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Mobility_Thermal_Skin_Rheology.f90
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MODULE MOBILITY_THERMAL_SKIN_RHEOLOGY
CONTAINS
SUBROUTINE fomega_a(Ai,h_a,delta_a,T_a,Ts_a,eta_a,Ds_a,omega_a,nu,Rheology,ERROR_CODE)
IMPLICIT NONE
INTEGER, INTENT(IN) :: Rheology
DOUBLE PRECISION , INTENT(IN) :: nu
DOUBLE PRECISION, PARAMETER :: pi = 3.14159265358979d0
DOUBLE PRECISION, INTENT(IN) :: Ai,h_a,delta_a,T_a,Ts_a,eta_a,Ds_a
DOUBLE PRECISION, INTENT(INOUT) :: omega_a
INTEGER, INTENT(INOUT) :: ERROR_CODE
IF (Rheology == 0) THEN
omega_a = (7.0d0/5.0d0)*T_a*delta_a**2*eta_a*nu - 7.0d0/5.0d0*T_a*&
& delta_a**2*eta_a - 3.0d0/2.0d0*T_a*delta_a*eta_a*h_a*nu + (3.0d0/&
& 2.0d0)*T_a*delta_a*eta_a*h_a + (3.0d0/5.0d0)*Ts_a*delta_a**2*&
& eta_a*nu - 3.0d0/5.0d0*Ts_a*delta_a**2*eta_a - 3.0d0/2.0d0*Ts_a*&
& delta_a*eta_a*h_a*nu + (3.0d0/2.0d0)*Ts_a*delta_a*eta_a*h_a - 2*&
& delta_a**2*eta_a*nu + 3*delta_a*eta_a*h_a*nu
! omega_a = (eta_a*delta_a)/10.d0*(nu*(-20.d0*delta_a+30.d0*h_a)+&
! &(1.d0-nu)*(6.d0*Ds_a*delta_a-15.d0*Ds_a*h_a-20.d0*T_a*delta_a+30.d0*T_a*h_a))
ELSEIF (Rheology == 1) THEN
ERROR_CODE = 1
ELSEIF (Rheology == 2) THEN
nutest:IF (nu /= 1.0) THEN
omega_a = -6.0d0*sqrt(pi)*T_a**2*delta_a**2*eta_a*nu*nu**(-T_a)*(&
& -log(nu))**(-1.5d0)*(T_a - Ts_a)**(-2.5d0)*log(nu)*erf(sqrt(-log(&
& nu))*sqrt(T_a - Ts_a)) + 3.0d0*sqrt(pi)*T_a**2*delta_a*eta_a*h_a*&
& nu*nu**(-T_a)*(-log(nu))**(-1.5d0)*(T_a - Ts_a)**(-2.5d0)*log(nu)&
& *erf(sqrt(-log(nu))*sqrt(T_a - Ts_a)) + 12.0d0*sqrt(pi)*T_a*Ts_a*&
& delta_a**2*eta_a*nu*nu**(-T_a)*(-log(nu))**(-1.5d0)*(T_a - Ts_a)&
& **(-2.5d0)*log(nu)*erf(sqrt(-log(nu))*sqrt(T_a - Ts_a)) - 6.0d0*&
& sqrt(pi)*T_a*Ts_a*delta_a*eta_a*h_a*nu*nu**(-T_a)*(-log(nu))**(&
& -1.5d0)*(T_a - Ts_a)**(-2.5d0)*log(nu)*erf(sqrt(-log(nu))*sqrt(&
& T_a - Ts_a)) + 6.0d0*T_a*delta_a**2*eta_a*nu*nu**(-Ts_a)*1.0/(&
& -log(nu))*(T_a - Ts_a)**(-2.0d0) + 3.0d0*sqrt(pi)*T_a*delta_a**2*&
& eta_a*nu*nu**(-T_a)*(-log(nu))**(-1.5d0)*(T_a - Ts_a)**(-2.5d0)*&
& erf(sqrt(-log(nu))*sqrt(T_a - Ts_a)) - 12.0d0*T_a*delta_a**2*&
& eta_a*nu*nu**(-T_a)*1.0/(-log(nu))*(T_a - Ts_a)**(-2.0d0) - 3.0d0&
& *T_a*delta_a*eta_a*h_a*nu*nu**(-Ts_a)*1.0/(-log(nu))*(T_a - Ts_a)&
& **(-2.0d0) + 3.0d0*T_a*delta_a*eta_a*h_a*nu*nu**(-T_a)*1.0/(-log(&
& nu))*(T_a - Ts_a)**(-2.0d0) - 6.0d0*sqrt(pi)*Ts_a**2*delta_a**2*&
& eta_a*nu*nu**(-T_a)*(-log(nu))**(-1.5d0)*(T_a - Ts_a)**(-2.5d0)*&
& log(nu)*erf(sqrt(-log(nu))*sqrt(T_a - Ts_a)) + 3.0d0*sqrt(pi)*&
& Ts_a**2*delta_a*eta_a*h_a*nu*nu**(-T_a)*(-log(nu))**(-1.5d0)*(T_a&
& - Ts_a)**(-2.5d0)*log(nu)*erf(sqrt(-log(nu))*sqrt(T_a - Ts_a)) -&
& 6.0d0*Ts_a*delta_a**2*eta_a*nu*nu**(-Ts_a)*1.0/(-log(nu))*(T_a -&
& Ts_a)**(-2.0d0) - 3.0d0*sqrt(pi)*Ts_a*delta_a**2*eta_a*nu*nu**(&
& -T_a)*(-log(nu))**(-1.5d0)*(T_a - Ts_a)**(-2.5d0)*erf(sqrt(-log(&
& nu))*sqrt(T_a - Ts_a)) + 12.0d0*Ts_a*delta_a**2*eta_a*nu*nu**(&
& -T_a)*1.0/(-log(nu))*(T_a - Ts_a)**(-2.0d0) + 3.0d0*Ts_a*delta_a*&
& eta_a*h_a*nu*nu**(-Ts_a)*1.0/(-log(nu))*(T_a - Ts_a)**(-2.0d0) -&
& 3.0d0*Ts_a*delta_a*eta_a*h_a*nu*nu**(-T_a)*1.0/(-log(nu))*(T_a -&
& Ts_a)**(-2.0d0) + 6.0d0*delta_a**2*eta_a*nu*nu**(-Ts_a)*1.0/(T_a&
& - Ts_a)/log(nu) + 6.0d0*sqrt(pi)*delta_a**2*eta_a*nu*nu**(-T_a)*&
& sqrt(-log(nu))*(T_a - Ts_a)**(-0.5d0)*erf(sqrt(-log(nu))*sqrt(T_a&
& - Ts_a))/log(nu) - 6.0d0*delta_a**2*eta_a*nu*nu**(-T_a)*1.0/(T_a&
& - Ts_a)/log(nu) - 3.0d0*sqrt(pi)*delta_a*eta_a*h_a*nu*nu**(-T_a)*&
& sqrt(-log(nu))*(T_a - Ts_a)**(-0.5d0)*erf(sqrt(-log(nu))*sqrt(T_a&
& - Ts_a))/log(nu)
ELSEIF (nu==1.0) THEN
omega_a = -2.0d0*delta_a**2*eta_a + 3.0d0*delta_a*eta_a*h_a
ELSE
ERROR_CODE = 1
ENDIF nutest
ELSE
ERROR_CODE = 1
ENDIF
END SUBROUTINE Fomega_A
SUBROUTINE fsigma_a(Ai,h_a,delta_a,T_a,Ts_a,eta_a,Ds_a,delta_a2,&
&sigma_a,nu,Rheology,ERROR_CODE)
IMPLICIT NONE
INTEGER, INTENT(IN) :: Rheology
DOUBLE PRECISION , INTENT(IN) :: nu
DOUBLE PRECISION, PARAMETER :: pi = 3.14159265358979d0
DOUBLE PRECISION, INTENT(IN) :: Ai,h_a,delta_a,T_a,Ts_a,eta_a,Ds_a,delta_a2
DOUBLE PRECISION, INTENT(INOUT) :: sigma_a
INTEGER, INTENT(INOUT) :: ERROR_CODE
IF (Rheology == 0) THEN
sigma_a = -38.0d0/105.0d0*T_a**2*delta_a**3*eta_a*nu + (38.0d0/&
& 105.0d0)*T_a**2*delta_a**3*eta_a + (1.0d0/3.0d0)*T_a**2*delta_a**&
& 2*eta_a*h_a*nu - 1.0d0/3.0d0*T_a**2*delta_a**2*eta_a*h_a + (9.0d0&
& /35.0d0)*T_a*Ts_a*delta_a**3*eta_a*nu - 9.0d0/35.0d0*T_a*Ts_a*&
& delta_a**3*eta_a - 1.0d0/6.0d0*T_a*Ts_a*delta_a**2*eta_a*h_a*nu +&
& (1.0d0/6.0d0)*T_a*Ts_a*delta_a**2*eta_a*h_a + (7.0d0/15.0d0)*T_a*&
& delta_a**3*eta_a*nu - 1.0d0/2.0d0*T_a*delta_a**2*eta_a*h_a*nu + (&
& 11.0d0/105.0d0)*Ts_a**2*delta_a**3*eta_a*nu - 11.0d0/105.0d0*Ts_a&
& **2*delta_a**3*eta_a - 1.0d0/6.0d0*Ts_a**2*delta_a**2*eta_a*h_a*&
& nu + (1.0d0/6.0d0)*Ts_a**2*delta_a**2*eta_a*h_a - 7.0d0/15.0d0*&
& Ts_a*delta_a**3*eta_a*nu + (1.0d0/2.0d0)*Ts_a*delta_a**2*eta_a*&
& h_a*nu
! sigma_a = (-1.d0/210.d0)*Ds_a*delta_a2*eta_a*(nu*(-98.d0*delta_a+105.d0*h_a)+&
! &(1-nu)*(22.d0*Ds_a*delta_a-35.d0*Ds_a*h_a-98.d0*T_a*delta_a+105.d0*T_a*h_a))
ELSEIF (Rheology == 1) THEN
ERROR_CODE = 1
ELSEIF (Rheology == 2) THEN
nutest:IF (nu /= 1.0) THEN
sigma_a = -6.0d0*sqrt(pi)*T_a**3*delta_a**3*eta_a*nu*nu**(-T_a)*(&
& -log(nu))**(-2.5d0)*(T_a - Ts_a)**(-2.5d0)*log(nu)**2*erf(sqrt(&
& -log(nu))*sqrt(T_a - Ts_a)) - 4.0d0*sqrt(pi)*T_a**3*delta_a**3*&
& eta_a*nu*nu**(-T_a)*(-log(nu))**(-1.5d0)*(T_a - Ts_a)**(-2.5d0)*&
& log(nu)*erf(sqrt(-log(nu))*sqrt(T_a - Ts_a)) + 3.0d0*sqrt(pi)*T_a&
& **3*delta_a**2*eta_a*h_a*nu*nu**(-T_a)*(-log(nu))**(-2.5d0)*(T_a&
& - Ts_a)**(-2.5d0)*log(nu)**2*erf(sqrt(-log(nu))*sqrt(T_a - Ts_a&
& )) + 2.0d0*sqrt(pi)*T_a**3*delta_a**2*eta_a*h_a*nu*nu**(-T_a)*(&
& -log(nu))**(-1.5d0)*(T_a - Ts_a)**(-2.5d0)*log(nu)*erf(sqrt(-log(&
& nu))*sqrt(T_a - Ts_a)) + 12.0d0*sqrt(pi)*T_a**2*Ts_a*delta_a**3*&
& eta_a*nu*nu**(-T_a)*(-log(nu))**(-2.5d0)*(T_a - Ts_a)**(-2.5d0)*&
& log(nu)**2*erf(sqrt(-log(nu))*sqrt(T_a - Ts_a)) + 6.0d0*sqrt(pi)*&
& T_a**2*Ts_a*delta_a**3*eta_a*nu*nu**(-T_a)*(-log(nu))**(-1.5d0)*(&
& T_a - Ts_a)**(-2.5d0)*log(nu)*erf(sqrt(-log(nu))*sqrt(T_a - Ts_a&
& )) - 6.0d0*sqrt(pi)*T_a**2*Ts_a*delta_a**2*eta_a*h_a*nu*nu**(-T_a&
& )*(-log(nu))**(-2.5d0)*(T_a - Ts_a)**(-2.5d0)*log(nu)**2*erf(sqrt&
& (-log(nu))*sqrt(T_a - Ts_a)) - 3.0d0*sqrt(pi)*T_a**2*Ts_a*delta_a&
& **2*eta_a*h_a*nu*nu**(-T_a)*(-log(nu))**(-1.5d0)*(T_a - Ts_a)**(&
& -2.5d0)*log(nu)*erf(sqrt(-log(nu))*sqrt(T_a - Ts_a)) + 6.0d0*T_a&
& **2*delta_a**3*eta_a*nu*nu**(-Ts_a)*(-log(nu))**(-2.0d0)*(T_a -&
& Ts_a)**(-2.0d0)*log(nu) + 4.0d0*T_a**2*delta_a**3*eta_a*nu*nu**(&
& -Ts_a)*1.0/(-log(nu))*(T_a - Ts_a)**(-2.0d0) + 3.0d0*sqrt(pi)*T_a&
& **2*delta_a**3*eta_a*nu*nu**(-T_a)*(-log(nu))**(-2.5d0)*(T_a -&
& Ts_a)**(-2.5d0)*log(nu)*erf(sqrt(-log(nu))*sqrt(T_a - Ts_a)) -&
& 12.0d0*T_a**2*delta_a**3*eta_a*nu*nu**(-T_a)*(-log(nu))**(-2.0d0)&
& *(T_a - Ts_a)**(-2.0d0)*log(nu) + 2.0d0*sqrt(pi)*T_a**2*delta_a**&
& 3*eta_a*nu*nu**(-T_a)*(-log(nu))**(-1.5d0)*(T_a - Ts_a)**(-2.5d0)&
& *erf(sqrt(-log(nu))*sqrt(T_a - Ts_a)) - 8.0d0*T_a**2*delta_a**3*&
& eta_a*nu*nu**(-T_a)*1.0/(-log(nu))*(T_a - Ts_a)**(-2.0d0) - 2.0d0&
& *T_a**2*delta_a**2*eta_a*h_a*nu*nu**(-Ts_a)*(-log(nu))**(-2.0d0)*&
& (T_a - Ts_a)**(-2.0d0)*log(nu) - 2.0d0*T_a**2*delta_a**2*eta_a*&
& h_a*nu*nu**(-Ts_a)*1.0/(-log(nu))*(T_a - Ts_a)**(-2.0d0) + 3.0d0*&
& T_a**2*delta_a**2*eta_a*h_a*nu*nu**(-T_a)*(-log(nu))**(-2.0d0)*(&
& T_a - Ts_a)**(-2.0d0)*log(nu) + 2.0d0*T_a**2*delta_a**2*eta_a*h_a&
& *nu*nu**(-T_a)*1.0/(-log(nu))*(T_a - Ts_a)**(-2.0d0) - 6.0d0*sqrt&
& (pi)*T_a*Ts_a**2*delta_a**3*eta_a*nu*nu**(-T_a)*(-log(nu))**(&
& -2.5d0)*(T_a - Ts_a)**(-2.5d0)*log(nu)**2*erf(sqrt(-log(nu))*sqrt&
& (T_a - Ts_a)) + 3.0d0*sqrt(pi)*T_a*Ts_a**2*delta_a**2*eta_a*h_a*&
& nu*nu**(-T_a)*(-log(nu))**(-2.5d0)*(T_a - Ts_a)**(-2.5d0)*log(nu)&
& **2*erf(sqrt(-log(nu))*sqrt(T_a - Ts_a)) - 6.0d0*T_a*Ts_a*delta_a&
& **3*eta_a*nu*nu**(-Ts_a)*(-log(nu))**(-2.0d0)*(T_a - Ts_a)**(&
& -2.0d0)*log(nu) - 2.0d0*T_a*Ts_a*delta_a**3*eta_a*nu*nu**(-Ts_a)*&
& 1.0/(-log(nu))*(T_a - Ts_a)**(-2.0d0) - 3.0d0*sqrt(pi)*T_a*Ts_a*&
& delta_a**3*eta_a*nu*nu**(-T_a)*(-log(nu))**(-2.5d0)*(T_a - Ts_a)&
& **(-2.5d0)*log(nu)*erf(sqrt(-log(nu))*sqrt(T_a - Ts_a)) + 12.0d0*&
& T_a*Ts_a*delta_a**3*eta_a*nu*nu**(-T_a)*(-log(nu))**(-2.0d0)*(T_a&
& - Ts_a)**(-2.0d0)*log(nu) - 1.0d0*sqrt(pi)*T_a*Ts_a*delta_a**3*&
& eta_a*nu*nu**(-T_a)*(-log(nu))**(-1.5d0)*(T_a - Ts_a)**(-2.5d0)*&
& erf(sqrt(-log(nu))*sqrt(T_a - Ts_a)) + 4.0d0*T_a*Ts_a*delta_a**3*&
& eta_a*nu*nu**(-T_a)*1.0/(-log(nu))*(T_a - Ts_a)**(-2.0d0) + 1.0d0&
& *T_a*Ts_a*delta_a**2*eta_a*h_a*nu*nu**(-Ts_a)*(-log(nu))**(-2.0d0&
& )*(T_a - Ts_a)**(-2.0d0)*log(nu) + 1.0d0*T_a*Ts_a*delta_a**2*&
& eta_a*h_a*nu*nu**(-Ts_a)*1.0/(-log(nu))*(T_a - Ts_a)**(-2.0d0) -&
& 3.0d0*T_a*Ts_a*delta_a**2*eta_a*h_a*nu*nu**(-T_a)*(-log(nu))**(&
& -2.0d0)*(T_a - Ts_a)**(-2.0d0)*log(nu) - 1.0d0*T_a*Ts_a*delta_a**&
& 2*eta_a*h_a*nu*nu**(-T_a)*1.0/(-log(nu))*(T_a - Ts_a)**(-2.0d0) -&
& 1.0d0*T_a*delta_a**3*eta_a*nu*nu**(-Ts_a)*(-log(nu))**(-2.0d0)*(&
& T_a - Ts_a)**(-2.0d0) - 2.0d0*T_a*delta_a**3*eta_a*nu*nu**(-Ts_a)&
& *1.0/(T_a - Ts_a)/log(nu) + 1.5d0*sqrt(pi)*T_a*delta_a**3*eta_a*&
& nu*nu**(-T_a)*(-log(nu))**(-2.5d0)*(T_a - Ts_a)**(-2.5d0)*erf(&
& sqrt(-log(nu))*sqrt(T_a - Ts_a)) - 2.0d0*T_a*delta_a**3*eta_a*nu*&
& nu**(-T_a)*(-log(nu))**(-2.0d0)*(T_a - Ts_a)**(-2.0d0) - 2.0d0*&
& sqrt(pi)*T_a*delta_a**3*eta_a*nu*nu**(-T_a)*sqrt(-log(nu))*(T_a -&
& Ts_a)**(-0.5d0)*erf(sqrt(-log(nu))*sqrt(T_a - Ts_a))/log(nu) +&
& 2.0d0*T_a*delta_a**3*eta_a*nu*nu**(-T_a)*1.0/(T_a - Ts_a)/log(nu&
& ) - 1.0d0*T_a*delta_a**2*eta_a*h_a*nu*nu**(-Ts_a)*(-log(nu))**(&
& -2.0d0)*(T_a - Ts_a)**(-2.0d0) + 1.0d0*T_a*delta_a**2*eta_a*h_a*&
& nu*nu**(-T_a)*(-log(nu))**(-2.0d0)*(T_a - Ts_a)**(-2.0d0) + 1.0d0&
& *sqrt(pi)*T_a*delta_a**2*eta_a*h_a*nu*nu**(-T_a)*sqrt(-log(nu))*(&
& T_a - Ts_a)**(-0.5d0)*erf(sqrt(-log(nu))*sqrt(T_a - Ts_a))/log(nu&
& ) - 2.0d0*sqrt(pi)*Ts_a**3*delta_a**3*eta_a*nu*nu**(-T_a)*(-log(&
& nu))**(-1.5d0)*(T_a - Ts_a)**(-2.5d0)*log(nu)*erf(sqrt(-log(nu))*&
& sqrt(T_a - Ts_a)) + 1.0d0*sqrt(pi)*Ts_a**3*delta_a**2*eta_a*h_a*&
& nu*nu**(-T_a)*(-log(nu))**(-1.5d0)*(T_a - Ts_a)**(-2.5d0)*log(nu)&
& *erf(sqrt(-log(nu))*sqrt(T_a - Ts_a)) - 2.0d0*Ts_a**2*delta_a**3*&
& eta_a*nu*nu**(-Ts_a)*1.0/(-log(nu))*(T_a - Ts_a)**(-2.0d0) -&
& 1.0d0*sqrt(pi)*Ts_a**2*delta_a**3*eta_a*nu*nu**(-T_a)*(-log(nu))&
& **(-1.5d0)*(T_a - Ts_a)**(-2.5d0)*erf(sqrt(-log(nu))*sqrt(T_a -&
& Ts_a)) + 4.0d0*Ts_a**2*delta_a**3*eta_a*nu*nu**(-T_a)*1.0/(-log(&
& nu))*(T_a - Ts_a)**(-2.0d0) + 1.0d0*Ts_a**2*delta_a**2*eta_a*h_a*&
& nu*nu**(-Ts_a)*(-log(nu))**(-2.0d0)*(T_a - Ts_a)**(-2.0d0)*log(nu&
& ) + 1.0d0*Ts_a**2*delta_a**2*eta_a*h_a*nu*nu**(-Ts_a)*1.0/(-log(&
& nu))*(T_a - Ts_a)**(-2.0d0) - 1.0d0*Ts_a**2*delta_a**2*eta_a*h_a*&
& nu*nu**(-T_a)*1.0/(-log(nu))*(T_a - Ts_a)**(-2.0d0) + 1.0d0*Ts_a*&
& delta_a**3*eta_a*nu*nu**(-Ts_a)*(-log(nu))**(-2.0d0)*(T_a - Ts_a)&
& **(-2.0d0) + 2.0d0*Ts_a*delta_a**3*eta_a*nu*nu**(-Ts_a)*1.0/(T_a&
& - Ts_a)/log(nu) - 1.5d0*sqrt(pi)*Ts_a*delta_a**3*eta_a*nu*nu**(&
& -T_a)*(-log(nu))**(-2.5d0)*(T_a - Ts_a)**(-2.5d0)*erf(sqrt(-log(&
& nu))*sqrt(T_a - Ts_a)) + 2.0d0*Ts_a*delta_a**3*eta_a*nu*nu**(-T_a&
& )*(-log(nu))**(-2.0d0)*(T_a - Ts_a)**(-2.0d0) + 2.0d0*sqrt(pi)*&
& Ts_a*delta_a**3*eta_a*nu*nu**(-T_a)*sqrt(-log(nu))*(T_a - Ts_a)**&
& (-0.5d0)*erf(sqrt(-log(nu))*sqrt(T_a - Ts_a))/log(nu) - 2.0d0*&
& Ts_a*delta_a**3*eta_a*nu*nu**(-T_a)*1.0/(T_a - Ts_a)/log(nu) +&
& 1.0d0*Ts_a*delta_a**2*eta_a*h_a*nu*nu**(-Ts_a)*(-log(nu))**(&
& -2.0d0)*(T_a - Ts_a)**(-2.0d0) - 1.0d0*Ts_a*delta_a**2*eta_a*h_a*&
& nu*nu**(-T_a)*(-log(nu))**(-2.0d0)*(T_a - Ts_a)**(-2.0d0) - 1.0d0&
& *sqrt(pi)*Ts_a*delta_a**2*eta_a*h_a*nu*nu**(-T_a)*sqrt(-log(nu))*&
& (T_a - Ts_a)**(-0.5d0)*erf(sqrt(-log(nu))*sqrt(T_a - Ts_a))/log(&
& nu)
ELSEIF (nu==1.0) THEN
sigma_a = 0.466666666666665d0*T_a*delta_a**3*eta_a - 0.5d0*T_a*&
&delta_a**2*eta_a*h_a - 0.466666666666667d0*Ts_a*delta_a**3*eta_a&
& + 0.5d0*Ts_a*delta_a**2*eta_a*h_a
ELSE
ERROR_CODE = 1
ENDIF nutest
ELSE
ERROR_CODE = 1
ENDIF
END SUBROUTINE Fsigma_A
SUBROUTINE fOmega_b(Bi,h_b,delta_b,T_b,Ts_b,eta_b,Ds_b,omega_b,nu,Rheology,ERROR_CODE)
IMPLICIT NONE
INTEGER, INTENT(IN) :: Rheology
DOUBLE PRECISION , INTENT(IN) :: nu
DOUBLE PRECISION, PARAMETER :: pi = 3.14159265358979d0
DOUBLE PRECISION, INTENT(IN) :: Bi,h_b,delta_b,T_b,Ts_b,eta_b
DOUBLE PRECISION, INTENT(IN) :: Ds_b
DOUBLE PRECISION, INTENT(INOUT) :: omega_b
INTEGER, INTENT(INOUT) :: ERROR_CODE
IF (Rheology == 0) THEN
omega_b = (7.0d0/5.0d0)*T_b*delta_b**2*eta_b*nu - 7.0d0/5.0d0*T_b*&
& delta_b**2*eta_b - 3.0d0/2.0d0*T_b*delta_b*eta_b*h_b*nu + (3.0d0/&
& 2.0d0)*T_b*delta_b*eta_b*h_b + (3.0d0/5.0d0)*Ts_b*delta_b**2*&
& eta_b*nu - 3.0d0/5.0d0*Ts_b*delta_b**2*eta_b - 3.0d0/2.0d0*Ts_b*&
& delta_b*eta_b*h_b*nu + (3.0d0/2.0d0)*Ts_b*delta_b*eta_b*h_b - 2*&
& delta_b**2*eta_b*nu + 3*delta_b*eta_b*h_b*nu
! omega_b = (eta_b*delta_b)/10.d0*(nu*(-20.d0*delta_b+30.d0*h_b)+&
! &(1.d0-nu)*(6.d0*Ds_b*delta_b-15.d0*Ds_b*h_b-20.d0*T_b*delta_b+30.d0*T_b*h_b))
ELSEIF (Rheology == 1) THEN
ERROR_CODE = 1
ELSEIF (Rheology == 2) THEN
nutest:IF (nu /= 1.0) THEN
omega_b = -6.0d0*sqrt(pi)*T_b**2*delta_b**2*eta_b*nu*nu**(-T_b)*(&
& -log(nu))**(-1.5d0)*(T_b - Ts_b)**(-2.5d0)*log(nu)*erf(sqrt(-log(&
& nu))*sqrt(T_b - Ts_b)) + 3.0d0*sqrt(pi)*T_b**2*delta_b*eta_b*h_b*&
& nu*nu**(-T_b)*(-log(nu))**(-1.5d0)*(T_b - Ts_b)**(-2.5d0)*log(nu)&
& *erf(sqrt(-log(nu))*sqrt(T_b - Ts_b)) + 12.0d0*sqrt(pi)*T_b*Ts_b*&
& delta_b**2*eta_b*nu*nu**(-T_b)*(-log(nu))**(-1.5d0)*(T_b - Ts_b)&
& **(-2.5d0)*log(nu)*erf(sqrt(-log(nu))*sqrt(T_b - Ts_b)) - 6.0d0*&
& sqrt(pi)*T_b*Ts_b*delta_b*eta_b*h_b*nu*nu**(-T_b)*(-log(nu))**(&
& -1.5d0)*(T_b - Ts_b)**(-2.5d0)*log(nu)*erf(sqrt(-log(nu))*sqrt(&
& T_b - Ts_b)) + 6.0d0*T_b*delta_b**2*eta_b*nu*nu**(-Ts_b)*1.0/(&
& -log(nu))*(T_b - Ts_b)**(-2.0d0) + 3.0d0*sqrt(pi)*T_b*delta_b**2*&
& eta_b*nu*nu**(-T_b)*(-log(nu))**(-1.5d0)*(T_b - Ts_b)**(-2.5d0)*&
& erf(sqrt(-log(nu))*sqrt(T_b - Ts_b)) - 12.0d0*T_b*delta_b**2*&
& eta_b*nu*nu**(-T_b)*1.0/(-log(nu))*(T_b - Ts_b)**(-2.0d0) - 3.0d0&
& *T_b*delta_b*eta_b*h_b*nu*nu**(-Ts_b)*1.0/(-log(nu))*(T_b - Ts_b)&
& **(-2.0d0) + 3.0d0*T_b*delta_b*eta_b*h_b*nu*nu**(-T_b)*1.0/(-log(&
& nu))*(T_b - Ts_b)**(-2.0d0) - 6.0d0*sqrt(pi)*Ts_b**2*delta_b**2*&
& eta_b*nu*nu**(-T_b)*(-log(nu))**(-1.5d0)*(T_b - Ts_b)**(-2.5d0)*&
& log(nu)*erf(sqrt(-log(nu))*sqrt(T_b - Ts_b)) + 3.0d0*sqrt(pi)*&
& Ts_b**2*delta_b*eta_b*h_b*nu*nu**(-T_b)*(-log(nu))**(-1.5d0)*(T_b&
& - Ts_b)**(-2.5d0)*log(nu)*erf(sqrt(-log(nu))*sqrt(T_b - Ts_b)) -&
& 6.0d0*Ts_b*delta_b**2*eta_b*nu*nu**(-Ts_b)*1.0/(-log(nu))*(T_b -&
& Ts_b)**(-2.0d0) - 3.0d0*sqrt(pi)*Ts_b*delta_b**2*eta_b*nu*nu**(&
& -T_b)*(-log(nu))**(-1.5d0)*(T_b - Ts_b)**(-2.5d0)*erf(sqrt(-log(&
& nu))*sqrt(T_b - Ts_b)) + 12.0d0*Ts_b*delta_b**2*eta_b*nu*nu**(&
& -T_b)*1.0/(-log(nu))*(T_b - Ts_b)**(-2.0d0) + 3.0d0*Ts_b*delta_b*&
& eta_b*h_b*nu*nu**(-Ts_b)*1.0/(-log(nu))*(T_b - Ts_b)**(-2.0d0) -&
& 3.0d0*Ts_b*delta_b*eta_b*h_b*nu*nu**(-T_b)*1.0/(-log(nu))*(T_b -&
& Ts_b)**(-2.0d0) + 6.0d0*delta_b**2*eta_b*nu*nu**(-Ts_b)*1.0/(T_b&
& - Ts_b)/log(nu) + 6.0d0*sqrt(pi)*delta_b**2*eta_b*nu*nu**(-T_b)*&
& sqrt(-log(nu))*(T_b - Ts_b)**(-0.5d0)*erf(sqrt(-log(nu))*sqrt(T_b&
& - Ts_b))/log(nu) - 6.0d0*delta_b**2*eta_b*nu*nu**(-T_b)*1.0/(T_b&
& - Ts_b)/log(nu) - 3.0d0*sqrt(pi)*delta_b*eta_b*h_b*nu*nu**(-T_b)*&
& sqrt(-log(nu))*(T_b - Ts_b)**(-0.5d0)*erf(sqrt(-log(nu))*sqrt(T_b&
& - Ts_b))/log(nu)
ELSEIF (nu==1.0) THEN
omega_b = -2.0d0*delta_b**2*eta_b + 3.0d0*delta_b*eta_b*h_b
ELSE
ERROR_CODE = 1
ENDIF nutest
ELSE
ERROR_CODE = 1
ENDIF
END SUBROUTINE FOmega_B
SUBROUTINE fsigma_b(Bi,h_b,delta_b,T_b,Ts_b,sigma_b,Ds_b,delta_b2,&
&eta_b,nu,Rheology,ERROR_CODE)
IMPLICIT NONE
INTEGER, INTENT(IN) :: Rheology
DOUBLE PRECISION , INTENT(IN) :: nu
DOUBLE PRECISION, PARAMETER :: pi = 3.14159265358979d0
DOUBLE PRECISION, INTENT(IN) :: Bi,h_b,delta_b,T_b,Ts_b,eta_b,Ds_b,delta_b2
DOUBLE PRECISION, INTENT(INOUT) :: sigma_b
INTEGER, INTENT(INOUT) :: ERROR_CODE
IF (Rheology == 0) THEN
sigma_b = -38.0d0/105.0d0*T_b**2*delta_b**3*eta_b*nu + (38.0d0/&
& 105.0d0)*T_b**2*delta_b**3*eta_b + (1.0d0/3.0d0)*T_b**2*delta_b**&
& 2*eta_b*h_b*nu - 1.0d0/3.0d0*T_b**2*delta_b**2*eta_b*h_b + (9.0d0&
& /35.0d0)*T_b*Ts_b*delta_b**3*eta_b*nu - 9.0d0/35.0d0*T_b*Ts_b*&
& delta_b**3*eta_b - 1.0d0/6.0d0*T_b*Ts_b*delta_b**2*eta_b*h_b*nu +&
& (1.0d0/6.0d0)*T_b*Ts_b*delta_b**2*eta_b*h_b + (7.0d0/15.0d0)*T_b*&
& delta_b**3*eta_b*nu - 1.0d0/2.0d0*T_b*delta_b**2*eta_b*h_b*nu + (&
& 11.0d0/105.0d0)*Ts_b**2*delta_b**3*eta_b*nu - 11.0d0/105.0d0*Ts_b&
& **2*delta_b**3*eta_b - 1.0d0/6.0d0*Ts_b**2*delta_b**2*eta_b*h_b*&
& nu + (1.0d0/6.0d0)*Ts_b**2*delta_b**2*eta_b*h_b - 7.0d0/15.0d0*&
& Ts_b*delta_b**3*eta_b*nu + (1.0d0/2.0d0)*Ts_b*delta_b**2*eta_b*&
& h_b*nu
! sigma_b = (-1.d0/210.d0)*Ds_b*delta_b2*eta_b*(nu*(-98.d0*delta_b+105.d0*h_b)+&
! &(1-nu)*(22.d0*Ds_b*delta_b-35.d0*Ds_b*h_b-98.d0*T_b*delta_b+105.d0*T_b*h_b))
ELSEIF (Rheology == 1) THEN
ERROR_CODE = 1
ELSEIF (Rheology == 2) THEN
nutest:IF (nu /= 1.0) THEN
sigma_b = -6.0d0*sqrt(pi)*T_b**3*delta_b**3*eta_b*nu*nu**(-T_b)*(&
& -log(nu))**(-2.5d0)*(T_b - Ts_b)**(-2.5d0)*log(nu)**2*erf(sqrt(&
& -log(nu))*sqrt(T_b - Ts_b)) - 4.0d0*sqrt(pi)*T_b**3*delta_b**3*&
& eta_b*nu*nu**(-T_b)*(-log(nu))**(-1.5d0)*(T_b - Ts_b)**(-2.5d0)*&
& log(nu)*erf(sqrt(-log(nu))*sqrt(T_b - Ts_b)) + 3.0d0*sqrt(pi)*T_b&
& **3*delta_b**2*eta_b*h_b*nu*nu**(-T_b)*(-log(nu))**(-2.5d0)*(T_b&
& - Ts_b)**(-2.5d0)*log(nu)**2*erf(sqrt(-log(nu))*sqrt(T_b - Ts_b&
& )) + 2.0d0*sqrt(pi)*T_b**3*delta_b**2*eta_b*h_b*nu*nu**(-T_b)*(&
& -log(nu))**(-1.5d0)*(T_b - Ts_b)**(-2.5d0)*log(nu)*erf(sqrt(-log(&
& nu))*sqrt(T_b - Ts_b)) + 12.0d0*sqrt(pi)*T_b**2*Ts_b*delta_b**3*&
& eta_b*nu*nu**(-T_b)*(-log(nu))**(-2.5d0)*(T_b - Ts_b)**(-2.5d0)*&
& log(nu)**2*erf(sqrt(-log(nu))*sqrt(T_b - Ts_b)) + 6.0d0*sqrt(pi)*&
& T_b**2*Ts_b*delta_b**3*eta_b*nu*nu**(-T_b)*(-log(nu))**(-1.5d0)*(&
& T_b - Ts_b)**(-2.5d0)*log(nu)*erf(sqrt(-log(nu))*sqrt(T_b - Ts_b&
& )) - 6.0d0*sqrt(pi)*T_b**2*Ts_b*delta_b**2*eta_b*h_b*nu*nu**(-T_b&
& )*(-log(nu))**(-2.5d0)*(T_b - Ts_b)**(-2.5d0)*log(nu)**2*erf(sqrt&
& (-log(nu))*sqrt(T_b - Ts_b)) - 3.0d0*sqrt(pi)*T_b**2*Ts_b*delta_b&
& **2*eta_b*h_b*nu*nu**(-T_b)*(-log(nu))**(-1.5d0)*(T_b - Ts_b)**(&
& -2.5d0)*log(nu)*erf(sqrt(-log(nu))*sqrt(T_b - Ts_b)) + 6.0d0*T_b&
& **2*delta_b**3*eta_b*nu*nu**(-Ts_b)*(-log(nu))**(-2.0d0)*(T_b -&
& Ts_b)**(-2.0d0)*log(nu) + 4.0d0*T_b**2*delta_b**3*eta_b*nu*nu**(&
& -Ts_b)*1.0/(-log(nu))*(T_b - Ts_b)**(-2.0d0) + 3.0d0*sqrt(pi)*T_b&
& **2*delta_b**3*eta_b*nu*nu**(-T_b)*(-log(nu))**(-2.5d0)*(T_b -&
& Ts_b)**(-2.5d0)*log(nu)*erf(sqrt(-log(nu))*sqrt(T_b - Ts_b)) -&
& 12.0d0*T_b**2*delta_b**3*eta_b*nu*nu**(-T_b)*(-log(nu))**(-2.0d0)&
& *(T_b - Ts_b)**(-2.0d0)*log(nu) + 2.0d0*sqrt(pi)*T_b**2*delta_b**&
& 3*eta_b*nu*nu**(-T_b)*(-log(nu))**(-1.5d0)*(T_b - Ts_b)**(-2.5d0)&
& *erf(sqrt(-log(nu))*sqrt(T_b - Ts_b)) - 8.0d0*T_b**2*delta_b**3*&
& eta_b*nu*nu**(-T_b)*1.0/(-log(nu))*(T_b - Ts_b)**(-2.0d0) - 2.0d0&
& *T_b**2*delta_b**2*eta_b*h_b*nu*nu**(-Ts_b)*(-log(nu))**(-2.0d0)*&
& (T_b - Ts_b)**(-2.0d0)*log(nu) - 2.0d0*T_b**2*delta_b**2*eta_b*&
& h_b*nu*nu**(-Ts_b)*1.0/(-log(nu))*(T_b - Ts_b)**(-2.0d0) + 3.0d0*&
& T_b**2*delta_b**2*eta_b*h_b*nu*nu**(-T_b)*(-log(nu))**(-2.0d0)*(&
& T_b - Ts_b)**(-2.0d0)*log(nu) + 2.0d0*T_b**2*delta_b**2*eta_b*h_b&
& *nu*nu**(-T_b)*1.0/(-log(nu))*(T_b - Ts_b)**(-2.0d0) - 6.0d0*sqrt&
& (pi)*T_b*Ts_b**2*delta_b**3*eta_b*nu*nu**(-T_b)*(-log(nu))**(&
& -2.5d0)*(T_b - Ts_b)**(-2.5d0)*log(nu)**2*erf(sqrt(-log(nu))*sqrt&
& (T_b - Ts_b)) + 3.0d0*sqrt(pi)*T_b*Ts_b**2*delta_b**2*eta_b*h_b*&
& nu*nu**(-T_b)*(-log(nu))**(-2.5d0)*(T_b - Ts_b)**(-2.5d0)*log(nu)&
& **2*erf(sqrt(-log(nu))*sqrt(T_b - Ts_b)) - 6.0d0*T_b*Ts_b*delta_b&
& **3*eta_b*nu*nu**(-Ts_b)*(-log(nu))**(-2.0d0)*(T_b - Ts_b)**(&
& -2.0d0)*log(nu) - 2.0d0*T_b*Ts_b*delta_b**3*eta_b*nu*nu**(-Ts_b)*&
& 1.0/(-log(nu))*(T_b - Ts_b)**(-2.0d0) - 3.0d0*sqrt(pi)*T_b*Ts_b*&
& delta_b**3*eta_b*nu*nu**(-T_b)*(-log(nu))**(-2.5d0)*(T_b - Ts_b)&
& **(-2.5d0)*log(nu)*erf(sqrt(-log(nu))*sqrt(T_b - Ts_b)) + 12.0d0*&
& T_b*Ts_b*delta_b**3*eta_b*nu*nu**(-T_b)*(-log(nu))**(-2.0d0)*(T_b&
& - Ts_b)**(-2.0d0)*log(nu) - 1.0d0*sqrt(pi)*T_b*Ts_b*delta_b**3*&
& eta_b*nu*nu**(-T_b)*(-log(nu))**(-1.5d0)*(T_b - Ts_b)**(-2.5d0)*&
& erf(sqrt(-log(nu))*sqrt(T_b - Ts_b)) + 4.0d0*T_b*Ts_b*delta_b**3*&
& eta_b*nu*nu**(-T_b)*1.0/(-log(nu))*(T_b - Ts_b)**(-2.0d0) + 1.0d0&
& *T_b*Ts_b*delta_b**2*eta_b*h_b*nu*nu**(-Ts_b)*(-log(nu))**(-2.0d0&
& )*(T_b - Ts_b)**(-2.0d0)*log(nu) + 1.0d0*T_b*Ts_b*delta_b**2*&
& eta_b*h_b*nu*nu**(-Ts_b)*1.0/(-log(nu))*(T_b - Ts_b)**(-2.0d0) -&
& 3.0d0*T_b*Ts_b*delta_b**2*eta_b*h_b*nu*nu**(-T_b)*(-log(nu))**(&
& -2.0d0)*(T_b - Ts_b)**(-2.0d0)*log(nu) - 1.0d0*T_b*Ts_b*delta_b**&
& 2*eta_b*h_b*nu*nu**(-T_b)*1.0/(-log(nu))*(T_b - Ts_b)**(-2.0d0) -&
& 1.0d0*T_b*delta_b**3*eta_b*nu*nu**(-Ts_b)*(-log(nu))**(-2.0d0)*(&
& T_b - Ts_b)**(-2.0d0) - 2.0d0*T_b*delta_b**3*eta_b*nu*nu**(-Ts_b)&
& *1.0/(T_b - Ts_b)/log(nu) + 1.5d0*sqrt(pi)*T_b*delta_b**3*eta_b*&
& nu*nu**(-T_b)*(-log(nu))**(-2.5d0)*(T_b - Ts_b)**(-2.5d0)*erf(&
& sqrt(-log(nu))*sqrt(T_b - Ts_b)) - 2.0d0*T_b*delta_b**3*eta_b*nu*&
& nu**(-T_b)*(-log(nu))**(-2.0d0)*(T_b - Ts_b)**(-2.0d0) - 2.0d0*&
& sqrt(pi)*T_b*delta_b**3*eta_b*nu*nu**(-T_b)*sqrt(-log(nu))*(T_b -&
& Ts_b)**(-0.5d0)*erf(sqrt(-log(nu))*sqrt(T_b - Ts_b))/log(nu) +&
& 2.0d0*T_b*delta_b**3*eta_b*nu*nu**(-T_b)*1.0/(T_b - Ts_b)/log(nu&
& ) - 1.0d0*T_b*delta_b**2*eta_b*h_b*nu*nu**(-Ts_b)*(-log(nu))**(&
& -2.0d0)*(T_b - Ts_b)**(-2.0d0) + 1.0d0*T_b*delta_b**2*eta_b*h_b*&
& nu*nu**(-T_b)*(-log(nu))**(-2.0d0)*(T_b - Ts_b)**(-2.0d0) + 1.0d0&
& *sqrt(pi)*T_b*delta_b**2*eta_b*h_b*nu*nu**(-T_b)*sqrt(-log(nu))*(&
& T_b - Ts_b)**(-0.5d0)*erf(sqrt(-log(nu))*sqrt(T_b - Ts_b))/log(nu&
& ) - 2.0d0*sqrt(pi)*Ts_b**3*delta_b**3*eta_b*nu*nu**(-T_b)*(-log(&
& nu))**(-1.5d0)*(T_b - Ts_b)**(-2.5d0)*log(nu)*erf(sqrt(-log(nu))*&
& sqrt(T_b - Ts_b)) + 1.0d0*sqrt(pi)*Ts_b**3*delta_b**2*eta_b*h_b*&
& nu*nu**(-T_b)*(-log(nu))**(-1.5d0)*(T_b - Ts_b)**(-2.5d0)*log(nu)&
& *erf(sqrt(-log(nu))*sqrt(T_b - Ts_b)) - 2.0d0*Ts_b**2*delta_b**3*&
& eta_b*nu*nu**(-Ts_b)*1.0/(-log(nu))*(T_b - Ts_b)**(-2.0d0) -&
& 1.0d0*sqrt(pi)*Ts_b**2*delta_b**3*eta_b*nu*nu**(-T_b)*(-log(nu))&
& **(-1.5d0)*(T_b - Ts_b)**(-2.5d0)*erf(sqrt(-log(nu))*sqrt(T_b -&
& Ts_b)) + 4.0d0*Ts_b**2*delta_b**3*eta_b*nu*nu**(-T_b)*1.0/(-log(&
& nu))*(T_b - Ts_b)**(-2.0d0) + 1.0d0*Ts_b**2*delta_b**2*eta_b*h_b*&
& nu*nu**(-Ts_b)*(-log(nu))**(-2.0d0)*(T_b - Ts_b)**(-2.0d0)*log(nu&
& ) + 1.0d0*Ts_b**2*delta_b**2*eta_b*h_b*nu*nu**(-Ts_b)*1.0/(-log(&
& nu))*(T_b - Ts_b)**(-2.0d0) - 1.0d0*Ts_b**2*delta_b**2*eta_b*h_b*&
& nu*nu**(-T_b)*1.0/(-log(nu))*(T_b - Ts_b)**(-2.0d0) + 1.0d0*Ts_b*&
& delta_b**3*eta_b*nu*nu**(-Ts_b)*(-log(nu))**(-2.0d0)*(T_b - Ts_b)&
& **(-2.0d0) + 2.0d0*Ts_b*delta_b**3*eta_b*nu*nu**(-Ts_b)*1.0/(T_b&
& - Ts_b)/log(nu) - 1.5d0*sqrt(pi)*Ts_b*delta_b**3*eta_b*nu*nu**(&
& -T_b)*(-log(nu))**(-2.5d0)*(T_b - Ts_b)**(-2.5d0)*erf(sqrt(-log(&
& nu))*sqrt(T_b - Ts_b)) + 2.0d0*Ts_b*delta_b**3*eta_b*nu*nu**(-T_b&
& )*(-log(nu))**(-2.0d0)*(T_b - Ts_b)**(-2.0d0) + 2.0d0*sqrt(pi)*&
& Ts_b*delta_b**3*eta_b*nu*nu**(-T_b)*sqrt(-log(nu))*(T_b - Ts_b)**&
& (-0.5d0)*erf(sqrt(-log(nu))*sqrt(T_b - Ts_b))/log(nu) - 2.0d0*&
& Ts_b*delta_b**3*eta_b*nu*nu**(-T_b)*1.0/(T_b - Ts_b)/log(nu) +&
& 1.0d0*Ts_b*delta_b**2*eta_b*h_b*nu*nu**(-Ts_b)*(-log(nu))**(&
& -2.0d0)*(T_b - Ts_b)**(-2.0d0) - 1.0d0*Ts_b*delta_b**2*eta_b*h_b*&
& nu*nu**(-T_b)*(-log(nu))**(-2.0d0)*(T_b - Ts_b)**(-2.0d0) - 1.0d0&
& *sqrt(pi)*Ts_b*delta_b**2*eta_b*h_b*nu*nu**(-T_b)*sqrt(-log(nu))*&
& (T_b - Ts_b)**(-0.5d0)*erf(sqrt(-log(nu))*sqrt(T_b - Ts_b))/log(&
& nu)
ELSEIF (nu==1.0) THEN
sigma_b = 0.466666666666665d0*T_b*delta_b**3*eta_b - 0.5d0*T_b*&
&delta_b**2*eta_b*h_b - 0.466666666666667d0*Ts_b*delta_b**3*eta_b&
& + 0.5d0*Ts_b*delta_b**2*eta_b*h_b
ELSE
ERROR_CODE = 1
ENDIF nutest
ELSE
ERROR_CODE = 1
ENDIF
END SUBROUTINE Fsigma_B
END MODULE MOBILITY_THERMAL_SKIN_RHEOLOGY