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()
vbo = vb.copy()
x_tracers.append(bx)
y_tracers.append(by)
# 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)
if u_differentiation_type == 'spectral':
ux, uy = ebdyc.gradient2(u, xder, yder, cutoff=True)
vx, vy = ebdyc.gradient2(v, xder, yder, cutoff=True)
elif u_differentiation_type == 'fourth':
ux, uy = ebdyc.gradient2(u, dx, dy, cutoff=False)
vx, vy = ebdyc.gradient2(v, dx, dy, cutoff=False)
else:
ux = EmbeddedFunction(ebdyc)
uy = EmbeddedFunction(ebdyc)
vx = EmbeddedFunction(ebdyc)
vy = EmbeddedFunction(ebdyc)
ux.define_via_function(lambda x, y: ux_function(x, y, t))
uy.define_via_function(lambda x, y: uy_function(x, y, t))
vx.define_via_function(lambda x, y: vx_function(x, y, t))
vy.define_via_function(lambda x, y: vy_function(x, y, t))
# now generate a new ebdy based on the moved boundary
# move the boundary with Forward Euler
bx = ebdy.bdy.x + dt * ub
by = ebdy.bdy.y + dt * vb
# repararmetrize the boundary
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 interpolated to new parametrization
ubo_new_parm = bu_interp(new_t)
vbo_new_parm = bv_interp(new_t)
# old boundary velocity at old parametrization
ubo = ub.copy()
vbo = vb.copy()
# take gradients of the velocity fields
ux, uy = ebdyc.gradient2(u)
vx, vy = ebdyc.gradient2(v)
# now generate a new ebdy based on the moved boundary
new_bdy = GSB(x=bx, y=by)
bh = new_bdy.dt * new_bdy.speed.min()
# construct embedded boundary
new_ebdy = EmbeddedBoundary(new_bdy,
True,
M,
bh / radial_upsampling,
pad_zone=0,
heaviside=MOL.step,
qfs_fsuf=4,
coordinate_scheme='nufft',
coordinate_tolerance=1e-12)
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)
ux, uy = ebdyc.gradient2(u, dx, dy, cutoff=False)
vx, vy = ebdyc.gradient2(v, dx, dy, cutoff=False)
print('Time to compute u gradients: {:0.1f}'.format(
(time.time() - st) * 1000))
st = time.time()
# now generate a new ebdy based on the moved boundary
new_bdy = GSB(*arc_length_parameterize(bx, by))
bh = new_bdy.dt * new_bdy.speed.min()
# construct embedded boundary
new_ebdy = EmbeddedBoundary(new_bdy, True, M, bh, pad_zone, MOL.step)
new_ebdyc = EmbeddedBoundaryCollection([
new_ebdy,
])
new_ebdyc.register_grid(grid)
print('Time to generate new ebdy and register grid: {:0.1f}'.format(
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 interpolated to new parametrization
ubo_new_parm = bu_interp(new_t)
vbo_new_parm = bv_interp(new_t)
# old boundary velocity at old parametrization
ubo = ub.copy()
vbo = vb.copy()
# keep track of boundary motion
x_tracers.append(bx)
y_tracers.append(by)
# take gradients of the velocity fields
ux, uy = ebdyc.gradient2(u)
vx, vy = ebdyc.gradient2(v)
# now generate a new ebdy based on the moved boundary
new_bdy = GSB(x=bx, y=by)
bh = new_bdy.dt * new_bdy.speed.min()
# construct embedded boundary
new_ebdy = EmbeddedBoundary(new_bdy,
True,
M,
bh / radial_upsampling,
pad_zone=pad_zone,
heaviside=MOL.step,
qfs_fsuf=qfs_fsuf,
coordinate_scheme=coordinate_scheme,
coordinate_tolerance=1e-8)