t = 0
dt = dt_lagrangian
x_tracers = []
y_tracers = []
while t < max_time - 1e-10:
# get the velocity fields at this time
u = EmbeddedFunction(ebdyc)
u.define_via_function(lambda x, y: u_function(x, y, t))
v = EmbeddedFunction(ebdyc)
v.define_via_function(lambda x, y: v_function(x, y, t))
# get the velocity fields on the boundary
ub = ebdyc.interpolate_radial_to_boundary(u).bdy_value_list[0]
vb = ebdyc.interpolate_radial_to_boundary(v).bdy_value_list[0]
# step of the first order method to get things started
if t == 0:
bx = ebdy.bdy.x + dt * ub
by = ebdy.bdy.y + dt * vb
bx, by, new_t = arc_length_parameterize(bx, by, return_t=True)
bu_interp = interp1d(0, 2 * np.pi, bdy.dt, ub, p=True)
bv_interp = interp1d(0, 2 * np.pi, bdy.dt, vb, p=True)
# old boundary velocity values have to be in the correct place
ubo_new_parm = bu_interp(new_t)
vbo_new_parm = bv_interp(new_t)
ubo = ub.copy()
c = c0.copy()
t = 0
while t < max_time - 1e-10:
st = time.time()
# get the velocity fields
u = EmbeddedFunction(ebdyc)
u.define_via_function(lambda x, y: u_function(x, y, t))
v = EmbeddedFunction(ebdyc)
v.define_via_function(lambda x, y: v_function(x, y, t))
print('Time to compute u: {:0.1f}'.format(
(time.time() - st) * 1000))
st = time.time()
# get the velocity fields on the boundary
ub = ebdyc.interpolate_radial_to_boundary(u)
vb = ebdyc.interpolate_radial_to_boundary(v)
print('Time to interp u to bdy: {:0.1f}'.format(
(time.time() - st) * 1000))
st = time.time()
# first, move the boundary with the fluid velocity
bx = ebdy.bdy.x + dt * ub.bdy_value_list[0]
by = ebdy.bdy.y + dt * vb.bdy_value_list[0]
print('Time to move bdy: {:0.1f}'.format(
(time.time() - st) * 1000))
st = time.time()
# take gradients of the velocity fields
dx = lambda f: fd_x_4(f, grid.xh, periodic_fix=True)
dy = lambda f: fd_y_4(f, grid.yh, periodic_fix=True)