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
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)