def rk2_step(sld_bodies, free_stream, vort_elems, dt):
k1 = np.zeros((len(vort_elems), 1), dtype=complex)
pos, strg, delta = np.array([
vort_elems[i].pos for i in range(len(vort_elems))
]), np.array([vort_elems[i].strg
for i in range(len(vort_elems))]), vort_elems[0].delta
poscp = [vort_elems[i].poscp for i in range(len(vort_elems))]
k1[:] += [
VPM.vel_body(sld_bodies, vort_elems[i].pos)
for i in range(len(vort_elems))
]
for i in range(len(vort_elems)):
k1[i] += free_stream
k1[:, 0] += vel_vort(pos, pos, strg, delta)
for i in range(len(vort_elems)):
vort_elems[i].pos += 0.5 * k1[i][0] * dt
for body in sld_bodies:
body.move_body(0.5 * dt)
VPM.depenetrator(sld_bodies, vort_elems)
A = VPM.get_coefficient_mat(sld_bodies)
b = VPM.get_rhs(sld_bodies, free_stream, vort_elems)
gamma = VPM.solve_gamma(sld_bodies, A, b)
k2 = np.zeros((len(vort_elems), 1), dtype=complex)
pos, strg, delta = np.array([
vort_elems[i].pos for i in range(len(vort_elems))
]), np.array([vort_elems[i].strg
for i in range(len(vort_elems))]), vort_elems[0].delta
poscp = [vort_elems[i].poscp for i in range(len(vort_elems))]
k2[:] += [
VPM.vel_body(sld_bodies, vort_elems[i].pos)
for i in range(len(vort_elems))
]
for i in range(len(vort_elems)):
k2[i] += free_stream
k2[:, 0] += vel_vort(pos, pos, strg, delta)
for i in range(len(vort_elems)):
vort_elems[i].poscp += k2[i][0] * dt
vort_elems[i].pos = cp.copy(vort_elems[i].poscp)
for body in sld_bodies:
body.move_body(0.5 * dt)
VPM.depenetrator(sld_bodies, vort_elems)
def plot_velfield(grid,SimulationData_pos,SimulationData_strg,body,fignum,Vinf=1+0j):
x,y = grid
z = x + 1j*y
vel = np.zeros_like(z,dtype = complex)
# print(np.shape(vel))
for i in range(np.shape(vel)[1]):
vel[i] = np.array([VPM.vel_body([body],z[i][j]) for j in range(np.shape(vel)[0])])[0] + Vinf
vel[i] += itg.vel_vort(z[i].copy(),SimulationData_pos.copy(),SimulationData_strg.copy(),body.get_pnl_len()[0]/np.pi)
plt.figure(fignum)
plt.quiver(x,y,vel.real,vel.imag,scale = 75.0)
plt.plot(body.get_vert().real,body.get_vert().imag,'b')
plt.gca().set_aspect('equal',adjustable='box')
plt.show()