def interface_residual(U_F, U_Fmid, P_Fmid, D_S, U_S, D_F, D_Fmid, L_U, L_D,
v_F, c_S, c_F, m_D, m_U, mu_F, N_F, dFSIlist,
Exact_SigmaF, G_S):
"""Residual for interface conditions on the FSI interface"""
forms = []
for dFSI in dFSIlist:
#Displacement Lagrange Multiplier
R_FSI = inner(m_D, D_F - D_S)('+') * dFSI
R_FSI += inner(c_F, L_D)('+') * dFSI
#Velocity Lagrange Multiplier
R_FSI += inner(m_U, U_F - U_S)('+') * dFSI
R_FSI += inner(v_F, L_U)('+') * dFSI
#Stress Continuity
if Exact_SigmaF is None or Exact_SigmaF == []:
#Calculated fluid traction on structure
Sigma_F = PiolaTransform(_Sigma_F(U_Fmid, P_Fmid, D_Fmid, mu_F),
D_Fmid)
R_FSI += -(inner(dot(Sigma_F('+'), N_F('-')), c_S('-'))) * dFSI
else:
#Prescribed fluid traction on structure
info("Using perscribed Fluid Stress on fsi boundary")
R_FSI += (inner(Exact_SigmaF('+'), c_S('-'))) * dFSI
#Optional boundary traction term
if G_S is not None and G_S != []:
info("Using additional FSI boundary traction term")
R_FSI += inner(G_S('-'), c_S('-')) * dFSI
forms.append(R_FSI)
return sum(forms)
def interface_residual(U_F,U_Fmid,P_Fmid,D_S,U_S,D_F,D_Fmid,L_U,L_D,v_F,c_S,
c_F,m_D,m_U,mu_F,N_F,dFSIlist,Exact_SigmaF,G_S):
"""Residual for interface conditions on the FSI interface"""
forms = []
for dFSI in dFSIlist:
#Displacement Lagrange Multiplier
R_FSI = inner(m_D, D_F - D_S)('+')*dFSI
R_FSI += inner(c_F, L_D)('+')*dFSI
#Velocity Lagrange Multiplier
R_FSI += inner(m_U,U_F - U_S)('+')*dFSI
R_FSI += inner(v_F,L_U)('+')*dFSI
#Stress Continuity
if Exact_SigmaF is None or Exact_SigmaF == []:
#Calculated fluid traction on structure
Sigma_F = PiolaTransform(_Sigma_F(U_Fmid, P_Fmid, D_Fmid, mu_F), D_Fmid)
R_FSI += -(inner(dot(Sigma_F('+'),N_F('-')),c_S('-')))*dFSI
else:
#Prescribed fluid traction on structure
info("Using perscribed Fluid Stress on fsi boundary")
R_FSI += (inner(Exact_SigmaF('+'),c_S('-')))*dFSI
#Optional boundary traction term
if G_S is not None and G_S != []:
info("Using additional FSI boundary traction term")
R_FSI += inner(G_S('-'),c_S('-'))*dFSI
forms.append(R_FSI)
return sum(forms)
def J_FSI(dU_F,dU_Fmid,dP_Fmid,dD_Fmid,U_Fmid,P_Fmid,D_Fmid,c_S,mu_F,N_F,dFSIlist):
"""Derivative of the Interface Residual"""
forms = []
Sigma_F = PiolaTransform(_Sigma_F(dU_Fmid, dP_Fmid, D_Fmid, mu_F), D_Fmid)
for dFSI in dFSIlist:
J_FSI = -(inner(c_S('-'),dot(Sigma_F('+'),N_F('-'))))*dFSI
J_FSI += -inner(c_S('-'),dot(dD_FSigmaF(D_Fmid,dD_Fmid,U_Fmid,P_Fmid,mu_F)('+'),N_F('-')))*dFSI
forms.append(J_FSI)
return sum(forms)
def fluid_residual(U_Fdot,
U_F,
U1_F,
P_F,
v_F,
q_F,
mu,
rho,
D_F,
N_F,
dx_Flist,
ds_DNlist,
ds_Flist,
F_F,
D_Fdot,
G_F=None):
#Fluid equation in the Domain
forms = []
for dx_F in dx_Flist:
Dt_U = rho * J(D_F) * (U_Fdot +
dot(grad(U_F), dot(inv(F(D_F)), U_F - D_Fdot)))
Sigma_F = PiolaTransform(_Sigma_F(U_F, P_F, D_F, mu), D_F)
#DT
R_F = inner(v_F, Dt_U) * dx_F
#Div Sigma F
R_F += inner(grad(v_F), Sigma_F) * dx_F
#Incompressibility
R_F += inner(q_F, div(J(D_F) * dot(inv(F(D_F)), U_F))) * dx_F
#Right hand side Fluid (body force)
if F_F is not None and F_F != []:
info("Using Fluid body force")
R_F += -inner(v_F, J(D_F) * F_F) * dx_F
forms.append(R_F)
#Use do nothing BC if specified
for ds_DN in ds_DNlist:
info("Using Do nothing Fluid BC")
DN_F = -inner(
v_F,
J(D_F) * dot((mu * inv(F(D_F)).T * grad(U_F).T - P_F * I(U_F)) *
inv(F(D_F)).T, N_F)) * ds_DN
forms.append(DN_F)
#Add boundary traction (sigma dot n) to fluid boundary if specified.
for ds_F in ds_Flist:
info("Using Fluid boundary Traction (Neumann) BC")
B_F = -inner(G_F, v_F) * ds_F
forms.append(B_F)
return sum(forms)
def J_FSI(dU_F, dU_Fmid, dP_Fmid, dD_Fmid, U_Fmid, P_Fmid, D_Fmid, c_S, mu_F,
N_F, dFSIlist):
"""Derivative of the Interface Residual"""
forms = []
Sigma_F = PiolaTransform(_Sigma_F(dU_Fmid, dP_Fmid, D_Fmid, mu_F), D_Fmid)
for dFSI in dFSIlist:
J_FSI = -(inner(c_S('-'), dot(Sigma_F('+'), N_F('-')))) * dFSI
J_FSI += -inner(
c_S('-'),
dot(
dD_FSigmaF(D_Fmid, dD_Fmid, U_Fmid, P_Fmid, mu_F)
('+'), N_F('-'))) * dFSI
forms.append(J_FSI)
return sum(forms)
def fluid_residual(U_Fdot,U_F,U1_F,P_F,v_F,q_F,mu,rho,D_F,N_F,dx_Flist,ds_DNlist,ds_Flist,
F_F,D_Fdot, G_F=None):
#Fluid equation in the Domain
forms = []
for dx_F in dx_Flist:
Dt_U = rho*J(D_F)*(U_Fdot + dot(grad(U_F),dot(inv(F(D_F)),U_F - D_Fdot)))
Sigma_F = PiolaTransform(_Sigma_F(U_F, P_F, D_F, mu), D_F)
#DT
R_F = inner(v_F, Dt_U)*dx_F
#Div Sigma F
R_F += inner(grad(v_F), Sigma_F)*dx_F
#Incompressibility
R_F += inner(q_F, div(J(D_F)*dot(inv(F(D_F)), U_F)))*dx_F
#Right hand side Fluid (body force)
if F_F is not None and F_F != []:
info("Using Fluid body force")
R_F += -inner(v_F,J(D_F)*F_F)*dx_F
forms.append(R_F)
#Use do nothing BC if specified
for ds_DN in ds_DNlist:
info("Using Do nothing Fluid BC")
DN_F = -inner(v_F, J(D_F)*dot((mu*inv(F(D_F)).T*grad(U_F).T - P_F*I(U_F))*inv(F(D_F)).T, N_F))*ds_DN
forms.append(DN_F)
#Add boundary traction (sigma dot n) to fluid boundary if specified.
for ds_F in ds_Flist:
info("Using Fluid boundary Traction (Neumann) BC")
B_F = -inner(G_F, v_F)*ds_F
forms.append(B_F)
return sum(forms)
