def dC2_dx(x, y):
# If called for x == 0 or x == Nx-1 return 0.0 (zero flux through boundaries).
if (x == 0 or x == Nx - 1):
return csNumber_t(0.0)
ci1 = C2(x + 1, y)
ci2 = C2(x - 1, y)
return (ci1 - ci2) / (2 * dx)
def dC2_dy(x, y):
# If called for y == 0 or y == Ny-1 return 0.0 (zero flux through boundaries).
if (y == 0 or y == Ny - 1):
return csNumber_t(0.0)
ci1 = C2(x, y + 1)
ci2 = C2(x, y - 1)
return (ci1 - ci2) / (2 * dy)
def d2C2_dy2(x, y):
# If called for y == 0 or y == Ny-1 return 0.0 (no diffusion through boundaries).
if (y == 0 or y == Ny - 1):
return csNumber_t(0.0)
ci1 = C2(x, y + 1)
ci = C2(x, y)
ci2 = C2(x, y - 1)
return (ci1 - 2 * ci + ci2) / (dy * dy)
def d2C2_dx2(x, y):
# If called for x == 0 or x == Nx-1 return 0.0 (no diffusion through boundaries).
if (x == 0 or x == Nx - 1):
return csNumber_t(0.0)
ci1 = C2(x + 1, y)
ci = C2(x, y)
ci2 = C2(x - 1, y)
return (ci1 - 2 * ci + ci2) / (dx * dx)
def CreateEquations(self, y, time):
# y is a list of csNumber_t objects representing model variables
C1_values = y[self.C1_start_index:self.C2_start_index]
C2_values = y[self.C2_start_index:self.Nequations]
dx = self.dx
dy = self.dy
Nx = self.Nx
Ny = self.Ny
x_domain = self.x_domain
y_domain = self.y_domain
# Math. functions
sin = pyOpenCS.sin
acos = pyOpenCS.acos
exp = pyOpenCS.exp
cs_max = pyOpenCS.max
nonzero = csNumber_t(1E-30)
def Kv(y):
return Kv0 * numpy.exp(y_domain[y] / 5.0)
def q3(time):
w = numpy.arccos(-1.0) / 43200.0
sinwt = cs_max(nonzero, sin(w * time))
return exp(-a3 / sinwt)
def q4(time):
w = numpy.arccos(-1.0) / 43200.0
sinwt = cs_max(nonzero, sin(w * time))
return exp(-a4 / sinwt)
def R1(c1, c2, time):
return -q1 * c1 * C3 - q2 * c1 * c2 + 2 * q3(time) * C3 + q4(
time) * c2
def R2(c1, c2, time):
return q1 * c1 * C3 - q2 * c1 * c2 - q4(time) * c2
def C1(x, y):
index = self.GetIndex(x, y)
return C1_values[index]
def C2(x, y):
index = self.GetIndex(x, y)
return C2_values[index]
# First order partial derivative per x.
def dC1_dx(x, y):
# If called for x == 0 or x == Nx-1 return 0.0 (zero flux through boundaries).
if (x == 0 or x == Nx - 1):
return csNumber_t(0.0)
ci1 = C1(x + 1, y)
ci2 = C1(x - 1, y)
return (ci1 - ci2) / (2 * dx)
def dC2_dx(x, y):
# If called for x == 0 or x == Nx-1 return 0.0 (zero flux through boundaries).
if (x == 0 or x == Nx - 1):
return csNumber_t(0.0)
ci1 = C2(x + 1, y)
ci2 = C2(x - 1, y)
return (ci1 - ci2) / (2 * dx)
# First order partial derivative per y.
def dC1_dy(x, y):
# If called for y == 0 or y == Ny-1 return 0.0 (zero flux through boundaries).
if (y == 0 or y == Ny - 1):
return csNumber_t(0.0)
ci1 = C1(x, y + 1)
ci2 = C1(x, y - 1)
return (ci1 - ci2) / (2 * dy)
def dC2_dy(x, y):
# If called for y == 0 or y == Ny-1 return 0.0 (zero flux through boundaries).
if (y == 0 or y == Ny - 1):
return csNumber_t(0.0)
ci1 = C2(x, y + 1)
ci2 = C2(x, y - 1)
return (ci1 - ci2) / (2 * dy)
# Second order partial derivative per x.
def d2C1_dx2(x, y):
# If called for x == 0 or x == Nx-1 return 0.0 (no diffusion through boundaries).
if (x == 0 or x == Nx - 1):
return csNumber_t(0.0)
ci1 = C1(x + 1, y)
ci = C1(x, y)
ci2 = C1(x - 1, y)
return (ci1 - 2 * ci + ci2) / (dx * dx)
def d2C2_dx2(x, y):
# If called for x == 0 or x == Nx-1 return 0.0 (no diffusion through boundaries).
if (x == 0 or x == Nx - 1):
return csNumber_t(0.0)
ci1 = C2(x + 1, y)
ci = C2(x, y)
ci2 = C2(x - 1, y)
return (ci1 - 2 * ci + ci2) / (dx * dx)
# Second order partial derivative per y.
def d2C1_dy2(x, y):
# If called for y == 0 or y == Ny-1 return 0.0 (no diffusion through boundaries).
if (y == 0 or y == Ny - 1):
return csNumber_t(0.0)
ci1 = C1(x, y + 1)
ci = C1(x, y)
ci2 = C1(x, y - 1)
return (ci1 - 2 * ci + ci2) / (dy * dy)
def d2C2_dy2(x, y):
# If called for y == 0 or y == Ny-1 return 0.0 (no diffusion through boundaries).
if (y == 0 or y == Ny - 1):
return csNumber_t(0.0)
ci1 = C2(x, y + 1)
ci = C2(x, y)
ci2 = C2(x, y - 1)
return (ci1 - 2 * ci + ci2) / (dy * dy)
eq = 0
equations = [None] * self.Nequations
# Component 2 (C1):
for x in range(Nx):
for y in range(Ny):
equations[eq] = V * dC1_dx(x,y) + \
Kh * d2C1_dx2(x,y) + \
Kv(y) * (0.2 * dC1_dy(x,y) + d2C1_dy2(x,y)) + \
R1(C1(x,y), C2(x,y), time)
eq += 1
# Component 2 (C2):
for x in range(Nx):
for y in range(Ny):
equations[eq] = V * dC2_dx(x,y) + \
Kh * d2C2_dx2(x,y) + \
Kv(y) * (0.2 * dC2_dy(x,y) + d2C2_dy2(x,y)) + \
R2(C1(x,y), C2(x,y), time)
eq += 1
return equations