def _compute_finite_vortex_deriv2(r1, r2, r2_deriv): r1_norm = add_ones_axis(compute_norm(r1)) r2_norm = add_ones_axis(compute_norm(r2)) r2_norm_deriv = compute_norm_deriv(r2, r2_deriv) r1_x_r2 = add_ones_axis(compute_cross(r1, r2)) r1_d_r2 = add_ones_axis(compute_dot(r1, r2)) r1_x_r2_deriv = compute_cross_deriv2(r1, r2_deriv) r1_d_r2_deriv = compute_dot_deriv(r1, r2_deriv) num = (1. / r1_norm + 1. / r2_norm) * r1_x_r2 num_deriv = (-r2_norm_deriv / r2_norm ** 2) * r1_x_r2 \ + (1. / r1_norm + 1. / r2_norm) * r1_x_r2_deriv den = r1_norm * r2_norm + r1_d_r2 den_deriv = r1_norm * r2_norm_deriv + r1_d_r2_deriv result = np.divide( num_deriv * den - num * den_deriv, den ** 2 * 4 * np.pi, out=np.zeros_like(num), where=np.abs(den)>tol ) return result
def _compute_semi_infinite_vortex(u, r): r_norm = compute_norm(r) u_x_r = compute_cross(u, r) u_d_r = compute_dot(u, r) num = u_x_r den = r_norm * (r_norm - u_d_r) return num / den / 4 / np.pi
def _compute_semi_infinite_vortex(u, r): r_norm = compute_norm(r) u_x_r = compute_cross(u, r) u_d_r = compute_dot(u, r) num = u_x_r den = r_norm * (r_norm - u_d_r) return num / den / 4 / np.pi
def _compute_finite_vortex(r1, r2): r1_norm = compute_norm(r1) r2_norm = compute_norm(r2) r1_x_r2 = compute_cross(r1, r2) r1_d_r2 = compute_dot(r1, r2) num = (1. / r1_norm + 1. / r2_norm) * r1_x_r2 den = r1_norm * r2_norm + r1_d_r2 result = num / den / 4 / np.pi result[np.abs(den) < tol] = 0. return result
def _compute_finite_vortex(r1, r2): r1_norm = compute_norm(r1) r2_norm = compute_norm(r2) r1_x_r2 = compute_cross(r1, r2) r1_d_r2 = compute_dot(r1, r2) num = (1. / r1_norm + 1. / r2_norm) * r1_x_r2 den = r1_norm * r2_norm + r1_d_r2 result = np.divide(num, den * 4 * np.pi, out=np.zeros_like(num), where=np.abs(den)>tol) return result
def _compute_finite_vortex(r1, r2): r1_norm = compute_norm(r1) r2_norm = compute_norm(r2) r1_x_r2 = compute_cross(r1, r2) r1_d_r2 = compute_dot(r1, r2) num = (1. / r1_norm + 1. / r2_norm) * r1_x_r2 den = r1_norm * r2_norm + r1_d_r2 result = num / den / 4 / np.pi result[np.abs(den) < tol] = 0. return result
def _compute_semi_infinite_vortex_deriv(u, r, r_deriv): r_norm = add_ones_axis(compute_norm(r)) r_norm_deriv = compute_norm_deriv(r, r_deriv) u_x_r = add_ones_axis(compute_cross(u, r)) u_x_r_deriv = compute_cross_deriv2(u, r_deriv) u_d_r = add_ones_axis(compute_dot(u, r)) u_d_r_deriv = compute_dot_deriv(u, r_deriv) num = u_x_r num_deriv = u_x_r_deriv den = r_norm * (r_norm - u_d_r) den_deriv = r_norm_deriv * (r_norm - u_d_r) + r_norm * (r_norm_deriv - u_d_r_deriv) return (num_deriv * den - num * den_deriv) / den ** 2 / 4 / np.pi
def _compute_semi_infinite_vortex_deriv(u, r, r_deriv): r_norm = add_ones_axis(compute_norm(r)) r_norm_deriv = compute_norm_deriv(r, r_deriv) u_x_r = add_ones_axis(compute_cross(u, r)) u_x_r_deriv = compute_cross_deriv2(u, r_deriv) u_d_r = add_ones_axis(compute_dot(u, r)) u_d_r_deriv = compute_dot_deriv(u, r_deriv) num = u_x_r num_deriv = u_x_r_deriv den = r_norm * (r_norm - u_d_r) den_deriv = r_norm_deriv * (r_norm - u_d_r) + r_norm * (r_norm_deriv - u_d_r_deriv) return (num_deriv * den - num * den_deriv) / den ** 2 / 4 / np.pi
def _compute_finite_vortex_deriv2(r1, r2, r2_deriv): r1_norm = add_ones_axis(compute_norm(r1)) r2_norm = add_ones_axis(compute_norm(r2)) r2_norm_deriv = compute_norm_deriv(r2, r2_deriv) r1_x_r2 = add_ones_axis(compute_cross(r1, r2)) r1_d_r2 = add_ones_axis(compute_dot(r1, r2)) r1_x_r2_deriv = compute_cross_deriv2(r1, r2_deriv) r1_d_r2_deriv = compute_dot_deriv(r1, r2_deriv) num = (1. / r1_norm + 1. / r2_norm) * r1_x_r2 num_deriv = (-r2_norm_deriv / r2_norm ** 2) * r1_x_r2 \ + (1. / r1_norm + 1. / r2_norm) * r1_x_r2_deriv den = r1_norm * r2_norm + r1_d_r2 den_deriv = r1_norm * r2_norm_deriv + r1_d_r2_deriv result = (num_deriv * den - num * den_deriv) / den**2 / 4 / np.pi result[np.abs(den) < tol] = 0. return result
def _compute_finite_vortex_deriv2(r1, r2, r2_deriv): r1_norm = add_ones_axis(compute_norm(r1)) r2_norm = add_ones_axis(compute_norm(r2)) r2_norm_deriv = compute_norm_deriv(r2, r2_deriv) r1_x_r2 = add_ones_axis(compute_cross(r1, r2)) r1_d_r2 = add_ones_axis(compute_dot(r1, r2)) r1_x_r2_deriv = compute_cross_deriv2(r1, r2_deriv) r1_d_r2_deriv = compute_dot_deriv(r1, r2_deriv) num = (1. / r1_norm + 1. / r2_norm) * r1_x_r2 num_deriv = (-r2_norm_deriv / r2_norm ** 2) * r1_x_r2 \ + (1. / r1_norm + 1. / r2_norm) * r1_x_r2_deriv den = r1_norm * r2_norm + r1_d_r2 den_deriv = r1_norm * r2_norm_deriv + r1_d_r2_deriv result = (num_deriv * den - num * den_deriv) / den ** 2 / 4 / np.pi result[np.abs(den) < tol] = 0. return result