def __init__(self, Na, Ns, Nc, X, Ac, y0, yd0, name ) :
Implicit_Problem.__init__(self,y0=y0,yd0=yd0,name=name)
self.T = 298.15 # Cell temperature, [K]
self.Ac = Ac # Cell coated area, [m^2]
# Control volumes and node points (mid node points and edge node points)
self.Ns = Ns
self.Na = Na
self.Nc = Nc
self.N = Na + Ns + Nc
self.X = X
self.x_e = numpy.linspace( 0.0, X, N+1 )
self.x_m = numpy.array( [ 0.5*(self.x_e[i+1]+self.x_e[i]) for i in range(N) ], dtype='d' )
self.vols = numpy.array( [ (self.x_e[i+1] - self.x_e[i]) for i in range(N)], dtype='d' )
# Useful sub-meshes for the phi_s functions
self.x_m_a = self.x_m[:Na]
self.x_m_c = self.x_m[-Nc:]
self.x_e_a = self.x_e[:Na+1]
self.x_e_c = self.x_e[-Nc-1:]
self.vols_a = self.vols[:Na]
self.vols_c = self.vols[-Nc:]
# Volume fraction vectors and matrices for effective parameters
self.La, self.Ls, self.Lc = self.Na*X/self.N, self.Ns*X/self.N, self.Nc*X/self.N
self.Na, self.Ns, self.Nc = Na, Ns, Nc
eps_a = 0.3
eps_s = 0.5
eps_c = 0.25
ba, bs, bc = 0.8, 0.5, 0.5
eps_a_vec = [ eps_a for i in range(Na) ] # list( eps_a + eps_a/2.*numpy.sin(numpy.linspace(0.,Na/4,Na)) ) # list(eps_a + eps_a*numpy.random.randn(Na)/5.) #
eps_s_vec = [ eps_s for i in range(Ns) ]
eps_c_vec = [ eps_c for i in range(Nc) ] # list( eps_c + eps_c/2.*numpy.sin(numpy.linspace(0.,Nc/4,Nc)) ) # list(eps_c + eps_c*numpy.random.randn(Nc)/5.) #
self.eps_m = numpy.array( eps_a_vec + eps_s_vec + eps_c_vec, dtype='d' )
self.k_m = 1./self.eps_m
self.eps_mb = numpy.array( [ ea**ba for ea in eps_a_vec ] + [ es**bs for es in eps_s_vec ] + [ ec**bc for ec in eps_c_vec ], dtype='d' )
self.eps_eff = numpy.array( [ ea**(1.+ba) for ea in eps_a_vec ] + [ es**(1.+bs) for es in eps_s_vec ] + [ ec**(1.+bc) for ec in eps_c_vec ], dtype='d' )
self.eps_a_eff = self.eps_eff[:Na]
self.eps_c_eff = self.eps_eff[-Nc:]
self.K_m = numpy.diag( self.k_m )
t_plus = 0.4
F = 96485.0
self.t_plus = t_plus
self.F = F
self.R_gas = 8.314
Rp_c = 6.5e-6
Rp_a = 12.0e-6
as_c = 3.*numpy.array(eps_c_vec, dtype='d')/Rp_c
as_a = 3.*numpy.array(eps_a_vec, dtype='d')/Rp_a
self.as_c = as_c
self.as_a = as_a
self.as_a_mean = 1./self.La*sum( [ asa*v for asa,v in zip(as_a, self.vols[:Na]) ] )
self.as_c_mean = 1./self.Lc*sum( [ asc*v for asc,v in zip(as_c, self.vols[-Nc:]) ] )
print 'asa diff', self.as_a_mean - as_a[0]
print 'asc diff', self.as_c_mean - as_c[0]
Ba = [ (1.-t_plus)*asa/ea for ea, asa in zip(eps_a_vec,as_a) ]
Bs = [ 0.0 for i in range(Ns) ]
Bc = [ (1.-t_plus)*asc/ec for ec, asc in zip(eps_c_vec,as_c) ]
self.B_ce = numpy.diag( numpy.array(Ba+Bs+Bc, dtype='d') )
# Bap = [ asa*F*dxa for asa,dxa in zip(as_a,self.vols_a) ]
# Bsp = [ 0.0 for i in range(Ns) ]
# Bcp = [ asc*F*dxc for asc,dxc in zip(as_c,self.vols_c) ]
Bap = [ asa*F for asa in as_a ]
Bsp = [ 0.0 for i in range(Ns) ]
Bcp = [ asc*F for asc in as_c ]
self.B2_pe = numpy.diag( numpy.array(Bap+Bsp+Bcp, dtype='d') )
# Solid phase parameters and j vector matrices
self.sig_a = 100. # [S/m]
self.sig_c = 100. # [S/m]
self.sig_a_eff = self.sig_a * self.eps_a_eff
self.sig_c_eff = self.sig_c * self.eps_c_eff
self.A_ps_a = flux_mat_builder( self.Na, self.x_m_a, numpy.ones_like(self.vols_a), self.sig_a_eff )
self.A_ps_c = flux_mat_builder( self.Nc, self.x_m_c, numpy.ones_like(self.vols_c), self.sig_c_eff )
self.A_ps_a[-1,-1] = 2*self.A_ps_a[-1,-1]
self.A_ps_c[ 0, 0] = 2*self.A_ps_c[ 0, 0]
Baps = numpy.array( [ asa*F*dxa for asa,dxa in zip(as_a, self.vols_a) ], dtype='d' )
Bcps = numpy.array( [ asc*F*dxc for asc,dxc in zip(as_c, self.vols_c) ], dtype='d' )
self.B_ps_a = numpy.diag( Baps )
self.B_ps_c = numpy.diag( Bcps )
self.B2_ps_a = numpy.zeros( self.Na, dtype='d' )
self.B2_ps_a[ 0] = -1.
self.B2_ps_c = numpy.zeros( self.Nc, dtype='d' )
self.B2_ps_c[-1] = -1.
def __init__(self, system, **kwargs):
Implicit_Problem.__init__(self, **kwargs)
self.name = 'ACAIE problem without concentration checks'
self.system = system
def __init__(self, N, Ac, y0, yd0, name ) :
Implicit_Problem.__init__(self,y0=y0,yd0=yd0,name=name)
self.Ac = Ac
self.T = 298.15
La = 65.0
Ls = 25.0
Lc = 55.0
Lt = (La+Ls+Lc)
X = Lt*1e-6 # [m]
Ns = int(N*(Ls/Lt))
Na = int(N*(La/Lt))
Nc = N - Ns - Na
print 'Na, Nc:', Na, Nc
self.N = N
self.X = X
self.x_e = numpy.linspace( 0.0, X, N+1 )
self.x_m = numpy.array( [ 0.5*(self.x_e[i+1]+self.x_e[i]) for i in range(N) ], dtype='d' )
self.vols = numpy.array( [ (self.x_e[i+1] - self.x_e[i]) for i in range(N)], dtype='d' )
### Diffusivity
self.La, self.Ls, self.Lc = La, Ls, Lc
self.Na, self.Ns, self.Nc = Na, Ns, Nc
eps_a = 0.25
eps_s = 0.5
eps_c = 0.2
ba, bs, bc = 1.2, 0.5, 0.5
eps_a_vec = [ eps_a for i in range(Na) ] # list( eps_a + eps_a/2.*numpy.sin(numpy.linspace(0.,Na/4,Na)) ) # list(eps_a + eps_a*numpy.random.randn(Na)/5.) #
eps_s_vec = [ eps_s for i in range(Ns) ]
eps_c_vec = [ eps_c for i in range(Nc) ] # list( eps_c + eps_c/2.*numpy.sin(numpy.linspace(0.,Nc/4,Nc)) ) # list(eps_c + eps_c*numpy.random.randn(Nc)/5.) #
self.eps_m = numpy.array( eps_a_vec + eps_s_vec + eps_c_vec, dtype='d' )
self.k_m = 1./self.eps_m
self.eps_mb = numpy.array( [ ea**ba for ea in eps_a_vec ] + [ es**bs for es in eps_s_vec ] + [ ec**bc for ec in eps_c_vec ], dtype='d' )
self.eps_eff = numpy.array( [ ea**(1.+ba) for ea in eps_a_vec ] + [ es**(1.+bs) for es in eps_s_vec ] + [ ec**(1.+bc) for ec in eps_c_vec ], dtype='d' )
self.K_m = numpy.diag( self.k_m )
self.pe0_ind = self.Na+self.Ns+self.Nc-3
t_plus = 0.4
F = 96485.0
self.t_plus = t_plus
self.F = F
self.R_gas = 8.314
Rp_c = 6.5e-6
Rp_a = 12.0e-6
as_c = 3.*numpy.array(eps_c_vec, dtype='d')/Rp_c
as_a = 3.*numpy.array(eps_a_vec, dtype='d')/Rp_a
self.as_c = as_c
self.as_a = as_a
self.as_a_mean = 1./self.La*sum( [ asa*v for asa,v in zip(as_a, self.vols[:Na]) ] )
self.as_c_mean = 1./self.Lc*sum( [ asc*v for asc,v in zip(as_c, self.vols[-Nc:]) ] )
print 'asa diff', self.as_a_mean - as_a[0]
print 'asc diff', self.as_c_mean - as_c[0]
Ba = [ (1.-t_plus)*asa/ea for ea, asa in zip(eps_a_vec,as_a) ]
Bs = [ 0.0 for i in range(Ns) ]
Bc = [ (1.-t_plus)*asc/ec for ec, asc in zip(eps_c_vec,as_c) ]
self.B_ce = numpy.diag( numpy.array(Ba+Bs+Bc, dtype='d') )
Bap = [ asa*F*v for asa,v in zip(as_a,self.vols[:Na]) ]
Bsp = [ 0.0 for i in range(Ns) ]
Bcp = [ asc*F*v for asc,v in zip(as_c,self.vols[-Nc:]) ]
# Bap = [ asa*F for asa in as_a ]
# Bsp = [ 0.0 for i in range(Ns) ]
# Bcp = [ asc*F for asc in as_c ]
self.B2_pe = numpy.diag( numpy.array(Bap+Bsp+Bcp, dtype='d') )
def __init__(self, Na, Ns, Nc, X, Ac, bsp_dir, y0, yd0, name):
Implicit_Problem.__init__(self, y0=y0, yd0=yd0, name=name)
self.T = 298.15 # Cell temperature, [K]
self.Ac = Ac # Cell coated area, [m^2]
# Control volumes and node points (mid node points and edge node points)
self.Ns = Ns
self.Na = Na
self.Nc = Nc
self.N = Na + Ns + Nc
self.X = X
self.num_diff_vars = N + Na + Nc
self.num_algr_vars = Na + Nc + N + Na + Nc
self.x_e = numpy.linspace(0.0, X, N + 1)
self.x_m = numpy.array(
[0.5 * (self.x_e[i + 1] + self.x_e[i]) for i in range(N)],
dtype='d')
self.vols = numpy.array([(self.x_e[i + 1] - self.x_e[i])
for i in range(N)],
dtype='d')
# Useful sub-meshes for the phi_s functions
self.x_m_a = self.x_m[:Na]
self.x_m_c = self.x_m[-Nc:]
self.x_e_a = self.x_e[:Na + 1]
self.x_e_c = self.x_e[-Nc - 1:]
self.vols_a = self.vols[:Na]
self.vols_c = self.vols[-Nc:]
# Volume fraction vectors and matrices for effective parameters
self.La, self.Ls, self.Lc = self.Na * X / self.N, self.Ns * X / self.N, self.Nc * X / self.N
self.Na, self.Ns, self.Nc = Na, Ns, Nc
eps_a = 0.25
eps_s = 0.5
eps_c = 0.2
ba, bs, bc = 1.2, 0.5, 0.5
eps_a_vec = [
eps_a for i in range(Na)
] # list( eps_a + eps_a/2.*numpy.sin(numpy.linspace(0.,Na/4,Na)) ) # list(eps_a + eps_a*numpy.random.randn(Na)/5.) #
eps_s_vec = [eps_s for i in range(Ns)]
eps_c_vec = [
eps_c for i in range(Nc)
] # list( eps_c + eps_c/2.*numpy.sin(numpy.linspace(0.,Nc/4,Nc)) ) # list(eps_c + eps_c*numpy.random.randn(Nc)/5.) #
self.eps_m = numpy.array(eps_a_vec + eps_s_vec + eps_c_vec, dtype='d')
self.k_m = 1. / self.eps_m
self.eps_mb = numpy.array([ea**ba for ea in eps_a_vec] +
[es**bs for es in eps_s_vec] +
[ec**bc for ec in eps_c_vec],
dtype='d')
self.eps_eff = numpy.array([ea**(1. + ba) for ea in eps_a_vec] +
[es**(1. + bs) for es in eps_s_vec] +
[ec**(1. + bc) for ec in eps_c_vec],
dtype='d')
self.eps_a_eff = self.eps_eff[:Na]
self.eps_c_eff = self.eps_eff[-Nc:]
self.K_m = numpy.diag(self.k_m)
t_plus = 0.43
F = 96485.0
self.t_plus = t_plus
self.F = F
self.R_gas = 8.314
Rp_a = 12.0e-6
Rp_c = 6.5e-6
self.Rp_a = Rp_a
self.Rp_c = Rp_c
as_a = 3. * (1.0 - numpy.array(eps_a_vec, dtype='d')) / Rp_a
as_c = 3. * (1.0 - numpy.array(eps_c_vec, dtype='d')) / Rp_c
self.as_a = as_a
self.as_c = as_c
self.as_a_mean = 1. / self.La * sum(
[asa * v for asa, v in zip(as_a, self.vols[:Na])])
self.as_c_mean = 1. / self.Lc * sum(
[asc * v for asc, v in zip(as_c, self.vols[-Nc:])])
print 'asa diff', self.as_a_mean - as_a[0]
print 'asc diff', self.as_c_mean - as_c[0]
Ba = [(1. - t_plus) * asa / ea for ea, asa in zip(eps_a_vec, as_a)]
Bs = [0.0 for i in range(Ns)]
Bc = [(1. - t_plus) * asc / ec for ec, asc in zip(eps_c_vec, as_c)]
self.B_ce = numpy.diag(numpy.array(Ba + Bs + Bc, dtype='d'))
Bap = [asa * F for asa in as_a]
Bsp = [0.0 for i in range(Ns)]
Bcp = [asc * F for asc in as_c]
self.B2_pe = numpy.diag(numpy.array(Bap + Bsp + Bcp, dtype='d'))
# Interpolators for De, ke
self.De_intp = build_interp_2d(
bsp_dir + 'data/Model_v1/Model_Pars/electrolyte/De.csv')
self.ke_intp = build_interp_2d(
bsp_dir + 'data/Model_v1/Model_Pars/electrolyte/kappa.csv')
self.fca_intp = build_interp_2d(
bsp_dir + 'data/Model_v1/Model_Pars/electrolyte/fca.csv')
self.ce_nom = 1000.0
######
## Solid phase parameters and j vector matrices
self.sig_a = 100. # [S/m]
self.sig_c = 40. # [S/m]
self.sig_a_eff = self.sig_a * (1.0 - self.eps_a_eff)
self.sig_c_eff = self.sig_c * (1.0 - self.eps_c_eff)
self.A_ps_a = flux_mat_builder(self.Na, self.x_m_a,
numpy.ones_like(self.vols_a),
self.sig_a_eff)
self.A_ps_c = flux_mat_builder(self.Nc, self.x_m_c,
numpy.ones_like(self.vols_c),
self.sig_c_eff)
# Grounding form for BCs (was only needed during testing, before BVK was incorporated for coupling
Baps = numpy.array(
[asa * F * dxa for asa, dxa in zip(as_a, self.vols_a)], dtype='d')
Bcps = numpy.array(
[asc * F * dxc for asc, dxc in zip(as_c, self.vols_c)], dtype='d')
self.B_ps_a = numpy.diag(Baps)
self.B_ps_c = numpy.diag(Bcps)
self.B2_ps_a = numpy.zeros(self.Na, dtype='d')
self.B2_ps_a[0] = -1.
self.B2_ps_c = numpy.zeros(self.Nc, dtype='d')
self.B2_ps_c[-1] = -1.
# Two parameter Solid phase diffusion model
Dsa = 1e-12
Dsc = 1e-14
self.Dsa = Dsa
self.Dsc = Dsc
self.csa_max = 30555.0 # [mol/m^3]
self.csc_max = 51554.0 # [mol/m^3]
self.B_cs_a = numpy.diag(
numpy.array([-3.0 / Rp_a for i in range(Na)], dtype='d'))
self.B_cs_c = numpy.diag(
numpy.array([-3.0 / Rp_c for i in range(Nc)], dtype='d'))
self.C_cs_a = numpy.eye(Na)
self.C_cs_c = numpy.eye(Nc)
self.D_cs_a = numpy.diag(
numpy.array([-Rp_a / Dsa / 5.0 for i in range(Na)], dtype='d'))
self.D_cs_c = numpy.diag(
numpy.array([-Rp_c / Dsc / 5.0 for i in range(Nc)], dtype='d'))
# bsp_dir = '/home/m_klein/Projects/battsimpy/'
# bsp_dir = '/home/mk-sim-linux/Battery_TempGrad/Python/batt_simulation/battsimpy/'
uref_a_map = numpy.loadtxt(
bsp_dir +
'/data/Model_v1/Model_Pars/solid/thermodynamics/uref_anode_x.csv',
delimiter=',')
uref_c_map = numpy.loadtxt(
bsp_dir +
'/data/Model_v1/Model_Pars/solid/thermodynamics/uref_cathode_x.csv',
delimiter=',')
duref_a = numpy.gradient(uref_a_map[:, 1]) / numpy.gradient(
uref_a_map[:, 0])
duref_c = numpy.gradient(uref_c_map[:, 1]) / numpy.gradient(
uref_c_map[:, 0])
if uref_a_map[1, 0] > uref_a_map[0, 0]:
self.uref_a_interp = scipy.interpolate.interp1d(
uref_a_map[:, 0], uref_a_map[:, 1])
self.duref_a_interp = scipy.interpolate.interp1d(
uref_a_map[:, 0], duref_a)
else:
self.uref_a_interp = scipy.interpolate.interp1d(
numpy.flipud(uref_a_map[:, 0]), numpy.flipud(uref_a_map[:, 1]))
self.duref_a_interp = scipy.interpolate.interp1d(
numpy.flipud(uref_a_map[:, 0]), numpy.flipud(duref_a))
if uref_c_map[1, 0] > uref_c_map[0, 0]:
self.uref_c_interp = scipy.interpolate.interp1d(
uref_c_map[:, 0], uref_c_map[:, 1])
self.duref_c_interp = scipy.interpolate.interp1d(
uref_c_map[:, 0], duref_c)
else:
self.uref_c_interp = scipy.interpolate.interp1d(
numpy.flipud(uref_c_map[:, 0]), numpy.flipud(uref_c_map[:, 1]))
self.duref_c_interp = scipy.interpolate.interp1d(
numpy.flipud(uref_c_map[:, 0]), numpy.flipud(duref_c))
# Plot the Uref data for verification
# xa = numpy.linspace( 0.05, 0.95, 50 )
# xc = numpy.linspace( 0.40, 0.95, 50 )
# plt.figure()
# plt.plot( uref_a_map[:,0], uref_a_map[:,1], label='Ua map' )
# plt.plot( uref_c_map[:,0], uref_c_map[:,1], label='Uc map' )
# plt.plot( xa, self.uref_a_interp(xa), label='Ua interp' )
# plt.plot( xc, self.uref_c_interp(xc), label='Uc interp' )
# plt.legend()
# plt.figure()
# plt.plot( uref_a_map[:,0], duref_a, label='dUa map' )
# plt.plot( uref_c_map[:,0], duref_c, label='dUc map' )
# plt.plot( xa, self.duref_a_interp(xa), label='dUa interp' )
# plt.plot( xc, self.duref_c_interp(xc), label='dUc interp' )
# plt.legend()
# plt.show()
# Reaction kinetics parameters
self.io_a = 5.0 # [A/m^2]
self.io_c = 5.0 # [A/m^2]
# System indices
self.ce_inds = range(self.N)
self.csa_inds = range(self.N, self.N + self.Na)
self.csc_inds = range(self.N + self.Na, self.N + self.Na + self.Nc)
c_end = self.N + self.Na + self.Nc
self.ja_inds = range(c_end, c_end + self.Na)
self.jc_inds = range(c_end + self.Na, c_end + self.Na + self.Nc)
self.pe_inds = range(c_end + self.Na + self.Nc,
c_end + self.Na + self.Nc + self.N)
self.pe_a_inds = range(c_end + self.Na + self.Nc,
c_end + self.Na + self.Nc + self.Na)
self.pe_c_inds = range(c_end + self.Na + self.Nc + self.Na + self.Ns,
c_end + self.Na + self.Nc + self.N)
self.pa_inds = range(c_end + self.Na + self.Nc + self.N,
c_end + self.Na + self.Nc + self.N + self.Na)
self.pc_inds = range(
c_end + self.Na + self.Nc + self.N + self.Na,
c_end + self.Na + self.Nc + self.N + self.Na + self.Nc)
def __init__(self, Na, Ns, Nc, Nra, Nrc, X, Ra, Rc, Ac, bsp_dir, y0, yd0,
name):
Implicit_Problem.__init__(self, y0=y0, yd0=yd0, name=name)
self.T = 298.15 # Cell temperature, [K]
self.Ac = Ac # Cell coated area, [m^2]
# Control volumes and node points (mid node points and edge node points)
self.Ns = Ns
self.Na = Na
self.Nc = Nc
self.N = Na + Ns + Nc
self.X = X
self.x_e = numpy.linspace(0.0, X, N + 1)
self.x_m = numpy.array(
[0.5 * (self.x_e[i + 1] + self.x_e[i]) for i in range(N)],
dtype='d')
self.vols = numpy.array([(self.x_e[i + 1] - self.x_e[i])
for i in range(N)],
dtype='d')
# Radial mesh
self.Nra = Nra
self.Nrc = Nrc
k = 0.8
self.r_e_a = nonlinspace(Ra, k, Nra)
self.r_m_a = numpy.array([
0.5 * (self.r_e_a[i + 1] + self.r_e_a[i]) for i in range(Nra - 1)
],
dtype='d')
self.r_e_c = nonlinspace(Rc, k, Nrc)
self.r_m_c = numpy.array([
0.5 * (self.r_e_c[i + 1] + self.r_e_c[i]) for i in range(Nrc - 1)
],
dtype='d')
self.vols_ra_e = numpy.array([1 / 3. * (self.r_m_a[0]**3)] + [
1 / 3. * (self.r_m_a[i + 1]**3 - self.r_m_a[i]**3)
for i in range(Nra - 2)
] + [1 / 3. * (self.r_e_a[-1]**3 - self.r_m_a[-1]**3)],
dtype='d')
self.vols_rc_e = numpy.array([1 / 3. * (self.r_m_c[0]**3)] + [
1 / 3. * (self.r_m_c[i + 1]**3 - self.r_m_c[i]**3)
for i in range(Nrc - 2)
] + [1 / 3. * (self.r_e_c[-1]**3 - self.r_m_c[-1]**3)],
dtype='d')
self.vols_ra_m = numpy.array([
1 / 3. * (self.r_e_a[i + 1]**3 - self.r_e_a[i]**3)
for i in range(Nra - 1)
],
dtype='d')
self.vols_rc_m = numpy.array([
1 / 3. * (self.r_e_c[i + 1]**3 - self.r_e_c[i]**3)
for i in range(Nrc - 1)
],
dtype='d')
# Useful sub-meshes for the phi_s functions
self.x_m_a = self.x_m[:Na]
self.x_m_c = self.x_m[-Nc:]
self.x_e_a = self.x_e[:Na + 1]
self.x_e_c = self.x_e[-Nc - 1:]
self.vols_a = self.vols[:Na]
self.vols_c = self.vols[-Nc:]
self.num_diff_vars = self.N + self.Nra * self.Na + self.Nrc * self.Nc
self.num_algr_vars = self.N + self.Na + self.Nc
# Volume fraction vectors and matrices for effective parameters
self.La, self.Ls, self.Lc = self.Na * X / self.N, self.Ns * X / self.N, self.Nc * X / self.N
self.Na, self.Ns, self.Nc = Na, Ns, Nc
eps_a = 0.3
eps_s = 0.5
eps_c = 0.25
ba, bs, bc = 0.8, 0.5, 0.5
eps_a_vec = [
eps_a for i in range(Na)
] # list( eps_a + eps_a/2.*numpy.sin(numpy.linspace(0.,Na/4,Na)) ) # list(eps_a + eps_a*numpy.random.randn(Na)/5.) #
eps_s_vec = [eps_s for i in range(Ns)]
eps_c_vec = [
eps_c for i in range(Nc)
] # list( eps_c + eps_c/2.*numpy.sin(numpy.linspace(0.,Nc/4,Nc)) ) # list(eps_c + eps_c*numpy.random.randn(Nc)/5.) #
self.eps_m = numpy.array(eps_a_vec + eps_s_vec + eps_c_vec, dtype='d')
self.k_m = 1. / self.eps_m
self.eps_mb = numpy.array([ea**ba for ea in eps_a_vec] +
[es**bs for es in eps_s_vec] +
[ec**bc for ec in eps_c_vec],
dtype='d')
self.eps_eff = numpy.array([ea**(1. + ba) for ea in eps_a_vec] +
[es**(1. + bs) for es in eps_s_vec] +
[ec**(1. + bc) for ec in eps_c_vec],
dtype='d')
self.eps_a_eff = self.eps_eff[:Na]
self.eps_c_eff = self.eps_eff[-Nc:]
self.K_m = numpy.diag(self.k_m)
t_plus = 0.4
F = 96485.0
self.t_plus = t_plus
self.F = F
self.R_gas = 8.314
self.Rp_a = Ra
self.Rp_c = Rc
as_a = 3. * numpy.array(eps_a_vec, dtype='d') / self.Rp_a
as_c = 3. * numpy.array(eps_c_vec, dtype='d') / self.Rp_c
self.as_a = as_a
self.as_c = as_c
self.as_a_mean = 1. / self.La * sum(
[asa * v for asa, v in zip(as_a, self.vols[:Na])])
self.as_c_mean = 1. / self.Lc * sum(
[asc * v for asc, v in zip(as_c, self.vols[-Nc:])])
print 'asa diff', self.as_a_mean - as_a[0]
print 'asc diff', self.as_c_mean - as_c[0]
# Electrolyte constant B_ce matrix
Ba = [(1. - t_plus) * asa / ea for ea, asa in zip(eps_a_vec, as_a)]
Bs = [0.0 for i in range(Ns)]
Bc = [(1. - t_plus) * asc / ec for ec, asc in zip(eps_c_vec, as_c)]
self.B_ce = numpy.diag(numpy.array(Ba + Bs + Bc, dtype='d'))
Bap = [asa * F for asa in as_a]
Bsp = [0.0 for i in range(Ns)]
Bcp = [asc * F for asc in as_c]
self.B2_pe = numpy.diag(numpy.array(Bap + Bsp + Bcp, dtype='d'))
# Solid phase parameters and j vector matrices
self.sig_a = 100. # [S/m]
self.sig_c = 100. # [S/m]
self.sig_a_eff = self.sig_a * self.eps_a_eff
self.sig_c_eff = self.sig_c * self.eps_c_eff
self.A_ps_a = flux_mat_builder(self.Na, self.x_m_a,
numpy.ones_like(self.vols_a),
self.sig_a_eff)
self.A_ps_c = flux_mat_builder(self.Nc, self.x_m_c,
numpy.ones_like(self.vols_c),
self.sig_c_eff)
# Grounding form for BCs (was only needed during testing, before BVK was incorporated for coupling
self.A_ps_a[-1, -1] = 2 * self.A_ps_a[-1, -1]
self.A_ps_c[0, 0] = 2 * self.A_ps_c[0, 0]
Baps = numpy.array(
[asa * F * dxa for asa, dxa in zip(as_a, self.vols_a)], dtype='d')
Bcps = numpy.array(
[asc * F * dxc for asc, dxc in zip(as_c, self.vols_c)], dtype='d')
self.B_ps_a = numpy.diag(Baps)
self.B_ps_c = numpy.diag(Bcps)
self.B2_ps_a = numpy.zeros(self.Na, dtype='d')
self.B2_ps_a[0] = -1.
self.B2_ps_c = numpy.zeros(self.Nc, dtype='d')
self.B2_ps_c[-1] = -1.
# Solid phase diffusion model
Dsa = 1e-12
Dsc = 1e-14
self.Dsa = Dsa
self.Dsc = Dsc
self.csa_max = 30555.0 # [mol/m^3]
self.csc_max = 51554.0 # [mol/m^3]
# Two parameter Solid phase diffusion model
# self.B_cs_a = numpy.diag( numpy.array( [-3.0/self.Rp_a for i in range(Na)], dtype='d' ) )
# self.B_cs_c = numpy.diag( numpy.array( [-3.0/self.Rp_c for i in range(Nc)], dtype='d' ) )
# self.C_cs_a = numpy.eye(Na)
# self.C_cs_c = numpy.eye(Nc)
# self.D_cs_a = numpy.diag( numpy.array( [-self.Rp_a/Dsa/5.0 for i in range(Na)], dtype='d' ) )
# self.D_cs_c = numpy.diag( numpy.array( [-self.Rp_c/Dsc/5.0 for i in range(Nc)], dtype='d' ) )
# 1D spherical diffusion model
self.A_csa_single = self.build_Ac_mat(
Nra, Dsa * numpy.ones_like(self.r_m_a), self.r_m_a, self.r_e_a,
self.vols_ra_e)
self.A_csc_single = self.build_Ac_mat(
Nrc, Dsc * numpy.ones_like(self.r_m_c), self.r_m_c, self.r_e_c,
self.vols_rc_e)
# b = self.A_csa_single.reshape(1,Nra,Nra).repeat(Na,axis=0)
b = [self.A_csa_single] * Na
self.A_cs_a = scipy.linalg.block_diag(*b)
b = [self.A_csc_single] * Nc
self.A_cs_c = scipy.linalg.block_diag(*b)
B_csa_single = numpy.array([0. for i in range(Nra)], dtype='d')
B_csa_single[-1] = -1. * self.r_e_a[-1]**2
A1 = self.build_Mc_A1mat(self.vols_ra_e)
self.B_csa_single = A1.dot(B_csa_single)
B_csc_single = numpy.array([0. for i in range(Nrc)], dtype='d')
B_csc_single[-1] = -1. * self.r_e_c[-1]**2
A1 = self.build_Mc_A1mat(self.vols_rc_e)
self.B_csc_single = A1.dot(B_csc_single)
b = [self.B_csa_single] * Na
self.B_cs_a = scipy.linalg.block_diag(*b).T
b = [self.B_csc_single] * Nc
self.B_cs_c = scipy.linalg.block_diag(*b).T
self.D_cs_a = scipy.linalg.block_diag(
*[[0.0 for i in range(self.Nra - 1)] + [1.0]] * Na)
self.D_cs_c = scipy.linalg.block_diag(
*[[0.0 for i in range(self.Nrc - 1)] + [1.0]] * Nc)
# OCV
Ua_path = bsp_dir + 'data/Model_v1/Model_Pars/solid/thermodynamics/uref_anode_bigx.csv'
Uc_path = bsp_dir + 'data/Model_v1/Model_Pars/solid/thermodynamics/uref_cathode_bigx.csv'
self.uref_a, self.uref_c, self.duref_a, self.duref_c = get_smooth_Uref_data(
Ua_path, Uc_path, ffa=0.4, ffc=0.2)
# Reaction kinetics parameters
self.io_a = 1.0 # [A/m^2]
self.io_c = 1.0 # [A/m^2]
## System indices
# Differential vars
self.ce_inds = range(self.N)
self.ce_inds_r = numpy.reshape(self.ce_inds, [len(self.ce_inds), 1])
self.ce_inds_c = numpy.reshape(self.ce_inds, [1, len(self.ce_inds)])
self.csa_inds = range(self.N, self.N + (self.Na * self.Nra))
self.csa_inds_r = numpy.reshape(self.csa_inds, [len(self.csa_inds), 1])
self.csa_inds_c = numpy.reshape(self.csa_inds, [1, len(self.csa_inds)])
self.csc_inds = range(
self.N + (self.Na * self.Nra),
self.N + (self.Na * self.Nra) + (self.Nc * self.Nrc))
self.csc_inds_r = numpy.reshape(self.csc_inds, [len(self.csc_inds), 1])
self.csc_inds_c = numpy.reshape(self.csc_inds, [1, len(self.csc_inds)])
# Algebraic vars
c_end = self.N + (self.Na * self.Nra) + (self.Nc * self.Nrc)
self.pe_inds = range(c_end, c_end + self.N)
self.pe_inds_r = numpy.reshape(self.pe_inds, [len(self.pe_inds), 1])
self.pe_inds_c = numpy.reshape(self.pe_inds, [1, len(self.pe_inds)])
self.pe_a_inds = range(c_end, c_end + self.Na)
self.pe_a_inds_r = numpy.reshape(self.pe_a_inds,
[len(self.pe_a_inds), 1])
self.pe_a_inds_c = numpy.reshape(self.pe_a_inds,
[1, len(self.pe_a_inds)])
self.pe_c_inds = range(c_end + self.Na + self.Ns,
c_end + self.Na + self.Ns + self.Nc)
self.pe_c_inds_r = numpy.reshape(self.pe_c_inds,
[len(self.pe_c_inds), 1])
self.pe_c_inds_c = numpy.reshape(self.pe_c_inds,
[1, len(self.pe_c_inds)])
self.pa_inds = range(c_end + self.N, c_end + self.N + self.Na)
self.pa_inds_r = numpy.reshape(self.pa_inds, [len(self.pa_inds), 1])
self.pa_inds_c = numpy.reshape(self.pa_inds, [1, len(self.pa_inds)])
self.pc_inds = range(c_end + self.N + self.Na,
c_end + self.N + self.Na + self.Nc)
self.pc_inds_r = numpy.reshape(self.pc_inds, [len(self.pc_inds), 1])
self.pc_inds_c = numpy.reshape(self.pc_inds, [1, len(self.pc_inds)])
# second set for manual jac version
c_end = 0
self.pe_inds2 = range(c_end, c_end + self.N)
self.pe_inds_r2 = numpy.reshape(self.pe_inds2, [len(self.pe_inds2), 1])
self.pe_inds_c2 = numpy.reshape(self.pe_inds2, [1, len(self.pe_inds2)])
self.pe_a_inds2 = range(c_end, c_end + self.Na)
self.pe_a_inds_r2 = numpy.reshape(self.pe_a_inds2,
[len(self.pe_a_inds2), 1])
self.pe_a_inds_c2 = numpy.reshape(self.pe_a_inds2,
[1, len(self.pe_a_inds2)])
self.pe_c_inds2 = range(c_end + self.Na + self.Ns,
c_end + self.Na + self.Ns + self.Nc)
self.pe_c_inds_r2 = numpy.reshape(self.pe_c_inds2,
[len(self.pe_c_inds2), 1])
self.pe_c_inds_c2 = numpy.reshape(self.pe_c_inds2,
[1, len(self.pe_c_inds2)])
self.pa_inds2 = range(c_end + self.N, c_end + self.N + self.Na)
self.pa_inds_r2 = numpy.reshape(self.pa_inds2, [len(self.pa_inds2), 1])
self.pa_inds_c2 = numpy.reshape(self.pa_inds2, [1, len(self.pa_inds2)])
self.pc_inds2 = range(c_end + self.N + self.Na,
c_end + self.N + self.Na + self.Nc)
self.pc_inds_r2 = numpy.reshape(self.pc_inds2, [len(self.pc_inds2), 1])
self.pc_inds_c2 = numpy.reshape(self.pc_inds2, [1, len(self.pc_inds2)])
def __init__(self, **kargs):
Implicit_Problem.__init__(self, **kargs)
self.name = 'Van der Pol (implicit) with time events'
self.my = 1.0/1e-6
def setup_model(self, y0, yd0, name):
"""
Setup the Assimulo implicit model to use IDA.
"""
Implicit_Problem.__init__(self, y0=y0, yd0=yd0, name=name)