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()
def diffusion_step(vort_list, nu, dt):
for j in range(len(vort_list)):
if abs(vort_list[j].strg) > 0.01:
n = int(abs(vort_list[j].strg) / 0.01)
vort_list[j].strg = np.sign(vort_list[j].strg) * 0.01 # + zeta[0]
temp = [
vort_list.append(
VPM.vortex(vort_list[j].pos, vort_list[j].strg,
vort_list[j].delta)) for i in range(n - 1)
]
zetax, zetay = nmdist([0, 0], [[2 * nu * dt, 0], [0, 2 * nu * dt]],
len(vort_list)).T
zeta = zetax + 1j * zetay
for i in range(len(vort_list)):
vort_list[i].pos += zeta[i]
return ret[n - 1:] / n def accelometer(SimulationData_pos,SimulationData_strg): tsteps = len(SimulationData_pos)-1 Xforce = [] Xmom = np.array([np.sum(np.array(SimulationData_pos[i+1]).real*np.array(SimulationData_strg[i+1])) for i in range(tsteps)]) Xforce = [(-(Xmom[i] - Xmom[i-1])/0.1) for i in range(1,len(Xmom))] Cd = np.array(Xforce)/(0.5*1*2) return Cd if __name__ == "__main__": body_list = [] body_list.append(VPM.sld_bd(ctr_circ_vert(0j,1,50),1,0j)) # body_list.append(VPM.sld_bd(ctr_circ_vert(3j,1,50),1,3j)) # body_list.append(VPM.sld_bd(ctr_circ_vert(3+0j,1,50),1,3+0j)) Vinf = 1+0j vort_pos = np.array([-2]*100) + 1j*np.linspace(-4,4,100) vort_list = [] #[VPM.vortex(1j,0,0.005)] # for i in range(len(vort_pos)): # #print(vort_pos[i]) # vort_list.append(VPM.vortex(vort_pos[i],0.0,0.005)) post,circt,t,vort_list = itg.simulate(body_list,Vinf,vort_list,0.002,2,0.1) # plotting_ParticlesPath(post,1)
def read_file(path):
return VPM.read_file(path)
def write_file(path, data):
VPM.write_file(path, data)
def simulate(sld_bodies, free_stream, vort_elems, nu, final_time, time_step):
t = np.linspace(0, final_time, (final_time / time_step) + 1)
position_t = []
position_t.append(
[cp.copy(vort_elems[j].pos) for j in range(len(vort_elems))])
circulation_t = []
circulation_t.append(
[cp.copy(vort_elems[j].strg) for j in range(len(vort_elems))])
vort_elems.append(VPM.vortex(0j, 0.0, 0.1))
A = VPM.get_coefficient_mat(sld_bodies)
b = VPM.get_rhs(sld_bodies, free_stream, vort_elems)
gamma = cp.copy(VPM.solve_gamma(sld_bodies, A, b))
new_blobs = VPM.slip_nullify(sld_bodies, vort_elems)
rk2_step(sld_bodies, free_stream, vort_elems, time_step)
len(vort_elems)
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
vort_elems.pop(-1)
for i in range(len(t)):
# print(i)
[vort_elems.append(new_blobs[i]) for i in range(len(new_blobs))]
diffusion_step(vort_elems, nu, time_step)
VPM.depenetrator(sld_bodies, vort_elems)
position_t.append(
[cp.copy(vort_elems[j].pos) for j in range(len(vort_elems))])
circulation_t.append(
[cp.copy(vort_elems[j].strg) for j in range(len(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)
new_blobs = VPM.slip_nullify(sld_bodies, vort_elems)
rk2_step(sld_bodies, free_stream, vort_elems, time_step)
len(vort_elems)
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
return position_t, circulation_t, t, vort_elems
