def all_tau(self, x, m):
"""
All the 4 stabilization parameters
"""
u, p = dl.split(x)
h2 = h_u2(self.metric, u, self.reg_norm * self.nu * self.nu)
tau = [
self.tau(self.nu + self.nu_t(m), u, self.metric),
h2 * self._u_norm(u)
]
return tau
def tau(self, nu, u, metric):
"""
Stabilization parameter
"""
h2 = h_u2(self.metric, u, self.reg_norm * self.nu * self.nu)
Pe = dl.Constant(.5) * h_dot_u(metric, u,
self.reg_norm * self.nu * self.nu) / nu
num = dl.Constant(1.) + dl.exp(dl.Constant(-2.) * Pe)
den = dl.Constant(1.) - dl.exp(dl.Constant(-2.) * Pe)
# [0.1 0.01]* [a1] = [ coth(.1) - 1./(.1) ]
# [1. 0.2 ] [a2] [ -csch(.1)^2 + 1./(.1)^2]
a1 = dl.Constant(0.333554921691650)
a2 = dl.Constant(-0.004435991517475)
tau_1 = (num / den - dl.Constant(1.) / Pe) * h_over_u(
metric, u, self.reg_norm * self.nu * self.nu)
tau_2 = (a1 + a2 * Pe) * dl.Constant(.5) * h2 / nu
return dl.conditional(dl.ge(Pe, .1), tau_1, tau_2)