def A1(self, x, t): # third-type
# Equation (38)
U = math.sqrt(self._v*self._v+4.*self._D*self._R* \
(self._lambda-self._alpha))
# Equation (37)
A1_ = \
self._v/(self._v+U)* \
exp_erf(0.5*x*(self._v-U)/self._D,
0.5*(self._R*x-U*t)/math.sqrt(self._D*self._R*t))+ \
self._v/(self._v-U)* \
exp_erf(0.5*x*(self._v+U)/self._D,
0.5*(self._R*x+U*t)/math.sqrt(self._D*self._R*t))+ \
0.5*self._v*self._v/(self._D*self._R*(self._lambda-self._alpha))* \
exp_erf(self._v*x/self._D+(self._alpha-self._lambda)*t,
0.5*(self._R*x+self._v*t)/math.sqrt(self._D*self._R*t))
return A1_
def A1_constant(self, x, t): # first-type
# Equation (42)
U = math.sqrt(self._v * self._v +
4. * self._D * self._R * self._lambda)
# Equation (41)
A1_constant_ = \
self._v/(self._v+U)* \
exp_erf(0.5*x*(self._v-U)/self._D,
0.5*(self._R*x-U*t)/math.sqrt(self._D*self._R*t))+ \
self._v/(self._v-U)* \
exp_erf(0.5*x*(self._v+U)/self._D,
0.5*(self._R*x+U*t)/math.sqrt(self._D*self._R*t))+ \
0.5*self._v*self._v/(self._D*self._R*self._lambda)* \
exp_erf(self._v*x/self._D-self._lambda*t,
0.5*(self._R*x+self._v*t)/math.sqrt(self._D*self._R*t))
return A1_constant_
def A3(self, x, t): # first-type
# Equation (46)
A3_ = \
0.5*math.erfc(0.5*(x-self._v*t)/math.sqrt(self._D*t))+ \
math.sqrt(self._v*self._v*t/(math.pi*self._D))* \
math.exp(-0.25*(x-self._v*t)*(x-self._v*t)/(self._D*t)) - \
0.5*(1.+self._v*x/self._D+self._v*self._v*t/self._D)* \
exp_erf(self._v*x/self._D,
0.5*(x+self._v*t)/math.sqrt(self._D*t))
return A3_
def A2(self, x, t): # first-type
# Equation (39)
A2_ = \
0.5*math.erfc(0.5*(self._R*x-self._v*t)/ \
math.sqrt(self._D*self._R*t))+ \
math.sqrt(self._v*self._v*t/(math.pi*self._D*self._R))* \
math.exp(-0.25*(self._R*x-self._v*t)*(self._R*x-self._v*t)/ \
(self._D*self._R*t))- \
0.5*(1.+self._v*x/self._D+self._v*self._v*t/(self._D*self._R))* \
exp_erf(self._v*x/self._D,
0.5*(self._R*x+self._v*t)/math.sqrt(self._D*self._R*t))
return A2_
def get_solution(self, t):
debug_push('Ogata get_solution')
dx = self._Lx / self._nx
c = np.zeros(self._nx)
x = self.get_rounded_even_spaced_numbers(dx, self._nx)
# Equations following (12), but prior ot (13)
for i in range(self._nx):
xx = x[i]
twosqrtDT = 2. * math.sqrt(self._D * t)
c[i] = 0.5*(special.erfc((xx-self._v*t)/twosqrtDT) + \
exp_erf(self._v*xx/self._D, \
(xx+self._v*t)/twosqrtDT))
c[:] *= self._c0
debug_pop()
return x, c