def BOUT_print(the_vars, rational=False):
"""Print the variables in BOUT++ style"""
for cur_var_key in the_vars.keys():
if rational:
the_vars[cur_var_key] = nsimplify(the_vars[cur_var_key])
the_vars[cur_var_key] = exprToStr(the_vars[cur_var_key])
the_vars[cur_var_key] = re.sub(r'\b' + "x" + r'\b', "geom:xl",
the_vars[cur_var_key])
the_vars[cur_var_key] = re.sub(r'\b' + "y" + r'\b', "geom:yl",
the_vars[cur_var_key])
print("\n[{}]".format(cur_var_key))
print(the_vars[cur_var_key])
#
# where
#
# zShift = int_{theta_0}^{theta} nu(theta) dtheta
#
# and nu(theta) is the field-line pitch
#
zShift = 0.0*theta #0.1*theta
nu = diff(zShift, theta)
shiftangle = zShift.subs( [(theta, 2*pi)] ) - zShift.subs( [(theta, 0.0)] )
y = symbols("y")
z = symbols("z")
replace = [ (phi, z + zShift), # z = phi - zShift
(theta, y) ] # y = theta
# Replace and print sources, solutions etc.
print("[mesh]")
print("zShift = "+exprToStr( zShift.subs(replace) ))
print("nu = "+exprToStr( nu.subs(replace) ))
print("shiftangle = "+exprToStr(shiftangle))
print("\n[f]")
print("solution = "+exprToStr( f.subs(replace) ))
print("\nsource = "+exprToStr( Sf.subs(replace) ))
nu = diff(zShift, theta)
I = diff(zShift,psi)
H = diff(zShift,theta)
shiftangle = zShift.subs( [(theta, 2*pin)] ) - zShift.subs( [(theta, 0.0)] )
yShift = 0.2*psi#0.05*(0.5-psi)*sin(theta) #0.2*psi #
eta = diff(yShift,psi)
G = 1 - diff(yShift,theta)
replace = [ (phi, z + zShift), (theta, y + yShift), (psi, x) ] # z = phi - zShift
#replace = [ (phi, z + zShift), (psi, x) ] # z = phi - zShift
# Replace and print sources, solutions etc.
print("[mesh]")
print("zShift = "+exprToStr( zShift.subs(replace) ))
print("nu = "+exprToStr( nu.subs(replace) ))
print("shiftangle = "+exprToStr(shiftangle.subs(replace)))
print("I = "+exprToStr(I.subs(replace)))
print("HH = "+exprToStr(H.subs(replace)))
print("")
print("eta = "+exprToStr(eta.subs(replace)))
print("yShift = "+exprToStr(yShift.subs(replace)))
print("G = "+exprToStr(G.subs(replace)))
print("\n[f]")
print("solution = "+exprToStr( f.subs(replace) ))
print("\nsource = "+exprToStr( Sf.subs(replace) ))
print("dfdpsi = "+exprToStr( dfdpsi.subs(replace) ))
print("dfdtheta = "+exprToStr( dfdtheta.subs(replace) ))
# Turn solution into real x and z coordinates
replace = [(y, metric.y * 2 * pi / Ly)]
f = f.subs(replace)
k = k.subs(replace)
##############################
# Calculate time derivatives
dfdt = Div_par(k * Grad_par(f))
#############################
# Calculate sources
Sf = diff(f, t) - dfdt
# Substitute back to get input y coordinates
replace = [(metric.y, y * Ly / (2 * pi))]
k = k.subs(replace)
f = f.subs(replace)
Sf = Sf.subs(replace)
print("[mesh]")
print("k = " + exprToStr(k))
print("\n[f]")
print("solution = " + exprToStr(f))
print("\nsource = " + exprToStr(Sf))
import sympy
from sympy import sin, cos, diff
x, t = sympy.symbols('y t')
v = sin(x)
rho = cos(x) + 4 + .01 * x**2 * sin(t)
m = rho * v
sympy.diff(m, x)
sympy.diff(-m, x)
rho_s = diff(rho, t) + diff(m, x)
p0 = sympy.symbols('p0')
p = rho * p0
v_s = rho * diff(v, t) + v * diff(v, x) + diff(p, x)
m_s = rho * v_s
from boutdata import mms
print('[rho]')
print('solution = ', mms.exprToStr(rho))
print('source = ', mms.exprToStr(rho_s))
#print('[m]')
#print('solution =',mms.exprToStr(m))
#print('source =',mms.exprToStr(m_s))
print('[v_n]')
print('solution =', mms.exprToStr(v))
print('source =', mms.exprToStr(v_s))
# Turn solution into real x and z coordinates
replace = [ (y, metric.y*2*pi/Ly) ]
f = f.subs(replace)
k = k.subs(replace)
##############################
# Calculate time derivatives
dfdt = Div_par( k * Grad_par(f) )
#############################
# Calculate sources
Sf = diff(f, t) - dfdt
# Substitute back to get input y coordinates
replace = [ (metric.y, y*Ly/(2*pi) ) ]
k = k.subs(replace)
f = f.subs(replace)
Sf = Sf.subs(replace)
print("[mesh]")
print("k = " + exprToStr(k))
print("\n[f]")
print("solution = " + exprToStr(f))
print("\nsource = " + exprToStr(Sf))
from sympy import symbols, cos, sin, diff
from boutdata.mms import exprToStr, y, t, pi
# Define the manufactured solution
f = y + cos(y) - sin(t) * cos(0.5 * y)
g = y**2 + sin(y) + cos(t) * cos(0.1 * y * y)
# Calculate gradients in x for boundaries
dfdy = diff(f, y)
dgdy = diff(g, y)
# Calculate sources
Sf = diff(f, t) - dgdy
Sg = diff(g, t) - dfdy
#######################
print("\n[f]")
print("solution = " + exprToStr(f))
print("ddy = " + exprToStr(dfdy))
print("source = " + exprToStr(Sf))
print("\n[g]")
print("solution = " + exprToStr(g))
print("ddy = " + exprToStr(dgdy))
print("source = " + exprToStr(Sg))
from sympy import symbols, cos, sin, diff
from boutdata.mms import exprToStr, y, t, pi
# Define the manufactured solution
f = y + cos(y) - sin(t)*cos(0.5*y)
g = y**2 + sin(y) + cos(t)*cos(0.1*y*y)
# Calculate gradients in x for boundaries
dfdy = diff(f, y)
dgdy = diff(g, y)
# Calculate sources
Sf = diff(f, t) - dgdy
Sg = diff(g, t) - dfdy
#######################
print("\n[f]")
print("solution = " + exprToStr(f))
print("ddy = " + exprToStr(dfdy))
print("source = " + exprToStr(Sf))
print("\n[g]")
print("solution = " + exprToStr(g))
print("ddy = " + exprToStr(dgdy))
print("source = " + exprToStr(Sg))
#############################
# Calculate sources
Sn = diff(n, t) - dndt
Sp = diff(p, t) - dpdt
Snv = diff(nv, t) - dnvdt
# Substitute back to get input y coordinates
replace = [ (metric.y, y*Ly/(2*pi) ) ]
n = n.subs(replace)
p = p.subs(replace)
nv = nv.subs(replace)
Sn = Sn.subs(replace)
Sp = Sp.subs(replace)
Snv = Snv.subs(replace)
print("[n]")
print("solution = " + exprToStr(n))
print("\nsource = " + exprToStr(Sn))
print("\n[p]")
print("solution = " + exprToStr(p))
print("\nsource = " + exprToStr(Sp))
print("\n[nv]")
print("solution = " + exprToStr(nv))
print("\nsource = " + exprToStr(Snv))
nu = diff(zShift, theta)
I = diff(zShift,psi)
H = diff(zShift,theta)
shiftangle = zShift.subs( [(theta, 2*pin)] ) - zShift.subs( [(theta, 0.0)] )
yShift = 0.2*psi#0.05*(0.5-psi)*sin(theta) #0.2*psi #
eta = diff(yShift,psi)
G = 1 - diff(yShift,theta)
replace = [ (phi, z + zShift), (theta, y + yShift), (psi, x) ] # z = phi - zShift
#replace = [ (phi, z + zShift), (psi, x) ] # z = phi - zShift
# Replace and print sources, solutions etc.
print("[mesh]")
print("zShift = "+exprToStr( zShift.subs(replace) ))
print("nu = "+exprToStr( nu.subs(replace) ))
print("shiftangle = "+exprToStr(shiftangle.subs(replace)))
print("I = "+exprToStr(I.subs(replace)))
print("HH = "+exprToStr(H.subs(replace)))
print("")
print("eta = "+exprToStr(eta.subs(replace)))
print("yShift = "+exprToStr(yShift.subs(replace)))
print("G = "+exprToStr(G.subs(replace)))
print("\n[f]")
print("solution = "+exprToStr( f.subs(replace) ))
print("\nsource = "+exprToStr( Sf.subs(replace) ))
print("dfdpsi = "+exprToStr( dfdpsi.subs(replace) ))
print("dfdtheta = "+exprToStr( dfdtheta.subs(replace) ))
# where
#
# zShift = int_{theta_0}^{theta} nu(theta) dtheta
#
# and nu(theta) is the field-line pitch
#
zShift = 0.0 * theta #0.1*theta
nu = diff(zShift, theta)
shiftangle = zShift.subs([(theta, 2 * pi)]) - zShift.subs([(theta, 0.0)])
y = symbols("y")
z = symbols("z")
replace = [
(phi, z + zShift), # z = phi - zShift
(theta, y)
] # y = theta
# Replace and print sources, solutions etc.
print("[mesh]")
print("zShift = " + exprToStr(zShift.subs(replace)))
print("nu = " + exprToStr(nu.subs(replace)))
print("shiftangle = " + exprToStr(shiftangle))
print("\n[f]")
print("solution = " + exprToStr(f.subs(replace)))
print("\nsource = " + exprToStr(Sf.subs(replace)))
#############################
# Calculate sources
Sn = diff(n, t) - dndt
Sp = diff(p, t) - dpdt
Snv = diff(nv, t) - dnvdt
# Substitute back to get input y coordinates
replace = [(metric.y, y * Ly / (2 * pi))]
n = n.subs(replace)
p = p.subs(replace)
nv = nv.subs(replace)
Sn = Sn.subs(replace)
Sp = Sp.subs(replace)
Snv = Snv.subs(replace)
print("[n]")
print("solution = " + exprToStr(n))
print("\nsource = " + exprToStr(Sn))
print("\n[p]")
print("solution = " + exprToStr(p))
print("\nsource = " + exprToStr(Sp))
print("\n[nv]")
print("solution = " + exprToStr(nv))
print("\nsource = " + exprToStr(Snv))