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AInondim.c
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AInondim.c
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#include <stdio.h>
#include <math.h>
#include <stdlib.h>
void main(){
int i, x, y, N;
int GridEdge = 200;
int GridCenter = GridEdge/2;
double p[200][200];
double a[200][200];
double ptemp[200][200];
double atemp[200][200];
double t = 0.0;
double dt;
double Tmax =1000.0;//Calculation Time
//Tmax = 1000.0
N=10000;
dt = Tmax / N;//TimeStep
int div = N / 10;
double k1p, k1a;
double k2p, k2a;
double k3p, k3a;
double k4p, k4a;
double fp(double, double, double), p0;
double fa(double, double, double), a0;
double Dp = 0.3; //<0.5
double Da = 0.3;
double thr = 0.5;
int Area = 0;
int range[100];
FILE *fout, *fout2;
fout=fopen("AIGreen.csv","w");
//fout2=fopen("AIGreenAreaFade2.csv","w");
//InitialCondition
for(x=0; x<GridEdge; x++){
for(y=0; y<GridEdge; y++){
p[x][y] = 0.01;
a[x][y] = 0.01;
if(p[x][y] > thr)
Area++;
}
}
//Output of InitialCondition
for(x=0;x<GridEdge; x++){
for(y=0; y<GridEdge; y++){
fprintf(fout,"%.4f",p[x][y]);
if(y!=GridEdge-1){
fprintf(fout," ,");
}
}
fprintf(fout,"\n");
}
//Iteration using Runge-Kutta Method
for (i = 0; i <= N; i++) {
//Stimulation
if (i == 1000){
for(x=0; x<GridEdge; x++){
for(y=0; y<GridEdge; y++){
//p[x][y] = 1.0*(exp(-((x-GridCenter)*(x-GridCenter)+(y-GridCenter)*(y-GridCenter))/2500));
p[x][y] = 1.0*(exp(-((x-70)*(x-70)+(y-60)*(y-60))/750)+exp(-((x-150)*(x-150)+(y-80)*(y-80))/450)+exp(-((x-100)*(x-100)+(y-150)*(y-150))/450));
}
}
}
//BoundaryCondition.TopLeft
x=0;
y=0;
k1p = dt * fp(p[x][y], a[x][y], t);
k1a = dt * fa(p[x][y], a[x][y], t);
k2p = dt * fp(p[x][y] + k1p / 2, a[x][y] + k1a / 2, t + dt / 2);
k2a = dt * fa(p[x][y] + k1p / 2, a[x][y] + k1a / 2, t + dt / 2);
k3p = dt * fp(p[x][y] + k2p / 2, a[x][y] + k2a / 2, t + dt / 2);
k3a = dt * fa(p[x][y] + k2p / 2, a[x][y] + k2a / 2, t + dt / 2);
k4p = dt * fp(p[x][y] + k3p, a[x][y] + k3a, t + dt);
k4a = dt * fa(p[x][y] + k3p, a[x][y] + k3a, t + dt);
ptemp[x][y] = p[x][y]+((k1p + 2 * k2p + 2 * k3p + k4p) / 6) + dt * Dp * (p[GridEdge-1][0] + p[x+1][0] + p[0][GridEdge-1] + p[0][y+1] - 4*p[0][0]);
atemp[x][y] = a[x][y]+((k1a + 2 * k2a + 2 * k3a + k4a) / 6) + dt * Da * (a[GridEdge-1][0] + a[x+1][0] + a[0][GridEdge-1] + a[0][y+1] - 4*a[0][0]);
//BoundaryCondition.BottomLeft
x=0;
y=GridEdge-1;
k1p = dt * fp(p[x][y], a[x][y], t);
k1a = dt * fa(p[x][y], a[x][y], t);
k2p = dt * fp(p[x][y] + k1p / 2, a[x][y] + k1a / 2, t + dt / 2);
k2a = dt * fa(p[x][y] + k1p / 2, a[x][y] + k1a / 2, t + dt / 2);
k3p = dt * fp(p[x][y] + k2p / 2, a[x][y] + k2a / 2, t + dt / 2);
k3a = dt * fa(p[x][y] + k2p / 2, a[x][y] + k2a / 2, t + dt / 2);
k4p = dt * fp(p[x][y] + k3p, a[x][y] + k3a, t + dt);
k4a = dt * fa(p[x][y] + k3p, a[x][y] + k3a, t + dt);
ptemp[x][y] = p[x][y]+((k1p + 2 * k2p + 2 * k3p + k4p) / 6) + dt * Dp * (p[GridEdge-1][GridEdge-1] +p[x+1][GridEdge-1] + p[0][y-1] + p[0][0] - 4*p[0][GridEdge-1]);
atemp[x][y] = a[x][y]+((k1a + 2 * k2a + 2 * k3a + k4a) / 6) + dt * Da * (a[GridEdge-1][GridEdge-1] +a[x+1][GridEdge-1] + a[0][y-1] + a[0][0] - 4*a[0][GridEdge-1]);
//BoundaryCondition.TopRight
x=GridEdge-1;
y=0;
k1p = dt * fp(p[x][y], a[x][y], t);
k1a = dt * fa(p[x][y], a[x][y], t);
k2p = dt * fp(p[x][y] + k1p / 2, a[x][y] + k1a / 2, t + dt / 2);
k2a = dt * fa(p[x][y] + k1p / 2, a[x][y] + k1a / 2, t + dt / 2);
k3p = dt * fp(p[x][y] + k2p / 2, a[x][y] + k2a / 2, t + dt / 2);
k3a = dt * fa(p[x][y] + k2p / 2, a[x][y] + k2a / 2, t + dt / 2);
k4p = dt * fp(p[x][y] + k3p, a[x][y] + k3a, t + dt);
k4a = dt * fa(p[x][y] + k3p, a[x][y] + k3a, t + dt);
ptemp[x][y] = p[x][y]+((k1p + 2 * k2p + 2 * k3p + k4p) / 6) + dt * Dp * (p[x-1][0] + p[0][0] + p[GridEdge-1][GridEdge-1] + p[GridEdge-1][y+1] - 4*p[GridEdge-1][0]);
atemp[x][y] = a[x][y]+((k1a + 2 * k2a + 2 * k3a + k4a) / 6) + dt * Da * (a[x-1][0] + a[0][0] + a[GridEdge-1][GridEdge-1] + a[GridEdge-1][y+1] - 4*a[GridEdge-1][0]);
//BoundaryCondition.BottomRight
x=GridEdge-1;
y=GridEdge-1;
k1p = dt * fp(p[x][y], a[x][y], t);
k1a = dt * fa(p[x][y], a[x][y], t);
k2p = dt * fp(p[x][y] + k1p / 2, a[x][y] + k1a / 2, t + dt / 2);
k2a = dt * fa(p[x][y] + k1p / 2, a[x][y] + k1a / 2, t + dt / 2);
k3p = dt * fp(p[x][y] + k2p / 2, a[x][y] + k2a / 2, t + dt / 2);
k3a = dt * fa(p[x][y] + k2p / 2, a[x][y] + k2a / 2, t + dt / 2);
k4p = dt * fp(p[x][y] + k3p, a[x][y] + k3a, t + dt);
k4a = dt * fa(p[x][y] + k3p, a[x][y] + k3a, t + dt);
ptemp[x][y] = p[x][y]+((k1p + 2 * k2p + 2 * k3p + k4p) / 6) + dt * Dp * (p[x-1][GridEdge-1] + p[0][GridEdge-1] + p[GridEdge-1][y-1] + p[GridEdge-1][0] - 4*p[GridEdge-1][GridEdge-1]);
atemp[x][y] = a[x][y]+((k1a + 2 * k2a + 2 * k3a + k4a) / 6) + dt * Da * (a[x-1][GridEdge-1] + a[0][GridEdge-1] + a[GridEdge-1][y-1] + a[GridEdge-1][0] - 4*a[GridEdge-1][GridEdge-1]);
//BoundaryCondition.Left
x=0;
for(y=1; y<GridEdge-1; y++){
k1p = dt * fp(p[x][y], a[x][y], t);
k1a = dt * fa(p[x][y], a[x][y], t);
k2p = dt * fp(p[x][y] + k1p / 2, a[x][y] + k1a / 2, t + dt / 2);
k2a = dt * fa(p[x][y] + k1p / 2, a[x][y] + k1a / 2, t + dt / 2);
k3p = dt * fp(p[x][y] + k2p / 2, a[x][y] + k2a / 2, t + dt / 2);
k3a = dt * fa(p[x][y] + k2p / 2, a[x][y] + k2a / 2, t + dt / 2);
k4p = dt * fp(p[x][y] + k3p, a[x][y] + k3a, t + dt);
k4a = dt * fa(p[x][y] + k3p, a[x][y] + k3a, t + dt);
ptemp[x][y] = p[x][y]+((k1p + 2 * k2p + 2 * k3p + k4p) / 6) + dt * Dp * (p[GridEdge-1][y] + p[x+1][y] + p[0][y-1] + p[0][y+1] - 4*p[0][y]);
atemp[x][y] = a[x][y]+((k1a + 2 * k2a + 2 * k3a + k4a) / 6) + dt * Da * (a[GridEdge-1][y] + a[x+1][y] + a[0][y-1] + a[0][y+1] - 4*a[0][y]);
}
//BoundaryCondition.Right
x=GridEdge-1;
for(y=1; y<GridEdge-1; y++){
k1p = dt * fp(p[x][y], a[x][y], t);
k1a = dt * fa(p[x][y], a[x][y], t);
k2p = dt * fp(p[x][y] + k1p / 2, a[x][y] + k1a / 2, t + dt / 2);
k2a = dt * fa(p[x][y] + k1p / 2, a[x][y] + k1a / 2, t + dt / 2);
k3p = dt * fp(p[x][y] + k2p / 2, a[x][y] + k2a / 2, t + dt / 2);
k3a = dt * fa(p[x][y] + k2p / 2, a[x][y] + k2a / 2, t + dt / 2);
k4p = dt * fp(p[x][y] + k3p, a[x][y] + k3a, t + dt);
k4a = dt * fa(p[x][y] + k3p, a[x][y] + k3a, t + dt);
ptemp[x][y] = p[x][y]+((k1p + 2 * k2p + 2 * k3p + k4p) / 6) + dt * Dp * (p[x-1][y] + p[0][y] + p[GridEdge-1][y-1] + p[GridEdge-1][y+1] -4*p[GridEdge-1][y]);
atemp[x][y] = a[x][y]+((k1a + 2 * k2a + 2 * k3a + k4a) / 6) + dt * Da * (a[x-1][y] + a[0][y] + a[GridEdge-1][y-1] + a[GridEdge-1][y+1] -4*a[GridEdge-1][y]);
}
//BoundaryCondition.Top
y=0;
for(x=1; x<GridEdge-1; x++){
k1p = dt * fp(p[x][y], a[x][y], t);
k1a = dt * fa(p[x][y], a[x][y], t);
k2p = dt * fp(p[x][y] + k1p / 2, a[x][y] + k1a / 2, t + dt / 2);
k2a = dt * fa(p[x][y] + k1p / 2, a[x][y] + k1a / 2, t + dt / 2);
k3p = dt * fp(p[x][y] + k2p / 2, a[x][y] + k2a / 2, t + dt / 2);
k3a = dt * fa(p[x][y] + k2p / 2, a[x][y] + k2a / 2, t + dt / 2);
k4p = dt * fp(p[x][y] + k3p, a[x][y] + k3a, t + dt);
k4a = dt * fa(p[x][y] + k3p, a[x][y] + k3a, t + dt);
ptemp[x][y] = p[x][y]+((k1p + 2 * k2p + 2 * k3p + k4p) / 6) + dt * Dp * (p[x-1][0] + p[x+1][0] + p[x][GridEdge-1] + p[x][y+1] -4*p[x][0]);
atemp[x][y] = a[x][y]+((k1a + 2 * k2a + 2 * k3a + k4a) / 6) + dt * Da * (a[x-1][0] + a[x+1][0] + a[x][GridEdge-1] + a[x][y+1] -4*a[x][0]);
}
//BoundaryCondition.Bottom
y=GridEdge-1;
for(x=1; x<GridEdge-1; x++){
k1p = dt * fp(p[x][y], a[x][y], t);
k1a = dt * fa(p[x][y], a[x][y], t);
k2p = dt * fp(p[x][y] + k1p / 2, a[x][y] + k1a / 2, t + dt / 2);
k2a = dt * fa(p[x][y] + k1p / 2, a[x][y] + k1a / 2, t + dt / 2);
k3p = dt * fp(p[x][y] + k2p / 2, a[x][y] + k2a / 2, t + dt / 2);
k3a = dt * fa(p[x][y] + k2p / 2, a[x][y] + k2a / 2, t + dt / 2);
k4p = dt * fp(p[x][y] + k3p, a[x][y] + k3a, t + dt);
k4a = dt * fa(p[x][y] + k3p, a[x][y] + k3a, t + dt);
ptemp[x][y] = p[x][y]+((k1p + 2 * k2p + 2 * k3p + k4p) / 6) + dt * Dp * (p[x-1][GridEdge-1] + p[x+1][GridEdge-1] + p[x][y-1] + p[x][0] -4*p[x][GridEdge-1]);
atemp[x][y] = a[x][y]+((k1a + 2 * k2a + 2 * k3a + k4a) / 6) + dt * Da * (a[x-1][GridEdge-1] + a[x+1][GridEdge-1] + a[x][y-1] + a[x][0] -4*a[x][GridEdge-1]);
}
//Others
for(x=1; x<GridEdge-1; x++){
for(y=1; y<GridEdge-1; y++){
k1p = dt * fp(p[x][y], a[x][y], t);
k1a = dt * fa(p[x][y], a[x][y], t);
k2p = dt * fp(p[x][y] + k1p / 2, a[x][y] + k1a / 2, t + dt / 2);
k2a = dt * fa(p[x][y] + k1p / 2, a[x][y] + k1a / 2, t + dt / 2);
k3p = dt * fp(p[x][y] + k2p / 2, a[x][y] + k2a / 2, t + dt / 2);
k3a = dt * fa(p[x][y] + k2p / 2, a[x][y] + k2a / 2, t + dt / 2);
k4p = dt * fp(p[x][y] + k3p, a[x][y] + k3a, t + dt);
k4a = dt * fa(p[x][y] + k3p, a[x][y] + k3a, t + dt);
ptemp[x][y] = p[x][y]+((k1p + 2 * k2p + 2 * k3p + k4p) / 6) + dt * Dp * (p[x-1][y] + p[x+1][y] + p[x][y-1]+ p[x][y+1] - 4*p[x][y]);
atemp[x][y] = a[x][y]+((k1a + 2 * k2a + 2 * k3a + k4a) / 6) + dt * Da * (a[x-1][y] + a[x+1][y] + a[x][y-1]+ a[x][y+1] - 4*a[x][y]);
}
}
//Update
for(x=0;x<GridEdge; x++){
for(y=0; y<GridEdge; y++){
p[x][y]=ptemp[x][y];
a[x][y]=atemp[x][y];
}
}
//Output
if(i%div == 0){
for(x=0;x<GridEdge; x++){
for(y=0; y<GridEdge; y++){
fprintf(fout,"%.4f",p[x][y]);
if(p[x][y] > thr)
Area++;
if(y!=GridEdge-1){
fprintf(fout," ,");
}
}
fprintf(fout,"\n");
}
range[i / div] = Area;
//fprintf(fout2, "%d\n", range[i / div]);
printf("%d", i);
Area = 0;
}
t = (i + 1) * dt;
}
}
double fp(double p, double a, double t){
double pa = 0.05;
double qa = 3.4;//
double ra = 0.8;
return pa + (qa*p*p/((1+p*p)*(1+a))) - ra*p;
}
double fa(double p, double a, double t){
double pi = 0.06;//
double qi = 6.0;
double ri = 1.0;//Fixed
//return pi + (qi*p*a/((1+p)*(1+a))) - ri*a; //Pattern RED
//return pi + (qi*p*a*a/((1+p)*(1+a*a))) - ri*a; //Pattern BLUE
return pi + (qi*p*p*a*a/((1+p*p)*(1+a*a))) - ri*a; //Pattern GREEN
}