def _dh(h):
lo, hi = h.limits()
dh = Array(lo, hi - 1)
for i in range(lo, hi):
dh.set(i, h.get(i + 1) - h.get(i))
return dh
def new_h(self, h_0):
n_cells = h_0.shape[0]
n_ghost = self._n_ghost
h = Array(1 - n_ghost, n_cells + n_ghost)
for i in range(n_cells):
h.set(i + 1, h_0[i])
return h
def _phi(self, theta):
phi = Array.empty_like(theta)
lo, hi = theta.limits()
for i in range(lo, hi + 1):
theta_mid = theta.get(i)
r = (1 + theta_mid) / 2
phi.set(i, max(0, min(r, 2, 2 * theta_mid)))
return phi
def _flux_lim(self, s, dh, dt, dx):
theta = self._theta(dh, s)
phi = self._phi(theta)
lo, hi = phi.limits()
lim_flux = Array.empty_like(phi)
for i in range(lo, hi + 1):
lim_wave = dh.get(i) * phi.get(i)
abs_s = abs(s.get(i))
lim_flux.set(i, 0.5 * abs_s * (1 - dt / dx * abs_s) * lim_wave)
return lim_flux
def _theta(self, dh, s):
lo, hi = dh.limits()
theta = Array(lo + 1, hi - 1)
for i in range(lo + 1, hi):
dh_mid = dh.get(i)
if dh_mid == 0:
theta.set(i, 0)
continue
dh_left = dh.get(i - 1)
dh_right = dh.get(i + 1)
s_mid = s.get(i)
if s_mid > 0:
theta.set(i, dh_left / dh_mid)
elif s_mid < 0:
theta.set(i, dh_right / dh_mid)
return theta
def new_s(self, h):
lo, hi = h.limits()
s = Array(lo, hi - 1)
return s
def new_f_x(self, h):
lo, hi = h.limits()
return Array(lo + self._n_ghost, hi - self._n_ghost)