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Main_openmp.cpp
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#include <iostream>
#include <stdlib.h>
#include <vector>
#include <cmath>
#include<algorithm>
#include <fstream>
#include <chrono>
#include <omp.h>
#include "Functions.h"
using namespace std;
using namespace std::chrono;
int main()
{
float binl = 0.01, ins_reg_low_x = 0, ins_reg_up_x = 0.05, ins_reg_low_y = 0, ins_reg_up_y = 0.05, ins_reg_low_z = 0, ins_reg_up_z = 1, dom_low_x = 0, dom_up_x = 0.05, dom_low_y = 0, dom_up_y = 0.05, dom_low_z = 0, dom_up_z = 1, rad_p1 = 0.005;
float dlx = dom_low_x, dux = dom_up_x, dly = dom_low_y, duy = dom_up_y, dlz = dom_low_z, duz = dom_up_z;
int no_particles, ghost_particles = 0, trialcounterlimit = 20, guessbincount = 100, no_timesteps = 5000000, dumpevery=1000,tcounter = 1, exitparticles = 0, ins_choice = 1, boundx = 3, boundy = 3, boundz = 1;
double Kn, Cn, Kt, Ct, G, pi = 2 * acos(0), timestep = pow(10, -6);
double Ym = 5 * pow(10, 8), Y, e = 0.6, poi = 0.2, m, R, density = 2500, gx =0 , gy = 0.0, gz =-1 , g = 9.81;
Functions F;
R = rad_p1 / 2;
m = (4.0 / 3.0) * pi * pow(rad_p1, 3) * density;
Y = pow((1 - pow(poi, 2)) * 2 / Ym, -1);
Kn = (4.0 / 3.0) * Y * sqrt(R);
Cn = 2 * sqrt(5.0 / 6.0) * (log(e) / sqrt(log(e) * log(e) + pi * pi)) * sqrt(2 * Y * sqrt(R) * m / 2);
G = Ym / (4 * (2 - poi) * (1 + poi));
Kt = 8 * G * sqrt(R);
Ct = 2 * sqrt(5.0 / 6.0) * (log(e) / sqrt(log(e) * log(e) + pi * pi)) * sqrt(8 * G * sqrt(R) * m / 2);
std::cout << m << " " << Kn << " " << Cn << " " << endl;
std::cout << " enter no of particles to be inserted" << endl;
cin >> no_particles;
auto start = high_resolution_clock::now(); // to measure the time span of simulation
ofstream oFile;
if (boundx == 3) // checking for periodic conditions
{
dom_low_x = dom_low_x - binl;
dom_up_x = dom_up_x + binl;
}
if (boundy == 3)
{
dom_low_y = dom_low_y - binl;
dom_up_y = dom_up_y + binl;
}
if (boundz == 3)
{
dom_low_z = dom_low_z - binl;
dom_up_z = dom_up_z + binl;
}
oFile.open(("dumpih.atom")); // opoening the dump file
if (!oFile)
{
cerr << "Unable to open file dumpih.atom";
exit(1);
}
oFile.precision(7);
vector<vector<double>> P(4 * no_particles, vector<double>(23, 0)); // main particle array/vector (P) intialization.
// P: flag type xpos ypos zpos vx vy vz fx fy fz wx wy wz Tx Ty Tz cxx cyy czz cxy cxz cyz
F.insert_particles(ins_choice, ins_reg_low_x, ins_reg_up_x, ins_reg_low_y, ins_reg_up_y, ins_reg_low_z, ins_reg_up_z, rad_p1, no_particles, trialcounterlimit, P);
cout << " check";
int binx = ceil((dom_up_x - dom_low_x) / binl); // calculations for total no of bins in x y z directions
int biny = ceil((dom_up_y - dom_low_y) / binl);
int binz = ceil((dom_up_z - dom_low_z) / binl);
int bincount;
double cx, cy, cz, Vx, Vy, Vz, Vtx, Vty, Vtz, Vnx, Vny, Vnz, Vtwx, Vtwy, Vtwz, Vdot_t, sx, sy, sz, s, Vttx, Vtty, Vttz, Vtt;
double d, cd, Fn, nx, ny, nz, Vrn, fx, fy, fz, ft, Ft, mu = 0.2, temp, temp1, temp2, Fx, Fy, Fz;
bincount = pow(binl, 3) / ((4.0 / 3.0) * pi * pow(rad_p1, 3)); // how many particles can be contained in a cube of size binl
bincount = min(int(15 * bincount), guessbincount);
cout << "bincout: " << bincount << endl;
vector<vector<vector<vector<float>>>> cbin(binx, vector<vector<vector<float>>> // contact bin array
(biny, vector<vector<float>>
(binz, vector<float>
(bincount, 0))));
vector<vector<vector<double>>> PP(no_particles, vector<vector<double>> // particle particle array ,to store the history of tangentiual contact
(4 * no_particles, vector<double>
(4, 0)));
while (tcounter <= no_timesteps)
{
ghost_particles = 0;
if (tcounter > 1000000)
{
gx = sin(0.3);
gz = -cos(0.3);
}
#pragma omp parallel for private(temp, temp1, temp2,cx, cy, cz, Vx, Vy, Vz, Vtx, Vty, Vtz, Vnx, Vny, Vnz, Vtwx, Vtwy, Vtwz, Vdot_t, sx, sy, sz, s, Vttx, Vtty, Vttz, Vtt,d, cd, Fn, nx, ny, nz, Vrn, fx, fy, fz, ft, Ft)
for (int i = 0; i < no_particles; i++)
{
if (P[i][0] == -1)
{
continue;
}
P[i][0] = 0;
P[i][2] = P[i][2] + P[i][5] * timestep + 0.5 * (P[i][8] / m) * timestep * timestep; // position updation velocity verlet scheme.
P[i][3] = P[i][3] + P[i][6] * timestep + 0.5 * (P[i][9] / m) * timestep * timestep;
P[i][4] = P[i][4] + P[i][7] * timestep + 0.5 * (P[i][10] / m) * timestep * timestep;
P[i][5] = P[i][5] + 0.5 * timestep * P[i][8] / m; // half velocity updation VV scheme.
P[i][6] = P[i][6] + 0.5 * timestep * P[i][9] / m;
P[i][7] = P[i][7] + 0.5 * timestep * P[i][10] / m;
P[i][11] = P[i][11] + 0.5 * timestep * P[i][14] / ((2 * m * rad_p1 * rad_p1) / 5); // half omega updation, VV scheme.
P[i][12] = P[i][12] + 0.5 * timestep * P[i][15] / ((2 * m * rad_p1 * rad_p1) / 5);
P[i][13] = P[i][13] + 0.5 * timestep * P[i][16] / ((2 * m * rad_p1 * rad_p1) / 5);
switch (boundx)
{
case(2):
if (P[i][2] >= dux)
{
P[i][0] = -1;
exitparticles++;
}
else if (P[i][2] < dlx)
{
P[i][0] = -1;
exitparticles++;
}break;
case(3):
if (P[i][2] >= dux)
{
P[i][2] = (P[i][2] - dux) + dlx;
}
else if (P[i][2] < dlx)
{
P[i][2] = (P[i][2] - dlx) + dux;
}break;
default:
break;
}
switch (boundy)
{
case(2):
if (P[i][3] >= duy)
{
P[i][0] = -1;
exitparticles++;
}
else if (P[i][3] < dly)
{
P[i][0] = -1;
exitparticles++;
}break;
case(3):
if (P[i][3] >= duy)
{
P[i][3] = (P[i][3] - duy) + dly;
}
else if (P[i][3] < dly)
{
P[i][3] = (P[i][3] - dly) + duy;
}break;
default:
break;
}
switch (boundz)
{
case(2):
if (P[i][4] >= duz)
{
P[i][0] = -1;
exitparticles++;
}
else if (P[i][4] < dlz)
{
P[i][0] = -1;
exitparticles++;
}break;
case(3):
if (P[i][4] >= duz)
{
P[i][4] = (P[i][4] - duz) + dlz;
}
else if (P[i][4] < dlz)
{
P[i][4] = (P[i][4] - dlz) + duz;
}break;
default:
break;
}
P[i][8] = m * gx * g; // intializing forces with gravity in the current timestep
P[i][9] = m * gy * g;
P[i][10] = m * gz * g;
P[i][14] = 0; // intializing torque = 0
P[i][15] = 0;
P[i][16] = 0;
int xb = floor((P[i][2] - dom_low_x) / binl);
int yb = floor((P[i][3] - dom_low_y) / binl);
int zb = floor((P[i][4] - dom_low_z) / binl);
switch (boundx)
{
case(1):
{
if (xb == 0) // near to the lower x domain
{
d = rad_p1 - (P[i][2] - dom_low_x);
if (d > 0)
{
Vx = P[i][5];
Fn = Kn * sqrt(2) * pow(d, 1.5) + Cn * sqrt(2 * sqrt(2)) * pow(d, 0.25) * Vx;
P[i][8] += Fn;
nx = (P[i][2] - dom_low_x) / abs(P[i][2] - dom_low_x);
ny = 0;
nz = 0;
Vtx = 0; // subtracting normal componentrs to get tangential component of center of mass velocity.
Vty = P[i][6];
Vtz = P[i][7];
Vtwx = 0; // Vtwx= Vtw2x-Vt1wx ; micro sliding due to relative rotation after taking v = w x(cross) r of each particle to get relative tangential velocity.
Vtwy = -rad_p1 * nx * P[i][13];
Vtwz = rad_p1 * nx * P[i][12];
Vttx = Vtx + Vtwx; // total micro sliding components in the tangential directions
Vtty = Vty + Vtwy;
Vttz = Vtz + Vtwz;
Vtt = sqrt(pow(Vttx, 2) + pow(Vtty, 2) + pow(Vttz, 2)); //magnitude of total tangential velocity
sx = Vttx * timestep; // tangential overlap
sy = Vtty * timestep;
sz = Vttz * timestep;
if (PP[i][i + no_particles][0] == tcounter - 1) // if wall is present, periodic particle allocation ids can be used for other purposes.
{ // here, paticle to wall id is taken as particle to the same periodic particle in that axis.
PP[i][i + no_particles][1] = PP[i][i + no_particles][1] + sx;
PP[i][i + no_particles][2] = PP[i][i + no_particles][2] + sy;
PP[i][i + no_particles][3] = PP[i][i + no_particles][3] + sz;
PP[i][i + no_particles][0] = tcounter;
}
else
{
PP[i][i + no_particles][1] = sx;
PP[i][i + no_particles][2] = sy;
PP[i][i + no_particles][3] = sz;
PP[i][i + no_particles][0] = tcounter;
}
s = sqrt(pow(PP[i][i + no_particles][1], 2) + pow(PP[i][i + no_particles][2], 2) + pow(PP[i][i + no_particles][3], 2)); // magnitude of total tangential overlap
if (s != 0)
{
ft = -(Kt * pow(d, 0.5) * s + Ct * pow(d, 0.25) * Vtt); //tangential force
if ((abs(ft) >= mu * abs(Fn)) && Vtt > 0)
{
Ft = -mu * abs(Fn);
PP[i][i + no_particles][1] = 0; // slip
PP[i][i + no_particles][2] = 0;
PP[i][i + no_particles][3] = 0;
P[i][8] += Ft * Vttx / Vtt; // tangential force components // cannot usse sx etc.. since its overlap for current timestep
P[i][9] += Ft * Vtty / Vtt;
P[i][10] += Ft * Vttz / Vtt;
temp = -rad_p1 * (ny * Ft * Vttz / Vtt - nz * Ft * Vtty / Vtt); // torque
temp1 = rad_p1 * (nx * Ft * Vttz / Vtt - nz * Ft * Vttx / Vtt);
temp2 = -rad_p1 * (nx * Ft * Vtty / Vtt - ny * Ft * Vttx / Vtt);
P[i][14] += temp; // torque updation
P[i][15] += temp1;
P[i][16] += temp2;
}
else
{
Ft = -min(abs(ft), mu * abs(Fn)); // tangnetial force with limit
fx = -(Kt * pow(d, 0.5) * PP[i][i + no_particles][1] + Ct * pow(d, 0.25) * Vttx);
fy = -(Kt * pow(d, 0.5) * PP[i][i + no_particles][2] + Ct * pow(d, 0.25) * Vtty);
fz = -(Kt * pow(d, 0.5) * PP[i][i + no_particles][3] + Ct * pow(d, 0.25) * Vttz);
P[i][8] += Ft * fx / ft; // tangential force components // cannot usse sx etc.. since its overlap for current timestep
P[i][9] += Ft * fy / ft;
P[i][10] += Ft * fz / ft;
temp = -rad_p1 * (ny * Ft * fz / ft - nz * Ft * fy / ft); // torque updation
temp1 = rad_p1 * (nx * Ft * fz / ft - nz * Ft * fx / ft);
temp2 = -rad_p1 * (nx * Ft * fy / ft - ny * Ft * fx / ft);
P[i][14] += temp;
P[i][15] += temp1;
P[i][16] += temp2;
}
}
}
}
else if (xb == binx - 1) // near to the upper x domain
{
d = rad_p1 - (dom_up_x - P[i][2]);
if (d > 0)
{
Vx = P[i][5];
Fn = -Kn * sqrt(2) * pow(d, 1.5) + Cn * sqrt(2 * sqrt(2)) * pow(d, 0.25) * Vx;
P[i][8] += Fn;
nx = (P[i][2] - dom_up_x) / abs(P[i][2] - dom_up_x);
Vtx = 0; // subtracting normal componentrs to get tangential component of center of mass velocity.
Vty = P[i][6];
Vtz = P[i][7];
Vtwx = 0; // Vtwx= Vtw2x-Vt1wx ; micro sliding due to relative rotation after taking v = w x(cross) r of each particle to get relative tangential velocity.
Vtwy = -rad_p1 * nx * P[i][13];
Vtwz = rad_p1 * nx * P[i][12];
Vttx = Vtx + Vtwx; // total micro sliding components in the tangential directions
Vtty = Vty + Vtwy;
Vttz = Vtz + Vtwz;
Vtt = sqrt(pow(Vttx, 2) + pow(Vtty, 2) + pow(Vttz, 2)); //magnitude of total tangential velocity
sx = Vttx * timestep; // tangential overlap
sy = Vtty * timestep;
sz = Vttz * timestep;
if (PP[i][i + no_particles][0] == tcounter - 1) // if wall is present, periopdic particle allocation ids can be used for other purposes.
{ // here, paticle to wall id is taken as particle to the same periodic particle in that axis.
PP[i][i + no_particles][1] = PP[i][i + no_particles][1] + sx;
PP[i][i + no_particles][2] = PP[i][i + no_particles][2] + sy;
PP[i][i + no_particles][3] = PP[i][i + no_particles][3] + sz;
PP[i][i + no_particles][0] = tcounter;
}
else
{
PP[i][i + no_particles][1] = sx;
PP[i][i + no_particles][2] = sy;
PP[i][i + no_particles][3] = sz;
PP[i][i + no_particles][0] = tcounter;
}
s = sqrt(pow(PP[i][i + no_particles][1], 2) + pow(PP[i][i + no_particles][2], 2) + pow(PP[i][i + no_particles][3], 2)); // magnitude of total tangential overlap
if (s != 0)
{
ft = -(Kt * pow(d, 0.5) * s + Ct * pow(d, 0.25) * Vtt); //tangential force
if ((abs(ft) >= mu * abs(Fn)) && Vtt > 0)
{
Ft = -mu * abs(Fn);
PP[i][i + no_particles][1] = 0; // slip
PP[i][i + no_particles][2] = 0;
PP[i][i + no_particles][3] = 0;
P[i][8] += Ft * Vttx / Vtt; // tangential force components // cannot usse sx etc.. since its overlap for current timestep
P[i][9] += Ft * Vtty / Vtt;
P[i][10] += Ft * Vttz / Vtt;
temp = -rad_p1 * (ny * Ft * Vttz / Vtt - nz * Ft * Vtty / Vtt); // torque
temp1 = rad_p1 * (nx * Ft * Vttz / Vtt - nz * Ft * Vttx / Vtt);
temp2 = -rad_p1 * (nx * Ft * Vtty / Vtt - ny * Ft * Vttx / Vtt);
P[i][14] += temp; // torque updation
P[i][15] += temp1;
P[i][16] += temp2;
}
else
{
Ft = -min(abs(ft), mu * abs(Fn)); // tangnetial force with limit
fx = -(Kt * pow(d, 0.5) * PP[i][i + no_particles][1] + Ct * pow(d, 0.25) * Vttx);
fy = -(Kt * pow(d, 0.5) * PP[i][i + no_particles][2] + Ct * pow(d, 0.25) * Vtty);
fz = -(Kt * pow(d, 0.5) * PP[i][i + no_particles][3] + Ct * pow(d, 0.25) * Vttz);
P[i][8] += Ft * fx / ft; // tangential force components // cannot usse sx etc.. since its overlap for current timestep
P[i][9] += Ft * fy / ft;
P[i][10] += Ft * fz / ft;
temp = -rad_p1 * (ny * Ft * fz / ft - nz * Ft * fy / ft); // torque updation
temp1 = rad_p1 * (nx * Ft * fz / ft - nz * Ft * fx / ft);
temp2 = -rad_p1 * (nx * Ft * fy / ft - ny * Ft * fx / ft);
P[i][14] += temp;
P[i][15] += temp1;
P[i][16] += temp2;
}
}
}
}
}break;
case(3):
{
if (xb == 1) // xb = 0 is ghost cell
{
P[no_particles + i][0] = -1; // ghost particles only impart forces and we dont calculate forces on them so this is kept as -1. the impart forces will be calculated as neighbour cell loop is executed.
P[no_particles + i][1] = 2; // just a type asignment for ghost particles
P[no_particles + i][2] = P[i][2] + (dux - dlx);
P[no_particles + i][3] = P[i][3];
P[no_particles + i][4] = P[i][4];
P[no_particles + i][5] = P[i][5];
P[no_particles + i][6] = P[i][6];
P[no_particles + i][7] = P[i][7];
P[no_particles + i][11] = P[i][11];
P[no_particles + i][12] = P[i][12];
P[no_particles + i][13] = P[i][13];
if (tcounter != cbin[binx - 1][yb][zb][1]) // to implement conditions when a bin is populated 1st time within a particular timestep iteration.
{
#pragma omp critical
{
cbin[binx - 1][yb][zb][0] = 0;
cbin[binx - 1][yb][zb][1] = tcounter;
}
}
#pragma omp critical
{
cbin[binx - 1][yb][zb][0]++;
cbin[binx - 1][yb][zb][cbin[binx - 1][yb][zb][0] + 1] = no_particles + i;
ghost_particles++;
}
}
else if (xb == binx - 2)
{
P[no_particles + i][0] = -1;
P[no_particles + i][1] = 2;
P[no_particles + i][2] = P[i][2] - (dux - dlx);
P[no_particles + i][3] = P[i][3];
P[no_particles + i][4] = P[i][4];
P[no_particles + i][5] = P[i][5];
P[no_particles + i][6] = P[i][6];
P[no_particles + i][7] = P[i][7];
P[no_particles + i][11] = P[i][11];
P[no_particles + i][12] = P[i][12];
P[no_particles + i][13] = P[i][13];
if (tcounter != cbin[0][yb][zb][1]) // to implement conditions when a bin is populated 1st time within a particular timestep iteration.
{
#pragma omp critical
{
cbin[0][yb][zb][0] = 0;
cbin[0][yb][zb][1] = tcounter;
}
}
#pragma omp critical
{
cbin[0][yb][zb][0]++;
cbin[0][yb][zb][cbin[0][yb][zb][0] + 1] = no_particles + i;
ghost_particles++;
}
}
}break;
default:
break;
}
switch (boundy)
{
case(1):
{
if (yb == 0)
{
d = rad_p1 - (P[i][3] - dom_low_y);
if (d > 0)
{
Vy = P[i][6];
Fn = Kn * sqrt(2) * pow(d, 1.5) + Cn * sqrt(2 * sqrt(2)) * pow(d, 0.25) * Vy;
P[i][9] += Fn;
ny = (P[i][3] - dom_low_y) / abs(P[i][3] - dom_low_y);
nx = 0;
nz = 0;
Vtx = P[i][5]; // subtracting normal componentrs to get tangential component of center of mass velocity.
Vty = 0;
Vtz = P[i][7];
Vtwx = rad_p1 * ny * P[i][13]; // Vtx= Vt1x-Vt2x ; micro sliding due to rotation after taking v = w x(cross) r of each particle and subtracting to get relative tangential velocity.
Vtwy = 0;
Vtwz = -rad_p1 * P[i][11] * ny;
Vttx = Vtx + Vtwx; // total micro sliding components in the tangential directions
Vtty = Vty + Vtwy;
Vttz = Vtz + Vtwz;
Vtt = sqrt(pow(Vttx, 2) + pow(Vtty, 2) + pow(Vttz, 2)); //magnitude of total tangential velocity
sx = Vttx * timestep; // tangential overlap
sy = Vtty * timestep;
sz = Vttz * timestep;
if (PP[i][i + 2 * no_particles][0] == tcounter - 1) // if wall is present, periopdic particle allocation ids can be used for other purposes.
{ // here, paticle to wall id is taken as particle to the same periodic particle in that axis.
PP[i][i + 2 * no_particles][1] = PP[i][i + 2 * no_particles][1] + sx;
PP[i][i + 2 * no_particles][2] = PP[i][i + 2 * no_particles][2] + sy;
PP[i][i + 2 * no_particles][3] = PP[i][i + 2 * no_particles][3] + sz;
PP[i][i + 2 * no_particles][0] = tcounter;
}
else
{
PP[i][i + 2 * no_particles][1] = sx;
PP[i][i + 2 * no_particles][2] = sy;
PP[i][i + 2 * no_particles][3] = sz;
PP[i][i + 2 * no_particles][0] = tcounter;
}
s = sqrt(pow(PP[i][i + 2 * no_particles][1], 2) + pow(PP[i][i + 2 * no_particles][2], 2) + pow(PP[i][i + 2 * no_particles][3], 2)); // magnitude of total tangential overlap
if (s != 0)
{
ft = -(Kt * pow(d, 0.5) * s + Ct * pow(d, 0.25) * Vtt); //tangential force
if ((abs(ft) >= mu * abs(Fn)) && Vtt > 0)
{
Ft = -mu * abs(Fn);
PP[i][i + 2 * no_particles][1] = 0; // slip
PP[i][i + 2 * no_particles][2] = 0;
PP[i][i + 2 * no_particles][3] = 0;
P[i][8] += Ft * Vttx / Vtt; // tangential force components // cannot usse sx etc.. since its overlap for current timestep
P[i][9] += Ft * Vtty / Vtt;
P[i][10] += Ft * Vttz / Vtt;
temp = -rad_p1 * (ny * Ft * Vttz / Vtt - nz * Ft * Vtty / Vtt); // torque
temp1 = rad_p1 * (nx * Ft * Vttz / Vtt - nz * Ft * Vttx / Vtt);
temp2 = -rad_p1 * (nx * Ft * Vtty / Vtt - ny * Ft * Vttx / Vtt);
P[i][14] += temp; // torque updation
P[i][15] += temp1;
P[i][16] += temp2;
}
else
{
Ft = -min(abs(ft), mu * abs(Fn)); // tangnetial force with limit
fx = -(Kt * pow(d, 0.5) * PP[i][i + 2 * no_particles][1] + Ct * pow(d, 0.25) * Vttx);
fy = -(Kt * pow(d, 0.5) * PP[i][i + 2 * no_particles][2] + Ct * pow(d, 0.25) * Vtty);
fz = -(Kt * pow(d, 0.5) * PP[i][i + 2 * no_particles][3] + Ct * pow(d, 0.25) * Vttz);
P[i][8] += Ft * fx / ft; // tangential force components // cannot usse sx etc.. since its overlap for current timestep
P[i][9] += Ft * fy / ft;
P[i][10] += Ft * fz / ft;
temp = -rad_p1 * (ny * Ft * fz / ft - nz * Ft * fy / ft); // torque updation
temp1 = rad_p1 * (nx * Ft * fz / ft - nz * Ft * fx / ft);
temp2 = -rad_p1 * (nx * Ft * fy / ft - ny * Ft * fx / ft);
P[i][14] += temp;
P[i][15] += temp1;
P[i][16] += temp2;
}
}
}
}
else if (yb == biny - 1)
{
d = rad_p1 - (dom_up_y - P[i][3]);
if (d > 0)
{
Vy = P[i][6];
Fn = -Kn * sqrt(2) * pow(d, 1.5) + Cn * sqrt(2 * sqrt(2)) * pow(d, 0.25) * Vy;
P[i][9] += Fn;
ny = (P[i][3] - dom_up_y) / abs(P[i][3] - dom_up_y);
Vtx = P[i][5]; // subtracting normal componentrs to get tangential component of center of mass velocity.
Vty = 0;
Vtz = P[i][7];
Vtwx = rad_p1 * ny * P[i][13]; // Vtx= Vt1x-Vt2x ; micro sliding due to rotation after taking v = w x(cross) r of each particle and subtracting to get relative tangential velocity.
Vtwy = 0;
Vtwz = -rad_p1 * P[i][11] * ny;
Vttx = Vtx + Vtwx; // total micro sliding components in the tangential directions
Vtty = Vty + Vtwy;
Vttz = Vtz + Vtwz;
Vtt = sqrt(pow(Vttx, 2) + pow(Vtty, 2) + pow(Vttz, 2)); //magnitude of total tangential velocity
sx = Vttx * timestep; // tangential overlap
sy = Vtty * timestep;
sz = Vttz * timestep;
if (PP[i][i + 2 * no_particles][0] == tcounter - 1) // if wall is present, periopdic particle allocation ids can be used for other purposes.
{ // here, paticle to wall id is taken as particle to the same periodic particle in that axis.
PP[i][i + 2 * no_particles][1] = PP[i][i + 2 * no_particles][1] + sx;
PP[i][i + 2 * no_particles][2] = PP[i][i + 2 * no_particles][2] + sy;
PP[i][i + 2 * no_particles][3] = PP[i][i + 2 * no_particles][3] + sz;
PP[i][i + 2 * no_particles][0] = tcounter;
}
else
{
PP[i][i + 2 * no_particles][1] = sx;
PP[i][i + 2 * no_particles][2] = sy;
PP[i][i + 2 * no_particles][3] = sz;
PP[i][i + 2 * no_particles][0] = tcounter;
}
s = sqrt(pow(PP[i][i + 2 * no_particles][1], 2) + pow(PP[i][i + 2 * no_particles][2], 2) + pow(PP[i][i + 2 * no_particles][3], 2)); // magnitude of total tangential overlap
if (s != 0)
{
ft = -(Kt * pow(d, 0.5) * s + Ct * pow(d, 0.25) * Vtt); //tangential force
if ((abs(ft) >= mu * abs(Fn)) && Vtt > 0)
{
Ft = -mu * abs(Fn);
PP[i][i + 2 * no_particles][1] = 0; //slip
PP[i][i + 2 * no_particles][2] = 0;
PP[i][i + 2 * no_particles][3] = 0;
P[i][8] += Ft * Vttx / Vtt; // tangential force components // cannot usse sx etc.. since its overlap for current timestep
P[i][9] += Ft * Vtty / Vtt;
P[i][10] += Ft * Vttz / Vtt;
temp = -rad_p1 * (ny * Ft * Vttz / Vtt - nz * Ft * Vtty / Vtt); // torque
temp1 = rad_p1 * (nx * Ft * Vttz / Vtt - nz * Ft * Vttx / Vtt);
temp2 = -rad_p1 * (nx * Ft * Vtty / Vtt - ny * Ft * Vttx / Vtt);
P[i][14] += temp; // torque updation
P[i][15] += temp1;
P[i][16] += temp2;
}
else
{
Ft = -min(abs(ft), mu * abs(Fn)); // tangnetial force with limit
fx = -(Kt * pow(d, 0.5) * PP[i][i + 2 * no_particles][1] + Ct * pow(d, 0.25) * Vttx);
fy = -(Kt * pow(d, 0.5) * PP[i][i + 2 * no_particles][2] + Ct * pow(d, 0.25) * Vtty);
fz = -(Kt * pow(d, 0.5) * PP[i][i + 2 * no_particles][3] + Ct * pow(d, 0.25) * Vttz);
P[i][8] += Ft * fx / ft; // tangential force components // cannot usse sx etc.. since its overlap for current timestep
P[i][9] += Ft * fy / ft;
P[i][10] += Ft * fz / ft;
temp = -rad_p1 * (ny * Ft * fz / ft - nz * Ft * fy / ft); // torque updation
temp1 = rad_p1 * (nx * Ft * fz / ft - nz * Ft * fx / ft);
temp2 = -rad_p1 * (nx * Ft * fy / ft - ny * Ft * fx / ft);
P[i][14] += temp;
P[i][15] += temp1;
P[i][16] += temp2;
}
}
}
}
}break;
case(3):
{
if (yb == 1)
{
P[2 * no_particles + i][0] = -1;
P[2 * no_particles + i][1] = 2;
P[2 * no_particles + i][2] = P[i][2];
P[2 * no_particles + i][3] = P[i][3] + (duy - dly);
P[2 * no_particles + i][4] = P[i][4];
P[2 * no_particles + i][5] = P[i][5];
P[2 * no_particles + i][6] = P[i][6];
P[2 * no_particles + i][7] = P[i][7];
P[2 * no_particles + i][11] = P[i][11];
P[2 * no_particles + i][12] = P[i][12];
P[2 * no_particles + i][13] = P[i][13];
if (tcounter != cbin[xb][biny - 1][zb][1]) // to implement conditions when a bin is populated 1st time within a particular timestep iteration.
{
#pragma omp critical
{
cbin[xb][biny - 1][zb][0] = 0;
cbin[xb][biny - 1][zb][1] = tcounter;
}
}
#pragma omp critical
{
cbin[xb][biny - 1][zb][0]++;
cbin[xb][biny - 1][zb][cbin[xb][biny - 1][zb][0] + 1] = 2 * no_particles + i;
ghost_particles++;
}
}
else if (yb == biny - 2)
{
P[2 * no_particles + i][0] = -1;
P[2 * no_particles + i][1] = 2;
P[2 * no_particles + i][2] = P[i][2];
P[2 * no_particles + i][3] = P[i][3] - (duy - dly);
P[2 * no_particles + i][4] = P[i][4];
P[2 * no_particles + i][5] = P[i][5];
P[2 * no_particles + i][6] = P[i][6];
P[2 * no_particles + i][7] = P[i][7];
P[2 * no_particles + i][11] = P[i][11];
P[2 * no_particles + i][12] = P[i][12];
P[2 * no_particles + i][13] = P[i][13];
if (tcounter != cbin[xb][0][zb][1]) // to implement conditions when a bin is populated 1st time within a particular timestep iteration.
{
#pragma omp critical
{
cbin[xb][0][zb][0] = 0;
cbin[xb][0][zb][1] = tcounter;
}
}
#pragma omp critical
{
cbin[xb][0][zb][0]++;
cbin[xb][0][zb][cbin[xb][0][zb][0] + 1] = 2 * no_particles + i;
ghost_particles++;
}
}
}break;
default:
break;
}
switch (boundz)
{
case(1):
{
if (zb == 0)
{
d = rad_p1 - (P[i][4] - dom_low_z);
if (d > 0)
{
Vz = P[i][7];
Fn = Kn * sqrt(2) * pow(d, 1.5) + Cn * sqrt(2 * sqrt(2)) * pow(d, 0.25) * Vz;
P[i][10] += Fn;
nz = (P[i][4] - dom_low_z) / abs(P[i][4] - dom_low_z);
nx = 0;
ny = 0;
P[i][5] = 0; //no velocity in x direction at z ground surface bumpy inclined plane
P[i][6] = 0;
Vtx = P[i][5]; // subtracting normal componentrs to get tangential component of center of mass velocity.
Vty = P[i][6];
Vtz = 0;
Vtwx = -rad_p1 * P[i][12] * nz; // Vtx= Vt1x-Vt2x ; micro sliding due to rotation after taking v = w x(cross) r of each particle and subtracting to get relative tangential velocity.
Vtwy = rad_p1 * P[i][11] * nz;
Vtwz = 0;
Vttx = Vtx + Vtwx; // total micro sliding components in the tangential directions
Vtty = Vty + Vtwy;
Vttz = Vtz + Vtwz;
Vtt = sqrt(pow(Vttx, 2) + pow(Vtty, 2) + pow(Vttz, 2)); //magnitude of total tangential velocity
sx = Vttx * timestep; // tangential overlap
sy = Vtty * timestep;
sz = Vttz * timestep;
if (PP[i][i + 3 * no_particles][0] == tcounter - 1) // if wall is present, periopdic particle allocation ids can be used for other purposes.
{ // here, paticle to wall id is taken as particle to the same periodic particle in that axis.
PP[i][i + 3 * no_particles][1] = PP[i][i + 3 * no_particles][1] + sx;
PP[i][i + 3 * no_particles][2] = PP[i][i + 3 * no_particles][2] + sy;
PP[i][i + 3 * no_particles][3] = PP[i][i + 3 * no_particles][3] + sz;
PP[i][i + 3 * no_particles][0] = tcounter;
}
else
{
PP[i][i + 3 * no_particles][1] = sx;
PP[i][i + 3 * no_particles][2] = sy;
PP[i][i + 3 * no_particles][3] = sz;
PP[i][i + 3 * no_particles][0] = tcounter;
}
s = sqrt(pow(PP[i][i + 3 * no_particles][1], 2) + pow(PP[i][i + 3 * no_particles][2], 2) + pow(PP[i][i + 3 * no_particles][3], 2)); // magnitude of total tangential overlap
if (s != 0)
{
ft = -(Kt * pow(d, 0.5) * s + Ct * pow(d, 0.25) * Vtt); //tangential force
if ((abs(ft) >= mu * abs(Fn)) && Vtt > 0)
{
Ft = -mu * abs(Fn);
PP[i][i + 3 * no_particles][1] = 0; // slip
PP[i][i + 3 * no_particles][2] = 0;
PP[i][i + 3 * no_particles][3] = 0;
P[i][8] += Ft * Vttx / Vtt; // tangential force components // cannot usse sx etc.. since its overlap for current timestep
P[i][9] += Ft * Vtty / Vtt;
P[i][10] += Ft * Vttz / Vtt;
temp = -rad_p1 * (ny * Ft * Vttz / Vtt - nz * Ft * Vtty / Vtt); // torque
temp1 = rad_p1 * (nx * Ft * Vttz / Vtt - nz * Ft * Vttx / Vtt);
temp2 = -rad_p1 * (nx * Ft * Vtty / Vtt - ny * Ft * Vttx / Vtt);
P[i][14] += temp; // torque updation
P[i][15] += temp1;
P[i][16] += temp2;
}
else
{
Ft = -min(abs(ft), mu * abs(Fn)); // tangnetial force with limit
fx = -(Kt * pow(d, 0.5) * PP[i][i + 3 * no_particles][1] + Ct * pow(d, 0.25) * Vttx);
fy = -(Kt * pow(d, 0.5) * PP[i][i + 3 * no_particles][2] + Ct * pow(d, 0.25) * Vtty);
fz = -(Kt * pow(d, 0.5) * PP[i][i + 3 * no_particles][3] + Ct * pow(d, 0.25) * Vttz);
P[i][8] += Ft * fx / ft; // tangential force components // cannot usse sx etc.. since its overlap for current timestep
P[i][9] += Ft * fy / ft;
P[i][10] += Ft * fz / ft;
temp = -rad_p1 * (ny * Ft * fz / ft - nz * Ft * fy / ft); // torque updation
temp1 = rad_p1 * (nx * Ft * fz / ft - nz * Ft * fx / ft);
temp2 = -rad_p1 * (nx * Ft * fy / ft - ny * Ft * fx / ft);
P[i][14] += temp;
P[i][15] += temp1;
P[i][16] += temp2;
}
}
}
}
else if (zb == binz - 1)
{
d = rad_p1 - (dom_up_z - P[i][4]);
if (d > 0)
{
Vz = P[i][7];
Fn = -Kn * sqrt(2) * pow(d, 1.5) + Cn * sqrt(2 * sqrt(2)) * pow(d, 0.25) * Vz;
P[i][10] += Fn;
nz = (P[i][4] - dom_up_z) / abs(P[i][4] - dom_up_z);
Vtx = P[i][5]; // subtracting normal componentrs to get tangential component of center of mass velocity.
Vty = P[i][6];
Vtz = 0;
Vtwx = -rad_p1 * P[i][12] * nz; // Vtx= Vt1x-Vt2x ; micro sliding due to rotation after taking v = w x(cross) r of each particle and subtracting to get relative tangential velocity.
Vtwy = rad_p1 * P[i][11] * nz;
Vtwz = 0;
Vttx = Vtx + Vtwx; // total micro sliding components in the tangential directions
Vtty = Vty + Vtwy;
Vttz = Vtz + Vtwz;
Vtt = sqrt(pow(Vttx, 2) + pow(Vtty, 2) + pow(Vttz, 2)); //magnitude of total tangential velocity
sx = Vttx * timestep; // tangential overlap
sy = Vtty * timestep;
sz = Vttz * timestep;
if (PP[i][i + 3 * no_particles][0] == tcounter - 1) // if wall is present, periopdic particle allocation ids can be used for other purposes.
{ // here, paticle to wall id is taken as particle to the same periodic particle in that axis.
PP[i][i + 3 * no_particles][1] = PP[i][i + 3 * no_particles][1] + sx;
PP[i][i + 3 * no_particles][2] = PP[i][i + 3 * no_particles][2] + sy;
PP[i][i + 3 * no_particles][3] = PP[i][i + 3 * no_particles][3] + sz;
PP[i][i + 3 * no_particles][0] = tcounter;
}
else
{
PP[i][i + 3 * no_particles][1] = sx;
PP[i][i + 3 * no_particles][2] = sy;
PP[i][i + 3 * no_particles][3] = sz;
PP[i][i + 3 * no_particles][0] = tcounter;
}
s = sqrt(pow(PP[i][i + 3 * no_particles][1], 2) + pow(PP[i][i + 3 * no_particles][2], 2) + pow(PP[i][i + 3 * no_particles][3], 2)); // magnitude of total tangential overlap
if (s != 0)
{
ft = -(Kt * pow(d, 0.5) * s + Ct * pow(d, 0.25) * Vtt); //tangential force
if ((abs(ft) >= mu * abs(Fn)) && Vtt > 0)
{
Ft = -mu * abs(Fn);
PP[i][i + 3 * no_particles][1] = 0; //slip
PP[i][i + 3 * no_particles][2] = 0;
PP[i][i + 3 * no_particles][3] = 0;
P[i][8] += Ft * Vttx / Vtt; // tangential force components // cannot usse sx etc.. since its overlap for current timestep
P[i][9] += Ft * Vtty / Vtt;
P[i][10] += Ft * Vttz / Vtt;
temp = -rad_p1 * (ny * Ft * Vttz / Vtt - nz * Ft * Vtty / Vtt); // torque
temp1 = rad_p1 * (nx * Ft * Vttz / Vtt - nz * Ft * Vttx / Vtt);
temp2 = -rad_p1 * (nx * Ft * Vtty / Vtt - ny * Ft * Vttx / Vtt);
P[i][14] += temp; // torque updation
P[i][15] += temp1;
P[i][16] += temp2;