(Source2D(s_x, z, -m_0))
+        elements.append(Source2D(s_x, -z, -m_0))
+    return eu.get_all_vel(elements, x, z)
+
+
+def get_rectangle_jet_vel_3d(x, y, z, length, height, k=100, m_0=1):
+    elements = []
+    for i in range(-k, k + 1):
+        for j in range(-k, k + 1):
+            s_x = i * length + x + (2 * x - length) * ((-1) ** i - 1) / 2
+            s_y = j * height + y + (2 * y - height) * ((-1) ** j - 1) / 2
+            if not (i == 0 and j == 0):
+                elements.append(Source3D(s_x, s_y, z, -m_0))
+            elements.append(Source3D(s_x, s_y, -z, -m_0))
+    return eu.get_all_vel_3d(elements, x, y, z)
+
+
+length = 2
+hs = np.linspace(0.1, 2, 5)
+theta_j_lists = []
+theta_bs = np.linspace(0.01, np.pi / 2)
+dist = 1
+for h in hs:
+    print(h)
+    angles = []
+    residuals = []
+    for theta_b in theta_bs:
+        x_b = dist * np.cos(theta_b)
+        z_b = dist * np.sin(theta_b)
+        vel = get_rectangle_jet_vel_3d(x_b, h / 2, z_b, length, h, k=int(round(50 / np.sqrt(h))))
+        residuals.append(abs(vel[1]))
+        angle = np.arctan2(vel[2], vel[0]) + np.pi / 2
+        angles.append(angle)
+    theta_j_lists.append(angles)
+    print(f"res = {np.mean(residuals)}")
+
+theta_js_2d = []
+for theta_b in theta_bs:
+    x_b = dist * np.cos(theta_b)
+    z_b = dist * np.sin(theta_b)
+    vel_2d = get_rectangle_jet_vel_2d(x_b, z_b, length)
+    angle_2d = np.arctan2(vel_2d[1], vel_2d[0]) + np.pi / 2
+    theta_js_2d.append(angle_2d)
+
+cmap = plt.cm.get_cmap()
+for h, theta_js in zip(hs, theta_j_lists):
+    plt.plot(theta_bs, theta_js, label=f"h = {h:.2f}", color=cmap(h / max(hs)))
+plt.plot(theta_bs, theta_js_2d, label="2D", color="red")
+plt.xlabel("$\\theta_b$")
+plt.ylabel("$\\theta_j$")
+plt.legend()
+plt.show()

numerical/potential_flow/elements.py

@@ -81,6 +81,21 @@ class Source(Element):
             return self.mag * (y - self.y_0) / (4 * math.pi * ((x - self.x_0) ** 2 + (y - self.y_0) ** 2) ** (3 / 2))
 
 
+class Source2D(Element):
+    mag = None
+
+    def __init__(self, x, y, magnitude):
+        self.x_0 = x
+        self.y_0 = y
+        self.mag = float(magnitude)
+
+    def get_vel_x(self, x, y, _):
+        return self.mag * (x - self.x_0) / (4 * math.pi * ((x - self.x_0) ** 2 + (y - self.y_0) ** 2))
+
+    def get_vel_y(self, x, y, _):
+        return self.mag * (y - self.y_0) / (4 * math.pi * ((x - self.x_0) ** 2 + (y - self.y_0) ** 2))
+
+
 class Source3D(Element3D):
     x_0 = None
     y_0 = None