def smooth_rc_old(dx, dy, nu, dt, riv_i, riv_j, n):
# elevation change along river course due to diffusional smoothing
for c in xrange(1, len(riv_i) - 1):
n_prev = n[riv_i[c - 1], riv_j[c - 1]]
n_cur = n[riv_i[c], riv_j[c]]
n_next = n[riv_i[c + 1], riv_j[c + 1]]
dwnst_dx, upst_dx = dx, dx
if is_diagonal_neighbor((riv_i[c], riv_j[c]), (riv_i[c + 1], riv_j[c + 1])):
dwnst_dx *= np.sqrt(2.)
if is_diagonal_neighbor((riv_i[c], riv_j[c]), (riv_i[c - 1], riv_j[c - 1])):
upst_dx *= np.sqrt(2.)
dwnst_dn = (n_next - n_cur) / dwnst_dx
upst_dn = (n_cur - n_prev) / upst_dx
mean_dx = (dwnst_dx + upst_dx) * .5
# NOTE: This is the old way but, I think, is incorrect. For
# non-uniform spacing of points you need to divide by the mean spacing.
#dn_rc = (nu * dt) / (dx ** 2.) * (dwnst_dn - upst_dn)
# This properly solves the second derivative with unequal spacing in x.
dn_rc = (nu / dx * dt) * (dwnst_dn - upst_dn) / mean_dx
n[riv_i[c], riv_j[c]] += dn_rc
return n
def calc_qs(nu, riv_i, riv_j, n, dx, dy, dt):
sed_flux = 0
dist = 0
if is_diagonal_neighbor((riv_i[-1], riv_j[-1]), (riv_i[-2], riv_j[-2])):
dist = np.sqrt(2.)
else:
dist = 1.
sed_flux = - (nu * dt) * ((n[riv_i[-1], riv_j[-1]] -
n[riv_i[-2], riv_j[-2]]) / dist)
return sed_flux