void
shell_n_dot_gradp_bc(double func[DIM],
double d_func[DIM][MAX_VARIABLE_TYPES + MAX_CONC][MDE],
const double time, /* current time */
const double dt, /* current time step size */
double xi[DIM], /* Local stu coordinates */
const Exo_DB *exo)
/***********************************************************************
*
* shell_n_dot_gradp_bc():
*
* Function which sets the pressure gradient at the side to be zero
*
* func = n .(-grad SH_FP + grad DisjPress)
*
*
* The boundary condition SHELL_FLOW_DEVELOPED_BC employs this function.
*
*
* Input:
*
* grad SH_FP = Lubrication pressure gradient
* grad_DisjPress = Disjoining pressure gradient
*
* Output:
*
* func[0] = value of the function mentioned above
* d_func[0][varType][lvardof] =
* Derivate of func[0] wrt
* the variable type, varType, and the local variable
* degree of freedom, lvardof, corresponding to that
* variable type.
*
* Author: K. Tjiptowidjojo (4/27/2011)
*
********************************************************************/
{
int j, ii, var;
int *n_dof = NULL;
int dof_map[MDE];
double grad_P[DIM];
double grad_DisjPress[DIM], dgrad_DisjPress_dH1[DIM][MDE], dgrad_DisjPress_dH2[DIM][MDE];
double phi_j;
double grad_phi_j[DIM], grad_II_phi_j[DIM];
double bound_normal[DIM];
/* Save the boundary normal vector */
for(ii = 0; ii < pd->Num_Dim; ii++)
{
bound_normal[ii] = fv->snormal[ii];
}
/*
* Prepare geometry
*/
n_dof = (int *)array_alloc (1, MAX_VARIABLE_TYPES, sizeof(int));
lubrication_shell_initialize(n_dof, dof_map, -1, xi, exo, 0);
/* Calculate pressure gradient */
Inn( fv->grad_sh_fp, grad_P );
/* Calculate disjoining pressure gradient and its sensitivities */
disjoining_pressure_model(fv->sh_fh, fv->grad_sh_fh, grad_DisjPress, dgrad_DisjPress_dH1, dgrad_DisjPress_dH2);
if (af->Assemble_LSA_Mass_Matrix)
{
return;
}
if (af->Assemble_Jacobian)
{
var = SHELL_FILMP;
if (pd->v[var])
{
for ( j=0; j<ei->dof[var]; j++)
{
for (ii = 0; ii < pd->Num_Dim; ii++)
{
grad_phi_j[ii] = bf[var]->grad_phi[j][ii];
grad_II_phi_j[ii] = 0.0;
}
Inn(grad_phi_j, grad_II_phi_j);
for (ii=0; ii<pd->Num_Dim; ii++)
{
d_func[0][var][j] += - grad_II_phi_j[ii] * bound_normal[ii];
}
}
}
var = SHELL_FILMH;
if (pd->v[var])
{
for ( j=0; j<ei->dof[var]; j++)
{
phi_j = bf[var]->phi[j];
for (ii = 0; ii < pd->Num_Dim; ii++)
{
grad_phi_j[ii] = bf[var]->grad_phi[j][ii];
grad_II_phi_j[ii] = 0.0;
}
Inn(grad_phi_j, grad_II_phi_j);
for (ii=0; ii<pd->Num_Dim; ii++)
{
d_func[0][var][j] += dgrad_DisjPress_dH1[ii][j] * grad_II_phi_j[ii] * bound_normal[ii];
d_func[0][var][j] += dgrad_DisjPress_dH2[ii][j] * phi_j * bound_normal[ii];
}
}
}
} /* end of if Assemble_Jacobian */
/* Calculate the residual contribution */
for (ii = 0; ii < pd->Num_Dim; ii++)
{
func[0] += (- grad_P[ii] + grad_DisjPress[ii]) * bound_normal[ii];
}
/* clean-up */
safe_free((void *) n_dof);
} /* END of routine shell_n_dot_gradp_bc */
void
shell_n_dot_flow_bc_confined(double func[DIM],
double d_func[DIM][MAX_VARIABLE_TYPES + MAX_CONC][MDE],
const double flowrate, /* imposed flow rate */
const double time, /* current time */
const double dt, /* current time step size */
double xi[DIM], /* Local stu coordinates */
const Exo_DB *exo)
/***********************************************************************
*
* shell_n_dot_flow_bc_confined():
*
* Function which evaluates the expression specifying the
* pressure gradient (or flow rate) at a quadrature point normal to the side
* of an element.
*
* func = - flowrate + n .( H^3 /(12*mu) * (-grad LUB_P)
* + 0.5 * (U_bot + U_top) * H )
*
* The boundary condition GRAD_LUB_PRESS_BC employs this function.
*
*
* Input:
*
* flowrate = specified on the bc card as the first float
* grad LUB_P = Lubrication pressure gradient
* U_top = Velocity of the top wall
* U_bot = Velocity of the bottom wall
* H = Distance between top and bottom wall
*
* Output:
*
* func[0] = value of the function mentioned above
* d_func[0][varType][lvardof] =
* Derivate of func[0] wrt
* the variable type, varType, and the local variable
* degree of freedom, lvardof, corresponding to that
* variable type.
*
*
* Author: K. Tjiptowidjojo (12/13/2010)
*
********************************************************************/
{
int j, ii, var;
int *n_dof = NULL;
int dof_map[MDE];
double grad_phi_j[DIM], grad_II_phi_j[DIM];
double bound_normal[DIM];
/* Save the boundary normal vector */
for(ii = 0; ii < pd->Num_Dim; ii++)
{
bound_normal[ii] = fv->snormal[ii];
}
/*
* Prepare geometry
*/
n_dof = (int *)array_alloc (1, MAX_VARIABLE_TYPES, sizeof(int));
lubrication_shell_initialize(n_dof, dof_map, -1, xi, exo, 0);
/* Calculate the flow rate and its sensitivties */
calculate_lub_q_v(R_LUBP, time, dt, xi, exo);
if (af->Assemble_LSA_Mass_Matrix)
{
return;
}
if (af->Assemble_Jacobian)
{
var = LUBP;
if (pd->v[var])
{
for ( j=0; j<ei->dof[var]; j++)
{
for (ii = 0; ii < pd->Num_Dim; ii++)
{
grad_phi_j[ii] = bf[var]->grad_phi[j][ii];
grad_II_phi_j[ii] = 0.0;
}
Inn(grad_phi_j, grad_II_phi_j);
for (ii=0; ii<pd->Num_Dim; ii++)
{
d_func[0][var][j] += LubAux->dq_dp1[ii][j] * grad_II_phi_j[ii] * bound_normal[ii];
}
}
}
} /* end of if Assemble_Jacobian */
/* Calculate the residual contribution */
func[0] = - flowrate;
for (ii = 0; ii < pd->Num_Dim; ii++)
{
func[0] += LubAux->q[ii] * bound_normal[ii];
}
/* clean-up */
safe_free((void *) n_dof);
} /* END of routine shell_n_dot_flow_bc_confined */
double
disjoining_pressure_model (double H, /* Film thickness or interfacial separation */
double grad_H[DIM], /* Film slope */
double grad_DisjPress[DIM], /* Disjoining pressure gradient */
double dgrad_DisjPress_dH1[DIM][MDE], /* Sensitivity of disjoining pressure w.r.t. film thickness */
double dgrad_DisjPress_dH2[DIM][MDE] ) /* Second derivative of disjoining pressure w.r.t. film thickness */
/******************************************************************************
*
* A function which computes disjoining pressure inside thin film
* This model is used for the lubrication capability
*
* Kris Tjiptowidjojo (January 26 2010)
*
*
******************************************************************************/
{
int i, j;
double DisjPress = 0.0;
double grad_II_H[DIM];
double angle;
double grad_angle[DIM];
double B = 0;
double dB_dangle = 0;
double f = 0;
double df_dH = 0, d2f_dH2 = 0;
double nexp;
double mexp;
double H_star;
double factor;
Inn(grad_H, grad_II_H);
memset(grad_angle, 0.0, sizeof(double)*DIM);
memset(grad_DisjPress, 0.0, sizeof(double)*DIM);
memset(dgrad_DisjPress_dH1, 0.0, sizeof(double)*DIM*MDE);
memset(dgrad_DisjPress_dH2, 0.0, sizeof(double)*DIM*MDE);
/************** CALCULATE DISJOINING PRESSURE AND ITS SENSITIVITIES **************/
if(mp->DisjPressModel == CONSTANT)
{
B = 0.0;
f = 0.0;
DisjPress = mp->DisjPress;
dB_dangle = 0.0;
df_dH = 0.0;
d2f_dH2 = 0.0;
}
else if(mp->DisjPressModel == TWO_TERM)
{
angle = mp->u_DisjPress_function_constants[0];
nexp = mp->u_DisjPress_function_constants[1];
mexp = mp->u_DisjPress_function_constants[2];
H_star = mp->u_DisjPress_function_constants[3];
factor = mp->u_DisjPress_function_constants[4];
B = (mp->surface_tension/H_star)* (nexp - 1.) * (mexp - 1.) * (1. - cos(angle * M_PIE/180.))
/ ( factor * (nexp - 1.) - (mexp - 1.) );
f = pow(H_star/H, nexp) - factor * pow(H_star/H , mexp);
DisjPress = B * f;
dB_dangle = (mp->surface_tension/H_star)* (nexp - 1.) * (mexp - 1.) * sin(angle * M_PIE/180.) * (M_PIE/180.)
/ ( factor * (nexp - 1.) - (mexp - 1.) );
df_dH = - nexp * pow(H_star,nexp)/pow(H, nexp + 1.)
+ factor * mexp * pow(H_star, mexp)/pow(H, mexp + 1.);
d2f_dH2 = nexp * (nexp + 1.) * pow(H_star,nexp)/pow(H, nexp + 2.)
- factor * mexp * (mexp + 1.) * pow(H_star, mexp)/pow(H, mexp + 2.);
}
else if(mp->DisjPressModel == TWO_TERM_EXT_CA)
{
if (!(efv->ev))
{
EH(-1,"Model TWO_TERM_EXT_CA requires contact angle input from external file !");
}
angle = fv->external_field[0];
Inn(fv->grad_ext_field[0], grad_angle);
nexp = mp->u_DisjPress_function_constants[0];
mexp = mp->u_DisjPress_function_constants[1];
H_star = mp->u_DisjPress_function_constants[2];
factor = mp->u_DisjPress_function_constants[3];
B = (mp->surface_tension/H_star)* (nexp - 1.) * (mexp - 1.) * (1. - cos(angle * M_PIE/180.))
/ ( factor * (nexp - 1.) - (mexp - 1.) );
f = pow(H_star/H, nexp) - factor * pow(H_star/H , mexp);
DisjPress = B * f;
dB_dangle = (mp->surface_tension/H_star)* (nexp - 1.) * (mexp - 1.) * sin(angle * M_PIE/180.) * (M_PIE/180.)
/ ( factor * (nexp - 1.) - (mexp - 1.) );
df_dH = - nexp * pow(H_star,nexp)/pow(H, nexp + 1.)
+ factor * mexp * pow(H_star, mexp)/pow(H, mexp + 1.);
d2f_dH2 = nexp * (nexp + 1.) * pow(H_star,nexp)/pow(H, nexp + 2.)
- factor * mexp * (mexp + 1.) * pow(H_star, mexp)/pow(H, mexp + 2.);
}
else if(mp->DisjPressModel == ONE_TERM)
{
B = mp->u_DisjPress_function_constants[0];
nexp = mp->u_DisjPress_function_constants[1];
H_star = mp->u_DisjPress_function_constants[2];
f = pow( H_star/H, nexp );
DisjPress = B * f;
dB_dangle = 0.0;
df_dH = - nexp * pow(H_star,nexp)/pow(H, nexp + 1.);
d2f_dH2 = nexp * (nexp + 1.) * pow(H_star,nexp)/pow(H, nexp + 2.);
}
else
{
EH(-1,"Not a supported disjoining pressure model");
}
/************** CALCULATE DISJOINING PRESSURE GRADIENT AND ITS SENSITIVITIES **************/
for (i = 0; i < DIM; i++)
{
grad_DisjPress[i] = dB_dangle * f * grad_angle[i]
+ B * df_dH * grad_II_H[i];
}
for (i = 0; i < DIM; i++)
{
for (j = 0; j < ei->dof[SHELL_FILMH]; j++)
{
dgrad_DisjPress_dH1[i][j] = B * df_dH;
}
}
for (i = 0; i < DIM; i++)
{
for (j = 0; j < ei->dof[SHELL_FILMH]; j++)
{
dgrad_DisjPress_dH2[i][j] = dB_dangle * df_dH * grad_angle[i]
+ B * d2f_dH2 * grad_II_H[i] ;
}
}
return(DisjPress);
}
