EXPORT void compute_body_force_x2(
Array3<double> curvature, // interface curvature
Array3<double> level_set, // level set field
Array3<double> surface_tension_body_force_x2, // x2 component of the body force due to
// CSF formulation of surface tension model
double mesh_width_x1, // grid spacing in x1 direction (uniform)
double mesh_width_x2, // grid spacing in x2 direction (uniform)
double mesh_width_x3, // grid spacing in x3 direction (uniform)
int number_primary_cells_i, // number of primary (pressure) cells in x1 direction
int number_primary_cells_j, // number of primary (pressure) cells in x2 direction
int number_primary_cells_k, // number of primary (pressure) cells in x3 direction
double rho_plus_over_rho_minus, // rho_plus / rho_minus indicated
double sigma_over_rho_minus, // sigma / rho_minus (scaled sigma)
double maximum_body_force_x2, // maximum body force in x2 direction
double total_body_force_x2, // total body force in x2 direction
double maximum_weighted_curvature, // maximum 'active' value of the curvature
// used to evaluate the capillary time step
// restriction
double smoothing_distance_factor // the smoothing distance is smoothing_distance_factor
)
{
double rho_minus_over_rho_mean= // rho_minus/( 0.5* (rho_plus + rho_minus))
2.0/(1.0+rho_plus_over_rho_minus);
double weighted_curvature=0; // curvature weighted by the derivative of
// the derivative of the heaviside of the level-set
double one_over_dx2 = // 1/(grid spacing in x2 direction)
1.0/(mesh_width_x2);
int i_index, j_index, k_index; // local variables for loop indexing
/* reset total and maximum body force */
maximum_body_force_x2=0.0;
total_body_force_x2=0.0;
/* set body force in x2 direction to zero */
set_constant_matrix2(number_primary_cells_i+2,number_primary_cells_j+1, number_primary_cells_k+2,
surface_tension_body_force_x2, 0.0);
for(i_index=1;i_index<number_primary_cells_i+1;i_index++)
{
for(j_index=0;j_index<number_primary_cells_j+1;j_index++)
{
for(k_index=1;k_index<number_primary_cells_k+1;k_index++)
{
/* weight the curvature with the derivative of the heaviside function */
/* this basically makes it only 'active' near the interface */
weighted_curvature=0.5*( curvature[i_index][j_index][k_index]+
curvature[i_index][j_index+1][k_index])*
computed_derivative_heaviside_function(
level_set[i_index][j_index][k_index],
level_set[i_index][j_index+1][k_index],
mesh_width_x1, mesh_width_x2, mesh_width_x3,
smoothing_distance_factor);
/* the surface tension body force is */
/* 2 * sigma * dPhi / dx * kappa * delta_a / (rho_p + rho_m) */
surface_tension_body_force_x2[i_index][j_index][k_index]=
-1.0*rho_minus_over_rho_mean*sigma_over_rho_minus*
one_over_dx2*(level_set[i_index][j_index+1][k_index]-
level_set[i_index][j_index][k_index])*
weighted_curvature;
/* update the maximum body force in the x2 direction */
maximum_body_force_x2=std::max(maximum_body_force_x2,
fabs(surface_tension_body_force_x2[i_index][j_index][k_index]));
/* update the maximum weighted curvature in the x2 direction */
maximum_weighted_curvature=std::max(maximum_weighted_curvature,
fabs(weighted_curvature));
total_body_force_x2+=surface_tension_body_force_x2[i_index][j_index][k_index];
}
}
}
// std::cerr<< " maximum body force x2 direction "<< maximum_body_force_x2 <<"\n";
// std::cerr<< " maximum weighted curvature x2 "<< maximum_weighted_curvature <<"\n";
}
EXPORT void compute_level_set_gradient(
Array3<double> level_set, // level set field at new time level
// after convection and reinitialization
// not mass conserving
Array3<double> d_level_set_d_x1, // first partial derivative of
// the level-set field wrt x1
// second order central approximation
Array3<double> d_level_set_d_x2, // first partial derivative of
// the level-set field wrt x2
// second order central approximation
Array3<double> d_level_set_d_x3, // first partial derivative of
// the level-set field wrt x3
// second order central approximation
int number_primary_cells_i, // number of primary (pressure) cells in x1 direction
int number_primary_cells_j, // number of primary (pressure) cells in x2 direction
int number_primary_cells_k // number of primary (pressure) cells in x3 direction
)
{
int i_index, j_index, k_index; // local variables for loop indexing
// int vector_length= // length of the one dimensional array
// (number_primary_cells_i+2)* // that results from reshaping the 3D
// (number_primary_cells_j+2)* // array of unknowns, with 1 virtual cell
// (number_primary_cells_k+2); // on all sides
/* set all first derivatives to zero, this takes care of all the virtual cells */
set_constant_matrix2(number_primary_cells_i+2, number_primary_cells_j+2,
number_primary_cells_k+2, d_level_set_d_x1, 0.0);
set_constant_matrix2(number_primary_cells_i+2, number_primary_cells_j+2,
number_primary_cells_k+2, d_level_set_d_x2, 0.0);
set_constant_matrix2(number_primary_cells_i+2, number_primary_cells_j+2,
number_primary_cells_k+2, d_level_set_d_x3, 0.0);
/* compute the gradient in all nonvirtual cells, using a central approximation */
/* to the first derivative */
/* note the nonvirtual cells start at index 1 and end at index number_primary_cells_* */
for(i_index=1;i_index<number_primary_cells_i+1;i_index++)
{
for(j_index=1;j_index<number_primary_cells_j+1;j_index++)
{
for(k_index=1;k_index<number_primary_cells_k+1;k_index++)
{
d_level_set_d_x1[i_index][j_index][k_index]=
0.5*(level_set[i_index+1][j_index ][k_index ]-
level_set[i_index-1][j_index ][k_index ]);
d_level_set_d_x2[i_index][j_index][k_index]=
0.5*(level_set[i_index ][j_index+1][k_index ]-
level_set[i_index ][j_index-1][k_index ]);
d_level_set_d_x3[i_index][j_index][k_index]=
0.5*(level_set[i_index ][j_index ][k_index+1]-
level_set[i_index ][j_index ][k_index-1]);
}
}
}
}
EXPORT int modify_volume_of_fluid_values(
Array3<double> level_set, // level-set field
Array3<double> volume_of_fluid, // volume of fluid field, uncorrected
// so with possible vapour cells and
// under/overfilled cells
Array3<double> volume_of_fluid_correction, // correction to the volume of fluid field
// to make it valid
Array3<double> invalid_vof_cells, // indication field to show what is wrong
// indicator field showing cells that are either
// within bounds =0
// underfilled =-1
// overfilled =+1
// vapour cells = 5
double mesh_width_x1, // grid spacing in x1 direction (uniform)
double mesh_width_x2, // grid spacing in x2 direction (uniform)
double mesh_width_x3, // grid spacing in x3 direction (uniform)
int number_primary_cells_i, // number of primary (pressure) cells in x1 direction
int number_primary_cells_j, // number of primary (pressure) cells in x2 direction
int number_primary_cells_k, // number of primary (pressure) cells in x3 direction
double volume_of_fluid_tolerance // tolerance for volume of fluid value
)
{
double current_level_set_value; // current level-set field value in the control volume
double current_volume_of_fluid_value; // current volume of fluid field value in
// the control volume
double correct_vof_value; // the value a cell with an invalid volume of
// fluid is set to: 1, 0 dependent on the sign
// of the level-set function
int number_cells_vof_out_of_bounds=0; // number of control volumes where the volume of fluid
// function is OUTSIDE the interval [0,1]
int number_cells_numerical_vapor=0; // number of control volumes where the volume of fluid
// function is INSIDE the interval [0,1]
// while the cell has 6 neighbours with the same sign:
// the cell is NOT an interface cell
int number_cells_invalid_volume_of_fluid; // sum of number of vapour cells and number of cells
int i_index, j_index, k_index; // local variables for loop indexing
int adapt_vof_value; // =1 adapt the volume of fluid value in this
// cell, because it has an invalid value
bool detailed_output=0; // =1, provide detailed output
// =0, provide non output
/* we start with the assumption that all volume of fluid values are valid */
set_constant_matrix2(number_primary_cells_i+2, number_primary_cells_j+2,
number_primary_cells_k+2, invalid_vof_cells, 0.0);
set_constant_matrix2(number_primary_cells_i+2, number_primary_cells_j+2,
number_primary_cells_k+2, volume_of_fluid_correction, 0.0);
/* all nonvirtual cells are modified */
/* the required modification is stored in volume_of_fluid_correction */
for(i_index=1;i_index<number_primary_cells_i+1;i_index++)
{
for(j_index=1;j_index<number_primary_cells_j+1;j_index++)
{
for(k_index=1;k_index<number_primary_cells_k+1;k_index++)
{
current_level_set_value=level_set[i_index][j_index][k_index];
current_volume_of_fluid_value=volume_of_fluid[i_index][j_index][k_index];
/* assume the cell has a valid vof value */
adapt_vof_value=0;
/* check if the cell is a vapour cell, when this update is applied */
if(
/* is the cell surrounded by neighbours with the same sign ?*/
(
(level_set[i_index-1][j_index ][k_index ]*current_level_set_value>0)&&
(level_set[i_index+1][j_index ][k_index ]*current_level_set_value>0)&&
(level_set[i_index ][j_index-1][k_index ]*current_level_set_value>0)&&
(level_set[i_index ][j_index+1][k_index ]*current_level_set_value>0)&&
(level_set[i_index ][j_index ][k_index+1]*current_level_set_value>0)&&
(level_set[i_index ][j_index ][k_index-1]*current_level_set_value>0)
)
&&
/* is the volume of fluid at the same time in the OPEN interval <0,1>? */
(current_volume_of_fluid_value<(1.0-volume_of_fluid_tolerance) &&
current_volume_of_fluid_value>(0.0+volume_of_fluid_tolerance))
)
{
/* then the cell is a vapour cell, and the volume_of_fluid_correction is not correct yet */
/* additional iterations are required */
/* update the number of vapour cells */
number_cells_numerical_vapor++;
adapt_vof_value=1;
invalid_vof_cells[i_index][j_index][k_index]=5.0;
}
if( (current_volume_of_fluid_value> 1.0+volume_of_fluid_tolerance)||
(current_volume_of_fluid_value < 0.0-volume_of_fluid_tolerance))
{
/* the volume of fluid value is out of bounds */
/* additional iterations are required */
/* update the number of out of bounds cells */
number_cells_vof_out_of_bounds++;
adapt_vof_value=1;
if(current_volume_of_fluid_value> 1.0+volume_of_fluid_tolerance)
{
invalid_vof_cells[i_index][j_index][k_index]=1.0;
}
else
{
invalid_vof_cells[i_index][j_index][k_index]=-1.0;
}
}
if(adapt_vof_value)
{
/* cell is either a vapour cell or an over/under filled cell */
/* the correct value shoul be either 1/0 depending on the sign */
/* of the level-set field */
correct_vof_value=0.5+sign(0.5,current_level_set_value);
if(current_level_set_value==0.0)
{
/* this is not really very likely to happen but still */
correct_vof_value=0.5;
}
volume_of_fluid_correction[i_index][j_index][k_index]=
volume_of_fluid[i_index][j_index][k_index]-correct_vof_value;
volume_of_fluid[i_index][j_index][k_index]=correct_vof_value;
}
}
}
}
number_cells_invalid_volume_of_fluid=number_cells_numerical_vapor+number_cells_vof_out_of_bounds;
/* for debugging mode show detailed output */
if(detailed_output)
{
dump_redistribution_for_debugging(level_set, volume_of_fluid,
level_set, invalid_vof_cells, volume_of_fluid_correction,
number_primary_cells_i, number_primary_cells_j, number_primary_cells_k,
mesh_width_x1, mesh_width_x2, mesh_width_x3, 1 );
for(i_index=1;i_index<number_primary_cells_i+1;i_index++)
{
for(j_index=1;j_index<number_primary_cells_j+1;j_index++)
{
for(k_index=1;k_index<number_primary_cells_k+1;k_index++)
{
if( fabs(invalid_vof_cells[i_index][j_index][k_index]-5.0)<0.0001)
{
std::cerr.setf(std::ios::scientific);
std::cerr<<" this is vapour cell "<< i_index <<" "<< j_index <<" "<<k_index <<" "<<level_set[i_index][j_index][k_index]<<" "<<volume_of_fluid[i_index][j_index][k_index] <<"\n";
std::cerr<<"with neighbours: level-set vof \n";
std::cerr<<" [i_index+1][j_index ][k_index ] "<<level_set[i_index+1][j_index ][k_index ]<< " "<<volume_of_fluid[i_index+1][j_index ][k_index ]<<"\n";
std::cerr<<" [i_index-1][j_index ][k_index ] "<<level_set[i_index-1][j_index ][k_index ]<< " "<<volume_of_fluid[i_index-1][j_index ][k_index ]<<"\n";
std::cerr<<" [i_index ][j_index+1][k_index ] "<<level_set[i_index ][j_index+1][k_index ]<< " "<<volume_of_fluid[i_index ][j_index+1][k_index ]<<"\n";
std::cerr<<" [i_index ][j_index-1][k_index ] "<<level_set[i_index ][j_index-1][k_index ]<< " "<<volume_of_fluid[i_index ][j_index+1][k_index ]<<"\n";
std::cerr<<" [i_index ][j_index ][k_index+1] "<<level_set[i_index ][j_index ][k_index+1]<< " "<<volume_of_fluid[i_index ][j_index ][k_index+1]<<"\n";
std::cerr<<" [i_index ][j_index ][k_index-1] "<<level_set[i_index ][j_index ][k_index-1]<< " "<<volume_of_fluid[i_index ][j_index ][k_index+1]<<"\n";
}
}
}
}
}
return number_cells_invalid_volume_of_fluid;
}
int main()
{
Array3<double> level_set; // level-set field
Array3<double> pressure; // pressure field
Array3<double> u_1_velocity_old; // velocity field at old time level x1 direction
Array3<double> u_2_velocity_old; // velocity field at old time level x2 direction
Array3<double> u_3_velocity_old; // velocity field at old time level x3 direction
Array3<double> u_1_velocity_new; // velocity field at new time level x1 direction
Array3<double> u_2_velocity_new; // velocity field at new time level x2 direction
Array3<double> u_3_velocity_new; // velocity field at new time level x3 direction
Array3<double> momentum_source_term_u_1; // source term of the momentum equation in x1 direction
// defined on all u1 points (including boundaries)
Array3<double> momentum_source_term_u_2; // source term of the momentum equation in x2 direction
// defined on all u1 points (including boundaries)
Array3<double> momentum_source_term_u_3; // source term of the momentum equation in x3 direction
// defined on all u1 points (including boundaries)
Array3<double> surface_tension_body_force_x1; // source term of the momentum equation in x1 direction
// defined on all u1 points (including boundaries)
Array3<double> surface_tension_body_force_x2; // source term of the momentum equation in x2 direction
// defined on all u1 points (including boundaries)
Array3<double> surface_tension_body_force_x3; // source term of the momentum equation in x3 direction
// defined on all u1 points (including boundaries)
Array3<double> scaled_density_u1; // scaled density for the controlvolumes
// of the momentum equation in x1 direction
Array3<double> scaled_density_u2; // scaled density for the controlvolumes
// of the momentum equation in x2 direction
Array3<double> scaled_density_u3; // scaled density for the controlvolumes
// of the momentum equation in x3 direction
boundary_face boundary_faces[6]; // array with all the information
// for the boundary conditions
double mesh_width_x1; // grid spacing in x1 direction (uniform)
double mesh_width_x2; // grid spacing in x2 direction (uniform)
double mesh_width_x3; // grid spacing in x3 direction (uniform)
int number_primary_cells_i; // number of primary (pressure) cells in x1 direction
int number_primary_cells_j; // number of primary (pressure) cells in x2 direction
int number_primary_cells_k; // number of primary (pressure) cells in x3 direction
int number_matrix_connections = 7; // number of connections in momentum matrix
vector gravity; // gravitational acceleration vector
double actual_time_step_navier_stokes; // time step used for level-set advection
// computed from all stability restrictions and
// possibly subscycling
double rho_plus_over_rho_minus; // ratio of the densities of the two phases
double smoothing_distance_factor; // the smoothing distance is smoothing_distance_factor
// times the smallest mesh width
double rho_minus_over_mu_minus; // this was the 'Reynolds' number
// in the original implementation of Sander
double mu_plus_over_mu_minus; // ratio of the viscosities of both phases
double tolerance_pressure = 1e-8; // the tolerance with which the system for the pressure is solved
int maximum_iterations_allowed_pressure=1e3; // maximum number of iterations allowed for the
// conjugate gradient method
double tolerance_velocity=1e-7; // the tolerance with which the system for the momentum predictor is solved
int maximum_iterations_allowed_velocity=1e2; // maximum number of iterations allowed for the
// conjugate gradient method
int continuous_surface_force_model = 1; // =1, the continuous surface force model is applied
// =0, the exact interface boundary conditions are applied
int source_terms_in_momentum_predictor =1; // =1, the source terms are applied in the momentum predictor
// equation
// =0, the source terms are applied in the momentum corrector
// equation
vector initial_velocity; // some initial velocity to fill the arrays
int i, j, k; // local variables for loop indexing
double x,y,z; // coordinates
double x_length = 1;
double y_length = 2;
double z_length = 3;
double a,b,c,d,e,f,g,h,l,m,n,o,p,q,r,s,t,u; // input coefficients
double u_1, u_2, u_3;
double viscosity_over_density;
double output_polynomial;
double scaled_density_constant = 1;
initial_velocity.u1 = 0.0;
initial_velocity.u2 = 0.0;
initial_velocity.u3 = 0.0;
smoothing_distance_factor = 2;
rho_plus_over_rho_minus = 10.0;
rho_minus_over_mu_minus = 1e20;
mu_plus_over_mu_minus = 1;
gravity.u1 = 00.0;
gravity.u2 = 00.0;
gravity.u3 = 00.0;
actual_time_step_navier_stokes = 0.1;
set_boundary_conditions(boundary_faces, initial_velocity);
// set_boundary_conditions(boundary_face[6], initial_velocity);
number_primary_cells_i = pow(2,1);
number_primary_cells_j = pow(2,2);
number_primary_cells_k = pow(2,2);
mesh_width_x1 = x_length/number_primary_cells_i;
mesh_width_x2 = y_length/number_primary_cells_j;
mesh_width_x3 = z_length/number_primary_cells_k;
viscosity_over_density = (1/scaled_density_constant)*compute_scaled_viscosity(100,mesh_width_x1,mesh_width_x2,mesh_width_x3, smoothing_distance_factor, rho_minus_over_mu_minus,mu_plus_over_mu_minus);
level_set.create(number_primary_cells_i+2,number_primary_cells_j+2,number_primary_cells_k+2);
set_constant_matrix2(number_primary_cells_i+2, number_primary_cells_j+2,
number_primary_cells_k+2, level_set, 0.1);
pressure.create(number_primary_cells_i+2, number_primary_cells_j+2, number_primary_cells_k+2);
set_constant_matrix2(number_primary_cells_i+2, number_primary_cells_j+2,
number_primary_cells_k+2, pressure, 10000.0);
// velocity old
u_1_velocity_old.create(number_primary_cells_i+1, number_primary_cells_j+2, number_primary_cells_k+2);
u_2_velocity_old.create(number_primary_cells_i+2, number_primary_cells_j+1, number_primary_cells_k+2);
u_3_velocity_old.create(number_primary_cells_i+2, number_primary_cells_j+2, number_primary_cells_k+1);
set_constant_matrix2(number_primary_cells_i+1, number_primary_cells_j+2,
number_primary_cells_k+2, u_1_velocity_old, initial_velocity.u1);
set_constant_matrix2(number_primary_cells_i+2, number_primary_cells_j+1,
number_primary_cells_k+2, u_2_velocity_old, initial_velocity.u2);
set_constant_matrix2(number_primary_cells_i+2, number_primary_cells_j+2,
number_primary_cells_k+1, u_3_velocity_old, initial_velocity.u3);
// multiple input sets of parameters
// a=1; b=2; c=3; d=4; e=5; f=6; g=7; h=8; l=9; m=1; n=2; o=3; p=4; q=5; r=6; s=7; t=8; u=9; // full test
a=0; b=0; c=3; d=4; e=5; f=6; g=7; h=8; l=0; m=0; n=-3; o=3; p=4; q=5; r=6; s=7; t=0; u=0; // divergence free velocity input b+m+n = 0
// a=0; b=2; c=0; d=4; e=0; f=6; g=0; h=8; l=0; m=1; n=0; o=3; p=0; q=5; r=0; s=7; t=0; u=9; // linear test
// a=0; b=0; c=0; d=0; e=0; f=0; g=0; h=1; l=0; m=0; n=0; o=0; p=0; q=0; r=0; s=0; t=0; u=0; // random test
// a=0; b=1; c=0; d=0; e=0; f=0; g=0; h=0; l=0; m=0; n=0; o=0; p=0; q=0; r=0; s=0; t=0; u=0; // random test
// a=1; b=2; c=3; d=4; e=5; f=6; g=7; h=8; l=9; m=1; n=2; o=3; p=4; q=5; r=6; s=7; t=8; u=9; // test for diffusion, only quadratic terms
for(i=0;i<number_primary_cells_i+2;i++)
{
for(j=0;j<number_primary_cells_j+2;j++)
{
for(k=0;k<number_primary_cells_k+2;k++)
{
x = x_length * i/number_primary_cells_i -0.5*mesh_width_x1;
// printf("x = %f \n",x);
y = y_length * j/number_primary_cells_j -0.5*mesh_width_x2;
// printf("y = %f \n",y);
z = z_length * k/number_primary_cells_k -0.5*mesh_width_x3;
if(i!=number_primary_cells_i+1)
{x += 0.5*mesh_width_x1;
// printf("x = %f \t",x);
u_1_velocity_old[i][j][k]= a*x*x+b*x +c*y*y+d*y +e*z*z+f*z; // 1st test
// u_1_velocity_old[i][j][k]= a*x*x+b*y*y+c*z*z +d*x*y+e*x*z +f*y*z; // 2nd test, only quadratic terms
// printf("u_1 = %f \n", u_1_velocity_old[i][j][k]);
x -= 0.5*mesh_width_x1;}
if(j!=number_primary_cells_j+1)
{y += 0.5*mesh_width_x2;
u_2_velocity_old[i][j][k]= g*x*x+h*x +l*y*y+m*y +n*z*z+o*z; // 1st test
// u_2_velocity_old[i][j][k]= g*x*x+h*y*y+l*z*z +m*x*y+n*x*z +o*y*z; // 2nd test, only quadratic terms
y -= 0.5*mesh_width_x2;}
if(k!=number_primary_cells_k+1)
{z += 0.5*mesh_width_x3;
u_3_velocity_old[i][j][k]= p*x*x+q*x +r*y*y+s*y +t*z*z+u*z; // 1st test
// u_3_velocity_old[i][j][k]= p*x*x+q*y*y+r*z*z +s*x*y+t*x*z +u*y*z; // 2nd test, only quadratic terms
z -= 0.5*mesh_width_x3;}
}
}
}
// velocity new
u_1_velocity_new.create(number_primary_cells_i+1, number_primary_cells_j+2, number_primary_cells_k+2);
u_2_velocity_new.create(number_primary_cells_i+2, number_primary_cells_j+1, number_primary_cells_k+2);
u_3_velocity_new.create(number_primary_cells_i+2, number_primary_cells_j+2, number_primary_cells_k+1);
set_constant_matrix2(number_primary_cells_i+1, number_primary_cells_j+2,
number_primary_cells_k+2, u_1_velocity_new, initial_velocity.u1);
set_constant_matrix2(number_primary_cells_i+2, number_primary_cells_j+1,
number_primary_cells_k+2, u_2_velocity_new, initial_velocity.u2);
set_constant_matrix2(number_primary_cells_i+2, number_primary_cells_j+2,
number_primary_cells_k+1, u_3_velocity_new, initial_velocity.u3);
// momentum source terms
momentum_source_term_u_1.create(number_primary_cells_i+1, number_primary_cells_j+2, number_primary_cells_k+2);
momentum_source_term_u_2.create(number_primary_cells_i+2, number_primary_cells_j+1, number_primary_cells_k+2);
momentum_source_term_u_3.create(number_primary_cells_i+2, number_primary_cells_j+2, number_primary_cells_k+1);
set_constant_matrix2(number_primary_cells_i+1, number_primary_cells_j+2,
number_primary_cells_k+2, momentum_source_term_u_1, 0.0);
set_constant_matrix2(number_primary_cells_i+2, number_primary_cells_j+1,
number_primary_cells_k+2, momentum_source_term_u_2, 0.0);
set_constant_matrix2(number_primary_cells_i+2, number_primary_cells_j+2,
number_primary_cells_k+1, momentum_source_term_u_3, 0.0);
// surface_tension_body_force
surface_tension_body_force_x1.create(number_primary_cells_i+1, number_primary_cells_j+2, number_primary_cells_k+2);
surface_tension_body_force_x2.create(number_primary_cells_i+2, number_primary_cells_j+1, number_primary_cells_k+2);
surface_tension_body_force_x3.create(number_primary_cells_i+2, number_primary_cells_j+2, number_primary_cells_k+1);
set_constant_matrix2(number_primary_cells_i+1, number_primary_cells_j+2,
number_primary_cells_k+2, surface_tension_body_force_x1, 0);
set_constant_matrix2(number_primary_cells_i+2, number_primary_cells_j+1,
number_primary_cells_k+2, surface_tension_body_force_x2, 0);
set_constant_matrix2(number_primary_cells_i+2, number_primary_cells_j+2,
number_primary_cells_k+1, surface_tension_body_force_x3, 0);
// scaled density
scaled_density_u1.create(number_primary_cells_i+1, number_primary_cells_j+2, number_primary_cells_k+2);
scaled_density_u2.create(number_primary_cells_i+2, number_primary_cells_j+1, number_primary_cells_k+2);
scaled_density_u3.create(number_primary_cells_i+2, number_primary_cells_j+2, number_primary_cells_k+1);
set_constant_matrix2(number_primary_cells_i+1, number_primary_cells_j+2,
number_primary_cells_k+2, scaled_density_u1, 1);
set_constant_matrix2(number_primary_cells_i+2, number_primary_cells_j+1,
number_primary_cells_k+2, scaled_density_u2, 1);
set_constant_matrix2(number_primary_cells_i+2, number_primary_cells_j+2,
number_primary_cells_k+1, scaled_density_u3, 1);
advance_flow_field(level_set, pressure,
u_1_velocity_old, u_2_velocity_old, u_3_velocity_old,
u_1_velocity_new, u_2_velocity_new, u_3_velocity_new,
momentum_source_term_u_1, momentum_source_term_u_2, momentum_source_term_u_3,
surface_tension_body_force_x1, surface_tension_body_force_x2, surface_tension_body_force_x3,
scaled_density_u1, scaled_density_u2, scaled_density_u3,
boundary_faces,
mesh_width_x1, mesh_width_x2, mesh_width_x3,
number_primary_cells_i, number_primary_cells_j, number_primary_cells_k,
number_matrix_connections, gravity,
actual_time_step_navier_stokes,
rho_plus_over_rho_minus,
smoothing_distance_factor,
rho_minus_over_mu_minus, mu_plus_over_mu_minus,
tolerance_pressure, maximum_iterations_allowed_pressure,
tolerance_velocity, maximum_iterations_allowed_velocity,
continuous_surface_force_model,
source_terms_in_momentum_predictor
);
// check for u,v,w momentum
for(i=1;i<number_primary_cells_i+1;i++)
{
for(j=1;j<number_primary_cells_j+1;j++)
{
for(k=1;k<number_primary_cells_k+1;k++)
{
x = x_length * i/number_primary_cells_i -0.5*mesh_width_x1;
y = y_length * j/number_primary_cells_j -0.5*mesh_width_x2;
z = z_length * k/number_primary_cells_k -0.5*mesh_width_x3;
printf("\n i=%i j=%i k=%i \n", i,j,k);
if(i!=number_primary_cells_i){
x += 0.5*mesh_width_x1;
u_1 = a*x*x+b*x +c*y*y+d*y +e*z*z+f*z;
u_2 = g*x*x+h*x +l*y*y+m*y +n*z*z+o*z;
u_3 = p*x*x+q*x +r*y*y+s*y +t*z*z+u*z;
output_polynomial = 2*u_1*(2*a*x+b) + u_1*(2*y*l+m) + u_2*(2*y*c+d) + u_1*(2*z*t+u) + u_3*(2*z*e+f) +viscosity_over_density*(2*2*a+2*c+2*e); // 1st test
// output_polynomial = viscosity_over_density*(4*a+2*b+m+2*c+t); // 2nd test, only quadratic terms
x -= 0.5*mesh_width_x1;
printf("\n u_1_velocity_old = %f \n", u_1);
printf("u_1_velocity_new = %f \n", u_1_velocity_new[i][j][k]);
printf("new - old = %f \n", u_1_velocity_new[i][j][k]-u_1);
printf("polynomial = %f \n", output_polynomial);
}
if(j!=number_primary_cells_j){
y += 0.5*mesh_width_x2;
u_1 = a*x*x+b*x +c*y*y+d*y +e*z*z+f*z;
u_2 = g*x*x+h*x +l*y*y+m*y +n*z*z+o*z;
u_3 = p*x*x+q*x +r*y*y+s*y +t*z*z+u*z;
output_polynomial = u_1*(2*x*g+h)+u_2*(2*x*a+b) + 2*u_2*(2*y*l+m) + u_3*(2*z*n+o)+u_2*(2*z*t+u) +viscosity_over_density*(2*2*l+2*g+2*n); // 1st test
// output_polynomial = viscosity_over_density*(4*h+2*g+d+2*l+u); // 2nd test, only quadratic terms
y -= 0.5*mesh_width_x2;
printf(" \n u_2_velocity_old = %f \n", u_2);
printf("u_2_velocity_new = %f \n", u_2_velocity_new[i][j][k]);
printf("new - old = %f \n", u_2_velocity_new[i][j][k]-u_2);
printf("polynomial = %f \n", output_polynomial);
}
if(k!=number_primary_cells_k){
z += 0.5*mesh_width_x3;
u_1 = a*x*x+b*x +c*y*y+d*y +e*z*z+f*z;
u_2 = g*x*x+h*x +l*y*y+m*y +n*z*z+o*z;
u_3 = p*x*x+q*x +r*y*y+s*y +t*z*z+u*z;
output_polynomial = u_1*(2*x*p+q)+u_3*(2*x*a+b) + u_2*(2*y*r+s)+u_3*(2*y*l+m) + 2*u_3*(2*z*t+u) +viscosity_over_density*(2*2*t+2*p+2*r); // 1st test
// output_polynomial = viscosity_over_density*(4*r+2*p+e+2*q+o); // 2nd test, only quadratic terms
z -= 0.5*mesh_width_x3;
printf("\n u_3_velocity_old = %f \n", u_3);
printf("u_3_velocity_new = %f \n", u_3_velocity_new[i][j][k]);
printf("new - old = %f \n", u_3_velocity_new[i][j][k]-u_3);
printf("polynomial = %f \n", output_polynomial);
}
}}}
// printf("u_1_velocity_new = %f \n", u_1_velocity_new[i][j][k]);
// printf("u_2_velocity_old = %f \n", u_2_velocity_old[i][j][k]);
// printf("u_2_velocity_new = %f \n", u_2_velocity_new[i][j][k]);
// printf("u_3_velocity_old = %f \n", u_3_velocity_old[i][j][k]);
// printf("u_3_velocity_new = %f \n", u_3_velocity_new[i][j][k]);
// printf("pressure = %f \n", pressure[i][j][k]);
printf("%s \n", "advance_flow_field_unit_test finish");
return 0;
}
EXPORT void solve_momentum_predictor_rk(
Array3<double> u_1_velocity_star, // velocity field at star time level x1 direction
Array3<double> u_2_velocity_star, // velocity field at star time level x2 direction
Array3<double> u_3_velocity_star, // velocity field at star time level x3 direction
Array3<double> u_1_velocity_old, // velocity field at old time level x1 direction
Array3<double> u_2_velocity_old, // velocity field at old time level x2 direction
Array3<double> u_3_velocity_old, // velocity field at old time level x3 direction
Array3<double> scaled_density_u1, // scaled density for the controlvolumes
Array3<double> scaled_density_u2, // scaled density for the controlvolumes
Array3<double> scaled_density_u3, // scaled density for the controlvolumes
Array3<double> momentum_source_term_u_1, // source term of the momentum equation in x1 direction
// defined on all u1 points (including boundaries)
Array3<double> momentum_source_term_u_2, // source term of the momentum equation in x2 direction
// defined on all u1 points (including boundaries)
Array3<double> momentum_source_term_u_3, // source term of the momentum equation in x3 direction
// defined on all u1 points (including boundaries)
Array3<double> level_set, // level-set field
double actual_time_step_navier_stokes, // time step used for level-set advection
// computed from all stability restrictions and
// possibly subscycling
int number_primary_cells_i, // number of primary (pressure) cells in x1 direction
int number_primary_cells_j, // number of primary (pressure) cells in x2 direction
int number_primary_cells_k, // number of primary (pressure) cells in x3 direction
double mesh_width_x1, // grid spacing in x1 direction (uniform)
double mesh_width_x2, // grid spacing in x2 direction (uniform)
double mesh_width_x3, // grid spacing in x3 direction (uniform)
double smoothing_distance_factor, // the smoothing distance is smoothing_distance_factor
double rho_plus_over_rho_minus, // ratio of the densities of the two phases
double rho_minus_over_mu_minus, // this was the 'Reynolds' number
// in the original implementation of Sander
double mu_plus_over_mu_minus, // ratio of the viscosities of both phases
boundary_face boundary_faces[6], // array with all the information
// for the boundary conditions
int source_terms_in_momentum_predictor, // =1, the source terms are applied in the momentum predictor
// equation
// =0, the source terms are applied in the momentum corrector
// equation
double actual_time // actual time
)
{
double sigma, zeta;
double actual_time_in_RK; // actual time used to evaluate the boundary conditon
Array3<double> u_1_old_con_diff; // contains the convection and diffusion terms of a previous RK-stage in the x1 direction
Array3<double> u_2_old_con_diff; // contains the convection and diffusion terms of a previous RK-stage in the x2 direction
Array3<double> u_3_old_con_diff; // contains the convection and diffusion terms of a previous RK-stage in the x3 direction
u_1_old_con_diff.create(number_primary_cells_i+1, number_primary_cells_j+2, number_primary_cells_k+2);
u_2_old_con_diff.create(number_primary_cells_i+2, number_primary_cells_j+1, number_primary_cells_k+2);
u_3_old_con_diff.create(number_primary_cells_i+2, number_primary_cells_j+2, number_primary_cells_k+1);
set_constant_matrix2(number_primary_cells_i+1, number_primary_cells_j+2, number_primary_cells_k+2, u_1_old_con_diff, 0.0);
set_constant_matrix2(number_primary_cells_i+2, number_primary_cells_j+1, number_primary_cells_k+2, u_2_old_con_diff, 0.0);
set_constant_matrix2(number_primary_cells_i+2, number_primary_cells_j+2, number_primary_cells_k+1, u_3_old_con_diff, 0.0);
Array3<double> u_1_new_con_diff; // contains the convection and diffusion terms of a RK-stage in the x1 direction
Array3<double> u_2_new_con_diff; // contains the convection and diffusion terms of a RK-stage in the x2 direction
Array3<double> u_3_new_con_diff; // contains the convection and diffusion terms of a RK-stage in the x3 direction
u_1_new_con_diff.create(number_primary_cells_i+1, number_primary_cells_j+2, number_primary_cells_k+2);
u_2_new_con_diff.create(number_primary_cells_i+2, number_primary_cells_j+1, number_primary_cells_k+2);
u_3_new_con_diff.create(number_primary_cells_i+2, number_primary_cells_j+2, number_primary_cells_k+1);
set_constant_matrix2(number_primary_cells_i+1, number_primary_cells_j+2, number_primary_cells_k+2, u_1_new_con_diff, 0.0);
set_constant_matrix2(number_primary_cells_i+2, number_primary_cells_j+1, number_primary_cells_k+2, u_2_new_con_diff, 0.0);
set_constant_matrix2(number_primary_cells_i+2, number_primary_cells_j+2, number_primary_cells_k+1, u_3_new_con_diff, 0.0);
// first step Runge-Kutta
sigma = 8.0/15.0; // parameter for new stage
zeta = 0.0; // parameter for previous stage
actual_time_in_RK = actual_time+(sigma+zeta-1)*actual_time_step_navier_stokes;
forward_euler(
u_1_velocity_star,u_2_velocity_star,u_3_velocity_star,
u_1_new_con_diff,u_2_new_con_diff,u_3_new_con_diff,
u_1_velocity_old,u_2_velocity_old,u_3_velocity_old,
u_1_old_con_diff,u_2_old_con_diff,u_3_old_con_diff,
scaled_density_u1,scaled_density_u2,scaled_density_u3,
momentum_source_term_u_1,momentum_source_term_u_2,momentum_source_term_u_3,
level_set, actual_time_step_navier_stokes,
sigma,zeta,
number_primary_cells_i,number_primary_cells_j,number_primary_cells_k,
mesh_width_x1,mesh_width_x2,mesh_width_x3,
smoothing_distance_factor,
rho_plus_over_rho_minus,rho_minus_over_mu_minus,mu_plus_over_mu_minus,
boundary_faces, source_terms_in_momentum_predictor,
actual_time_in_RK
);
// second step Runge-Kutta
Array3<double> u_1_velocity_star_star; // velocity field at star_star time level x1 direction
Array3<double> u_2_velocity_star_star; // velocity field at star_star time level x2 direction
Array3<double> u_3_velocity_star_star; // velocity field at star_star time level x3 direction
/* allocate memory for tentative velocity field u star_star */
u_1_velocity_star_star.create(number_primary_cells_i+1, number_primary_cells_j+2, number_primary_cells_k+2);
u_2_velocity_star_star.create(number_primary_cells_i+2, number_primary_cells_j+1, number_primary_cells_k+2);
u_3_velocity_star_star.create(number_primary_cells_i+2, number_primary_cells_j+2, number_primary_cells_k+1);
sigma = 5.0/12.0; // parameter for new stage
zeta = -17.0/60.0; // parameter for previous stage
actual_time_in_RK = actual_time_in_RK + (sigma+zeta)*actual_time_step_navier_stokes;
forward_euler(
u_1_velocity_star_star,u_2_velocity_star_star,u_3_velocity_star_star,
u_1_new_con_diff,u_2_new_con_diff,u_3_new_con_diff,
u_1_velocity_star,u_2_velocity_star,u_3_velocity_star,
u_1_old_con_diff,u_2_old_con_diff,u_3_old_con_diff,
scaled_density_u1,scaled_density_u2,scaled_density_u3,
momentum_source_term_u_1,momentum_source_term_u_2,momentum_source_term_u_3,
level_set, actual_time_step_navier_stokes,
sigma,zeta,
number_primary_cells_i,number_primary_cells_j,number_primary_cells_k,
mesh_width_x1,mesh_width_x2,mesh_width_x3,
smoothing_distance_factor,
rho_plus_over_rho_minus,rho_minus_over_mu_minus,mu_plus_over_mu_minus,
boundary_faces, source_terms_in_momentum_predictor,
actual_time_in_RK
);
// third step Runge-Kutta
sigma = 3.0/4.0; // parameter for new stage
zeta = -5.0/12.0; // parameter for previous stage
actual_time_in_RK = actual_time_in_RK + (sigma+zeta)*actual_time_step_navier_stokes;
forward_euler(
u_1_velocity_star,u_2_velocity_star,u_3_velocity_star, // u_star is reused to reduce the number of allocations it can also be seen as u_star_star_star
u_1_new_con_diff,u_2_new_con_diff,u_3_new_con_diff,
u_1_velocity_star_star,u_2_velocity_star_star,u_3_velocity_star_star,
u_1_old_con_diff,u_2_old_con_diff,u_3_old_con_diff,
scaled_density_u1,scaled_density_u2,scaled_density_u3,
momentum_source_term_u_1,momentum_source_term_u_2,momentum_source_term_u_3,
level_set, actual_time_step_navier_stokes,
sigma,zeta,
number_primary_cells_i,number_primary_cells_j,number_primary_cells_k,
mesh_width_x1,mesh_width_x2,mesh_width_x3,
smoothing_distance_factor,
rho_plus_over_rho_minus,rho_minus_over_mu_minus,mu_plus_over_mu_minus,
boundary_faces, source_terms_in_momentum_predictor,
actual_time_in_RK
);
u_1_old_con_diff.destroy();
u_2_old_con_diff.destroy();
u_3_old_con_diff.destroy();
u_1_new_con_diff.destroy();
u_2_new_con_diff.destroy();
u_3_new_con_diff.destroy();
u_1_velocity_star_star.destroy();
u_2_velocity_star_star.destroy();
u_3_velocity_star_star.destroy();
}
