元胞自动机模型之格子气自动机模拟气体扩散模型
元胞自动机是定义在一个由具有离散有限状态的元胞组成的元胞空间上，并且按照一定的局部规则，在离散的时间维上演化的动力学系统。
这里采用的是格子气自动机的HPP模型，每个格子上的粒子只能向四个方向之一运动，这里用四位数表示格位信息。粒子的演化规则可以分为两个阶段：运动阶段和碰撞阶段。运动阶段，粒子按照指定的方向向邻近格点运动，在碰撞阶段，粒子按照指点的规则改变原来的运动方向。
模拟发现，经过一段时间后，气体分子比较均匀的分布在空间整个空格上。
源代码：
#include "cell.h"
cell::cell()
{
m = 200;
n = m;
dx = 1.0 / m;
dy = 1.0 / n;
maxTime = 1500;
stheta = -0.0; //the standary line of open boundary
boubdaryTheta = 5; //the open boundary of the circle;
elem.assign(m + 1, vector<node>(n + 1));
int imax = m + 1;
int jmax = n + 1;
for (int i = 0; i < imax; ++i) {
for (int j = 0; j < jmax; ++j) {
//node temp(i*dx, j*dy);
elem[i][j].x = i*dx;
elem[i][j].y = j*dy;
elem[i][j].get_phi();
}
}
}
node::node()
{
x = 0.0;
y = 0.0;
i =false;
j = false;
k = false;
l= false;
E = false;
N= false;
W = false;
S = false;
}
void node::operator=(const node temp) {
x = temp.x;
y = temp.y;
i = temp.i;
j = temp.j;
k = temp.k;
l = temp.l;
E = temp.E;
N = temp.N;
W = temp.W;
S = temp.S;
}
node::node(double fx,double fy)
{
x = fx;
y = fy;
i = false;
j = false;
k = false;
l = false;
E = false;
N = false;
W = false;
S = false;
}
node::~node()
{
}
void cell::initial() {
int imax = elem.size();
int jmax = elem[0].size();
//time_t nowtime = time(nullptr);
int nowtime = 2;
auto seed = my_rand(nowtime);
int random = seed;
for (int i = 0; i < imax; ++i) {
for (int j = 0; j < jmax; ++j) {
elem[i][j].i = false; elem[i][j].j = false; elem[i][j].k = false;elem[i][j].l = false;
if (elem[i][j].phi>0) {
seed = my_rand(seed);
random = 1.0 * (seed% m) / m;
if (random < 0.25) {
elem[i][j].i = true; elem[i][j].k = true;
}
else if (random < 0.5) {
elem[i][j].j = true; elem[i][j].l = true;
}
else if (random < 0.75) {
elem[i][j].k = true; elem[i][j].i = true;
}
else if(random<1){
elem[i][j].l = true; elem[i][j].j = true;
}
else {
cout << "random error in initial!" << endl; cin.get();
}
//cout << "come to here " << endl;
}
}
}
}
void cell::output(int time) {
string tempa = "axissym_";
int temp = 10000 + time;
stringstream ss;
string str;
ss << temp;
ss >> str;
string title = tempa + str + ".plt";
ofstream fcout;
fcout.open(title);
int imax = m + 1;
int jmax = n + 1;
int maxParticleNum = 0;
for (int i = 0; i < imax; ++i) {
for (int j = 0; j < jmax; ++j) {
if (elem[i][j].i || elem[i][j].j || elem[i][j].k || elem[i][j].l ) {
maxParticleNum++;
}
}
}
fcout << " title=random " << endl;
fcout << " VARIABLES = \"X\",\"Y \" " << endl;
fcout << "zone I= " << maxParticleNum << ",datapacking=POINT" << endl;
for (int i = 0; i < imax; ++i) {
for (int j = 0; j < jmax; ++j) {
if (elem[i][j].i || elem[i][j].j || elem[i][j].k || elem[i][j].l) {
fcout << i*dx << " " << j*dy << endl;
}
}
}
fcout.close();
}
double node::get_phi() {
//the ceter point of the circle is(x0, y0), and ridics is r;
double x0 = 0.5; double y0 = 0.5;
double r = 0.2;
phi = r - sqrt((x - x0)*(x - x0) + (y - y0)*(y - y0));
return phi;
}
cell::~cell()
{
}
void cell::impact()
{
//cout << "in impact !" << endl;
int imax = elem.size();
int jmax = elem[0].size();
for (int i = 1; i < imax-1; ++i) {
for (int j = 1; j < jmax-1; ++j) {
elem[i][j].i = false; elem[i][j].j = false; elem[i][j].k = false; elem[i][j].l = false;
if (elem[i][j].E || elem[i][j].N || !elem[i][j].W || !elem[i][j].S) {
if (elem[i][j].E && !elem[i][j].N && !elem[i][j].W && !elem[i][j].S) { //one particle comes fome East
elem[i][j].k = true;
}
else if ( !elem[i][j].E && !elem[i][j].N && elem[i][j].W && !elem[i][j].S) { //one particle comes fome West
elem[i][j].i = true;
}
else if (!elem[i][j].E && elem[i][j].N && !elem[i][j].W && !elem[i][j].S) { //one particle comes fome North
elem[i][j].l = true;
}
else if (!elem[i][j].E && !elem[i][j].N && !elem[i][j].W && elem[i][j].S) { //one particle comes fome South
elem[i][j].j = true;
}
else if (!elem[i][j].E && elem[i][j].N && !elem[i][j].W && elem[i][j].S) { //two particles come fome South and North
elem[i][j].k = true; elem[i][j].i = true;
}
else if (elem[i][j].E && !elem[i][j].N && !elem[i][j].W && elem[i][j].S) { //two particles come fome South and East
elem[i][j].j = true; elem[i][j].k = true;
}
else if (!elem[i][j].E && !elem[i][j].N && elem[i][j].W && elem[i][j].S) { //two particles come fome South and West
elem[i][j].j = true; elem[i][j].i = true;
}
else if (!elem[i][j].E && elem[i][j].N && elem[i][j].W && !elem[i][j].S) { //two particles come fome North and West
elem[i][j].i = true; elem[i][j].l = true;
}
else if (elem[i][j].E && elem[i][j].N && !elem[i][j].W && !elem[i][j].S) { //two particles come fome North and East
elem[i][j].l = true; elem[i][j].k = true;
}
else if (elem[i][j].E && !elem[i][j].N && elem[i][j].W && !elem[i][j].S) { //two particles come fome East and West
elem[i][j].j = true; elem[i][j].l = true;
}
else if (!elem[i][j].E && elem[i][j].N && elem[i][j].W && elem[i][j].S) { //three particles except coming fome East
elem[i][j].j = true; elem[i][j].i = true; elem[i][j].l = true;
}
else if (elem[i][j].E && elem[i][j].N && !elem[i][j].W && elem[i][j].S) { //three particles except coming fome West
elem[i][j].j = true; elem[i][j].k = true; elem[i][j].l = true;
}
else if (elem[i][j].E && elem[i][j].N && elem[i][j].W && !elem[i][j].S) { //three particles except coming fome South
elem[i][j].i = true; elem[i][j].k = true; elem[i][j].l = true;
}
else if (elem[i][j].E && !elem[i][j].N && elem[i][j].W && elem[i][j].S) { //three particles except coming fome North
elem[i][j].i = true; elem[i][j].k = true; elem[i][j].j = true;
}
else if (elem[i][j].E && elem[i][j].N && elem[i][j].W && elem[i][j].S) { //four particles
elem[i][j].i = true; elem[i][j].k = true; elem[i][j].j = true; elem[i][j].l = true;
}
}
}
}
for (int i = 0; i < imax;++i) { //the uppest and the lowest boundary
elem[i][0].i = false; elem[i][0].j = false; elem[i][0].k = false; elem[i][0].l = false;
elem[i][jmax-1].i = false; elem[i][jmax-1].j = false; elem[i][jmax-1].k = false; elem[i][jmax-1].l = false;
if (elem[i][0].N) {
int temp = 0;
elem[i][0].j = true;
}
if (elem[i][jmax-1].S) {
elem[i][jmax-1].l = true;
}
}
int temp = 0;
for (int j = 0; j < jmax; ++j) { //the left and the right boundary
elem[0][j].i = false; elem[0][j].j = false; elem[0][j].k = false; elem[0][j].l = false;
elem[imax-1][j].i = false; elem[imax-1][j].j = false; elem[imax-1][j].k = false; elem[imax-1][j].l = false;
if (elem[0][j].E) {
elem[0][j].i = true;
}
if (elem[imax-1][j].W) {
elem[imax-1][j].k = true;
}
}
temp = 0;
}
void cell::move()
{
//cout << "in move !" << endl;
node norign(0.5, 0.5);
double theta = 0.0;
int imax = elem.size();
int jmax = elem[0].size();
for (int i = 0; i < imax; ++i) {
for (int j = 0; j < jmax; ++j) {
elem[i][j].E = false; elem[i][j].N = false; elem[i][j].W = false; elem[i][j].S = false;
}
}
for (int i = 0; i < imax; ++i) {
for (int j = 0; j < jmax; ++j) {
if (elem[i][j].i) {
if (elem[i + 1][j].phi * elem[i][j].phi <= 0) {
theta = get_theta(norign, elem[i][j]);
if (abs(theta - stheta) > boubdaryTheta) {
elem[i][j].E = true;
}
else {
elem[i + 1][j].W = true;
}
}
else {
elem[i + 1][j].W = true;
}
}
if (elem[i][j].j) {
if (elem[i][j].phi * elem[i][j+1].phi <= 0) {
theta = get_theta(norign, elem[i][j]);
if (abs(theta - stheta) > boubdaryTheta) {
elem[i][j].N = true;
}
else {
elem[i][j+1].S = true;
}
}
else {
elem[i][j+1].S = true;
}
}
if (elem[i][j].k) {
if (elem[i][j].phi * elem[i-1][j].phi <= 0) {
theta = get_theta(norign, elem[i][j]);
if (abs(theta - stheta) > boubdaryTheta) {
elem[i][j].W = true;
}
else {
elem[i-1][j].E = true;
}
}
else {
elem[i-1][j].E = true;
}
}
if (elem[i][j].l) {
if (elem[i][j].phi * elem[i][j - 1].phi <= 0) {
theta = get_theta(norign, elem[i][j]);
if (abs(theta - stheta) > boubdaryTheta) {
elem[i][j].S = true;
}
else {
elem[i][j - 1].N = true;
}
}
else {
elem[i][j-1].N = true;
}
}
}
}
}
double cell::get_theta(const node & norign, const node & nodeb)
//get the theta by giving origin point and another point
{
const double PI = 3.14159;
double x = nodeb.x-norign.x;
double y = nodeb.y-norign.y;
double thet = 0.0;
if (x==0) {
if (y > 0) {
thet = 90;
}
else if (y < 0) {
thet = -90;
}
}
else {
thet = atan2(y, x);
}
thet = thet * 180 / PI;
return thet;
}
void cell::cmain() {
node anode(0, 0);
node bnode(-1, -2);
double th = get_theta(anode, bnode);
cout << th << endl;
initial();
output(0);
for (int i = 0; i < maxTime; ++i) {
output(i);
cout << "time = " << i << endl;
for (int j = 0; j != 20; ++j,++i) {
/*cout << "time = " << i << endl;*/
move();
impact();
}
}
}
int main() {
cell solver;
solver.cmain();
cout << sizeof(solver) << endl;
int temp = 2;
auto timeseed=my_rand(2);
time_t nowtime = time(nullptr);
//int nowtime = time(nullptr);
cout << "press any button to exit " <<timeseed <<" "<<nowtime<< endl;
cin.get();
return 0;
}
int my_rand(int z)
// 16807 way to create random numbers
// z is the seed number, num is the total random number to create
{
//z(n+1)=(a*z(n)+b) mod m
//describe m=a*q+r to avoid that the number is large than the computer can bear
const int m = pow(2, 31) - 1;
const int a = 16807;
const int q = 127773;
const int r = 2836;
int random = a*(z%q) - r*(z / q);
if (random<0)
{
random = m + random;
}
//z is the seed number
//z = temp;
//double t = z*1.0 / m;
//cRandom cr;
//cr.random = t;
//cr.seed = z;
return random;
}
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