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)
# let's get the points that need to be interpolated to
gp = new_ebdyc.grid_phys
ap = new_ebdyc.radial_pts
aax = np.concatenate([gp.x, ap.x])
aay = np.concatenate([gp.y, ap.y])
aap = PointSet(x=aax, y=aay)
AP_key = ebdy.register_points(aap.x, aap.y)
# now we need to interpolate onto things
AEP = ebdy.registered_partitions[AP_key]
# generate a holding ground for the new c
c_new = EmbeddedFunction(new_ebdyc)
c_new.zero()
# get departure points
xd_all = np.zeros(aap.N)
yd_all = np.zeros(aap.N)
# advect those in the annulus
c1, c2, c3 = AEP.get_categories()
c1n, c2n, c3n = AEP.get_category_Ns()
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)
# let's get the points that need to be interpolated to
gp = new_ebdyc.grid_pna
ap = new_ebdyc.radial_pts
aax = np.concatenate([gp.x, ap.x])
aay = np.concatenate([gp.y, ap.y])
aap = PointSet(x=aax, y=aay)
AP_key = ebdy.register_points(aap.x, aap.y)
# now we need to interpolate onto things
AEP = ebdy.registered_partitions[AP_key]
# generate a holding ground for the new c
c_new = EmbeddedFunction(new_ebdyc)
c_new.zero()
# get departure points
xd_all = np.zeros(aap.N)
yd_all = np.zeros(aap.N)
# advect those in the annulus
c1, c2, c3 = AEP.get_categories()
c1n, c2n, c3n = AEP.get_category_Ns()
xn = gx.copy()
yn = gy.copy()
resx, resy = objective_function(xn, yn)
res = np.hypot(resx, resy).max()
tol = 1e-12
i = 0
print('\nInverting departure point system')
while res > tol:
Jxx, Jxy, Jyx, Jyy = Jacobian(xn, yn)
det = Jxx*Jyy - Jxy*Jyx
idet = 1.0/det
dx = -idet*(Jyy*resx - Jyx*resy)
dy = -idet*(-Jxy*resx + Jxx*resy)
xn = xn + dx
yn = yn + dy
ebdy.register_points(xn, yn, nearly_radial=True)
# xn += dx
# yn += dy
resx, resy = objective_function(xn, yn)
res = np.hypot(resx, resy).max()
i += 1
print(i, '{:0.1e}'.format(res))
cu2 = ebdy.interpolate_radial_to_points(c, xn, yn)
time_departure = time.time()-st
### linearized departure based semi-lagrangian advector
st = time.time()
# get departure points
nt = np.prod(xr.shape)
SLM = np.zeros([nt,] + [2,2], dtype=float)
SLR = np.zeros([nt,] + [2,], dtype=float)
])
new_ebdyc.register_grid(grid)
print('Time to generate new ebdy and register grid: {:0.1f}'.format(
(time.time() - st) * 1000))
st = time.time()
# let's get the points that need to be interpolated to
gp = new_ebdyc.grid_pna
ap = new_ebdyc.radial_pts
from pybie2d.point_set import PointSet
aax = np.concatenate([gp.x, ap.x])
aay = np.concatenate([gp.y, ap.y])
aap = PointSet(x=aax, y=aay)
AP_key = ebdy.register_points(aap.x, aap.y)
print('Time to register new points with old ebdy |A: {:0.1f}'.format(
(time.time() - st) * 1000))
st = time.time()
# register these with ebdy
gp_key = ebdy.register_points(gp.x, gp.y)
print('Time to register new points with old ebdy |g: {:0.1f}'.format(
(time.time() - st) * 1000))
st = time.time()
ap_key = ebdy.register_points(ap.x, ap.y, nearly_radial=True)
print('Time to register new points with old ebdy |a: {:0.1f}'.format(
(time.time() - st) * 1000))
st = time.time()
# now we need to interpolate onto things
coordinate_tolerance=1e-12)
new_ebdyc = EmbeddedBoundaryCollection([
new_ebdy,
])
umax = np.sqrt((u * u + v * v).data, where=np.logical_not(u.mask)).max()
new_ebdyc.register_grid(grid, danger_zone_distance=2 * umax * dt)
# let's get the points that need to be interpolated to
gp = new_ebdyc.grid_pna
ap = new_ebdyc.radial_pts
aax = np.concatenate([gp.x, ap.x])
aay = np.concatenate([gp.y, ap.y])
aap = PointSet(x=aax, y=aay)
AP_key = ebdy.register_points(aap.x,
aap.y,
danger_zone=new_ebdy.in_danger_zone,
gi=new_ebdy.guess_inds)
# now we need to interpolate onto things
AEP = ebdy.registered_partitions[AP_key]
# generate a holding ground for the new c
c_new = EmbeddedFunction(new_ebdyc)
c_new.zero()
# get departure points
xd_all = np.zeros(aap.N)
yd_all = np.zeros(aap.N)
# advect those in the annulus
c1, c2, c3 = AEP.get_categories()
qfs_fsuf=qfs_fsuf,
coordinate_scheme=coordinate_scheme,
coordinate_tolerance=1e-8)
new_ebdyc = EmbeddedBoundaryCollection([
new_ebdy,
])
new_ebdyc.register_grid(grid)
# let's get the points that need to be interpolated to
gp = new_ebdyc.grid_pna
ap = new_ebdyc.radial_pts
aax = np.concatenate([gp.x, ap.x])
aay = np.concatenate([gp.y, ap.y])
aap = PointSet(x=aax, y=aay)
AP_key = ebdy.register_points(aap.x, aap.y)
# now we need to interpolate onto things
AEP = ebdy.registered_partitions[AP_key]
# generate a holding ground for the new c
c_new = EmbeddedFunction(new_ebdyc)
c_new.zero()
# advect those in the annulus
c1, c2, c3 = AEP.get_categories()
c1n, c2n, c3n = AEP.get_category_Ns()
c12 = np.logical_or(c1, c2)
# category 1 and 2 (use Eulerian scheme)
cx, cy = ebdyc.gradient2(c)
ecnew = c - dt * (u * cx + v * cy) - dt * scaled_nonlinearity(c)