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test2a_c_block.c
500 lines (446 loc) · 12.9 KB
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test2a_c_block.c
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#include <stdio.h>
#include <math.h>
/*This is the rewriting of Rocco's matlab code to C*/
#define xnum 151
#define ynum 61
#define nb 5 //number of block
double Max (double *a)
{
double maxinum=*a;
int m,n,r;
for(m=0;m<ynum;m++)
for(n=0;n<xnum;n++)
{
r=m*xnum;
if(*(a+r+n)>maxinum)
{
maxinum=*(a+r+n);
}
}
return maxinum;
}
double Max1 (double a, double b)
{
if(a>b)
return a;
else
return b;
}
double Min (double *a)
{
double minimum=*a;
int m,n,r;
for(m=0;m<ynum;m++)
for(n=0;n<xnum;n++)
{
r=m*xnum;
if(*(a+r+n)<minimum)
{
minimum=*(a+r+n);
}
}
return minimum;
}
/*double Min (double a[ynum][xnum])
{
double minimum=a[0][0];
int m,n;
for(m=0;m<ynum;m++)
for(n=0;n<xnum;n++)
{
//r=m*xnum;
if(a[m][n]<minimum)
{
minimum=a[m][n];
}
}
return minimum;
}*/
double Min1 (double a, double b)
{
if(a<b)
return a;
else
return b;
}
void solver(double dx_, double dy_, double dt_, double *h0_, double *h1_,
double *Kx_, double *Ky_, double *Ss_, double *Q_, double xlS_,
double xrS_,double v0_,double *x_)
{
int i,j,r;
double ka,kb,kc,kd,vxa,vxb,vyc,vyd;
double kappa_1;
// internal values following pages 139-140 in Gerya's book
for(i=1;i<ynum-1;i++)
{
for(j=1;j<xnum-1;j++)
{
r=i*xnum;
ka=(*(Kx_+r+j-1)+*(Kx_+r+j))/2;
kb=(*(Kx_+r+j+1)+*(Kx_+r+j))/2;
kc=(*(Ky_+r-xnum+j)+*(Ky_+r+j))/2;
kd=(*(Ky_+r+xnum+j)+*(Ky_+r+j))/2;
vxa=-ka*(*(h0_+r+j)-*(h0_+r+j-1))/dx_;
vxb=-kb*(*(h0_+r+j+1)-*(h0_+r+j))/dx_;
vyc=-kc*(*(h0_+r+j)-*(h0_+r-xnum+j))/dy_;
vyd=-kd*(*(h0_+r+xnum+j)-*(h0_+r+j))/dy_;
kappa_1=dt_/(*(Ss_+r+j));
*(h1_+r+j)=*(h0_+r+j)+*(Q_+r+j)/(*(Ss_+r+j))
-kappa_1*((vxb-vxa)/dx_+(vyd-vyc)/dy_);
}
}
//fix surface hydraulic values to 0
for (j=0;j<xnum;j++)
*(h1_+j)=0;
//left and right sides boundary condition: no flow
for (i=1;i<ynum-1;i++)
{
r=i*xnum;
*(h1_+r)=*(h1_+r+1); //left side
*(h1_+r+xnum-1)=*(h1_+r+xnum-2);//right side
}
//Bottom boundary condition: no flow
for (i=0;i<xnum;i++)
*(h1_+(ynum-1)*xnum+i)=*(h1_+(ynum-2)*xnum+i);
//fix vertical flow in the source region at the bottom
r=xnum*(ynum-1);
for (j=0;j<xnum;j++)
{
if((*(x_+j)>=xlS_)&&(*(x_+j)<=xrS_))
{
kc=(*(Ky_+r-xnum+j)+*(Ky_+r+j))/2;
*(h1_+r+j)=-v0_*dy_/kc+*(h1_+r-xnum+j);
}
}
}
void flow(double dx_,double dy_,double *h, double *Kx_, double *Ky_,
double *v1x_,double *v1y_, double *v1_)
{
int i,j,r;
double ka,kb,kc,kd,vxa,vxb,vyc,vyd;
//internal values following pages 139-140 in Gerya's book
for(i=1;i<ynum-1;i++)
{
for(j=1;j<xnum-1;j++)
{
r=i*xnum;
ka=(*(Kx_+r+j-1)+*(Kx_+r+j))/2;
kb=(*(Kx_+r+j+1)+*(Kx_+r+j))/2;
kc=(*(Ky_+r-xnum+j)+*(Ky_+r+j))/2;
kd=(*(Ky_+r+xnum+j)+*(Ky_+r+j))/2;
vxa=-ka*(*(h+r+j)-*(h+r+j-1))/dx_;
vxb=-kb*(*(h+r+j+1)-*(h+r+j))/dx_;
vyc=-kc*(*(h+r+j)-*(h+r-xnum+j))/dy_;
vyd=-kd*(*(h+r+xnum+j)-*(h+r+j))/dy_;
*(v1x_+r+j)=(vxb+vxa)/2;
*(v1y_+r+j)=(vyd+vyc)/2;
//*(v1_+r+j)=sqrt((*(v1x_+r+j))*(*(v1x_+r+j))+(*(v1y_+r+j))*(*(v1y_+r+j)));
}
}
//surface values flow
for(j=1;j<xnum-1;j++)
{
ka=(*(Kx_+j-1)+*(Kx_+j))*0.5;
kb=(*(Kx_+j+1)+*(Kx_+j))*0.5;
kd=(*(Ky_+j)+*(Ky_+xnum+j))*0.5;
vxa=-ka*(0-0)/dx_;
vxb=-kb*(0-0)/dx_;
vyd=-kd*(*(h+xnum+j)-0)/dy_;
*(v1x_+j)=0.5*(vxb+vxa);
*(v1y_+j)=vyd;
//*(v1_+j)=sqrt((*(v1x_+j))*(*(v1x_+j))+(*(v1y_+j))*(*(v1y_+j)));
}
//surface//the left up corner// I think we can calculate the four corners in the end
kb=(*(Kx_+1)+*(Kx_))*0.5;
kd=(*(Ky_+xnum)+*(Ky_))*0.5;
vxb=-kb*(*(h+1)-*(h))/dx_;
vyd=-kd*(*(h+xnum)-*(h))/dy_;
*(v1x_)=vxb;
*(v1y_)=vyd;
//*(v1_)=sqrt((*v1x_)*(*v1x_)+(*v1y_)*(*v1y_));
//surface//the right up corner
ka=(*(Kx_+xnum-2)+*(Kx_+xnum-1))*0.5;
kd=(*(Ky_+xnum+xnum-1)+*(Ky_+xnum-1))*0.5;
vxa=-ka*(*(h+xnum-1)-*(h+xnum-2))/dx_;
vyd=-kd*(*(h+xnum+xnum-1)-*(h+xnum-1))/dy_;
*(v1x_+xnum-1)=vxa;
*(v1y_+xnum-1)=vyd;
//bottom values flow
r=(ynum-1)*xnum;
for(j=1;j<xnum-1;j++)
{
ka=(*(Kx_+r+j-1)+*(Kx_+r+j))*0.5;
kb=(*(Kx_+r+j+1)+*(Kx_+r+j))*0.5;
kc=(*(Ky_+r-xnum+j)+*(Ky_+r+j))*0.5;
vxa=-ka*(*(h+r+j)-*(h+r+j-1))/dx_;
vxb=-kb*(*(h+r+j+1)-*(h+r+j))/dx_;
vyc=-kc*(*(h+r+j)-*(h+r-xnum+j))/dy_;
*(v1x_+r+j)=(vxa+vxb)*0.5;
*(v1y_+r+j)=vyc;
}
//bottom//left corner
kb=(*(Kx_+r+1)+*(Kx_+r))*0.5;
kc=(*(Ky_+r)+*(Ky_+r-xnum))*0.5;
vxb=-kb*(*(h+r+1)-*(h+r))/dx_;
vyc=-kc*(*(h+r)-*(h+r-xnum))/dy_;
*(v1x_+r)=vxb;
*(v1y_+r)=vyc;
//bottom//right corner
ka=(*(Kx_+r+xnum-1)+*(Kx_+r+xnum-2))*0.5;
kc=(*(Ky_+r+xnum-1)+*(Ky_+r-xnum+xnum-1))*0.5;
vxa=-ka*(*(h+r+xnum-1)-*(h+r+xnum-2))/dx_;
vyc=-kc*(*(h+r+xnum-1)-*(h+r-xnum+xnum-1))/dy_;
*(v1x_+r+xnum-1)=vxa;
*(v1y_+r+xnum-1)=vyc;
//left
for(i=1;i<ynum-1;i++)
{
r=i*xnum;
kb=(*(Kx_+r+1)+*(Kx_+r))*0.5;
kc=(*(Ky_+r)+*(Ky_+r-xnum))*0.5;
kd=(*(Ky_+r+xnum)+*(Ky_+r))*0.5;
vxb=-kb*(*(h+r+1)-*(h+r))/dx_;
vyc=-kc*(*(h+r)-*(h+r-xnum))/dy_;
vyd=-kd*(*(h+r+xnum)-*(h+r))/dy_;
*(v1x_+r)=vxb;
*(v1y_+r)=(vyc+vyd)*0.5;
}
//left//up corner
kb=(*(Kx_+1)+*(Kx_))*0.5;
kd=(*(Ky_+xnum)+*(Ky_))*0.5;
vxb=-kb*(*(h+1)-*(h))/dx_;
vyd=-kd*(*(h+xnum)-*(h))/dy_;
*(v1x_)=vxb;
*(v1y_)=vyd;
//left//bottom corner
r=xnum*(ynum-1);
kb=(*(Kx_+r+1)+*(Kx_+r))*0.5;
kc=(*(Ky_+r)+*(Ky_+r-xnum))*0.5;
vxb=-kb*(*(h+r+1)-*(h+r))/dx_;
vyc=-kc*(*(h+r)-*(h+r-xnum))/dy_;
*(v1x_+r)=vxb;
*(v1y_+r)=vyc;
//right
for(i=1;i<ynum-1;i++)
{
r=i*xnum;
ka=(*(Kx_+r+xnum-1)+*(Kx_+r+xnum-2))*0.5;
kc=(*(Ky_+r+xnum-1)+*(Ky_+r-xnum+xnum-1))*0.5;
kd=(*(Ky_+r+xnum-1)+*(Ky_+r+xnum+xnum-1))*0.5;
vxa=-ka*(*(h+r+xnum-1)-*(h+r+xnum-2))/dx_;
vyc=-kc*(*(h+r+xnum-1)-*(h+r-xnum+xnum-1))/dy_;
vyd=-kd*(*(h+r+xnum+xnum-1)-*(h+r+xnum-1))/dy_;
*(v1x_+r+xnum-1)=vxa;
*(v1y_+r+xnum-1)=(vyc+vyd)*0.5;
}
//right//top corner
ka=(*(Kx_+xnum-1)+*(Kx_+xnum-2))*0.5;
kd=(*(Ky_+xnum+xnum-1)+*(Ky_+xnum-1))*0.5;
vxa=-ka*(*(h+xnum-1)-*(h+xnum-2))/dx_;
vyd=-kd*(*(h+xnum+xnum-1)-*(h+xnum-1))/dy_;
*(v1x_+xnum-1)=vxa;
*(v1y_+xnum-1)=vyd;
//right//bottom corner
r=xnum*(ynum-1);
ka=(*(Kx_+r+xnum-1)+*(Kx_+r+xnum-2))*0.5;
kc=(*(Ky_+r+xnum-1)+*(Ky_+r-xnum+xnum-1))*0.5;
vxa=-ka*(*(h+r+xnum-1)-*(h+r+xnum-2))/dx_;
vyc=-kc*(*(h+r+xnum-1)-*(h+r-xnum+xnum-1))/dy_;
*(v1x_+r+xnum-1)=vxa;
*(v1y_+r+xnum-1)=vyc;
//calculate v1
for(i=0;i<ynum;i++)
for(j=0;j<xnum;j++)
{
r=i*xnum;
*(v1_+r+j)=sqrt(*(v1x_+r+j)*(*(v1x_+r+j))+*(v1y_+r+j)*(*(v1y_+r+j)));
}
}
void main()
{
int i=0,j=0,r=0;
//Model size
double xsize=5e5;
double ysize=5e4;
//Number of time steps
int maxtnum=200000;
//grid size
double dx=xsize/(xnum-1);
double dy=ysize/(ynum-1);
//Grid step
double xstp,ystp;
double x[xnum],y[ynum];
xstp=xsize/(xnum-1); //horizontal
ystp=ysize/(ynum-1); //vertical
for(i=0;i<xnum;i++)
{
*(x+i)=xstp*i;
}
for(i=0;i<ynum;i++)
{
*(y+i)=ystp*i;
}
//Initial hydraulic uniform head value
double H0=0;
double h0[ynum][xnum];
double h1[ynum][xnum];
double *h0p,*h1p;
h0p=&h0[0][0];
h1p=&h1[0][0];
//background permeability for x and y direction.
double kxbg=1;
double kybg=1.5;
//Source at the bottom
double Ls=3500;
double xlS=0.5*xsize-0.5*Ls;
double xrS=0.5*xsize+0.5*Ls;
double v0=100/Ls;
//printf("\n%f,%f",xlS,xrS);
//high K blocks
//int nb=5; //number of blocks
double Kbx[nb],Kby[nb]; //K for different block
double xc[nb],yc[nb];//positions of the center points of blocks
double L[nb],W[nb];//length and width of block
double xlb[nb],xrb[nb],ytb[nb],ybb[nb];//edges of the blocks
//Block a
xc[0]=xsize*0.5-3e4;
yc[0]=25e3;
L[0]=28e3;W[0]=10e3;
Kbx[0]=kxbg*5;
Kby[0]=kybg*5;
//block b
xc[1]=xsize*0.5+5e3;
yc[1]=20e3;
L[1]=15e3;W[1]=15e3;
Kbx[1]=kxbg*4;
Kby[1]=kybg*4;
//block c
xc[2]=xsize*0.5+50e3;
yc[2]=18e3;
L[2]=12e3;W[2]=12e3;
Kbx[2]=kxbg*15;
Kby[2]=kybg*5;
//block d
xc[3]=xsize*0.5+50e3+80e3;
yc[3]=15e3;
L[3]=12e3;W[3]=12e3;
Kbx[3]=kxbg*15;
Kby[3]=kybg*15;
//block e
xc[4]=xsize*0.5+110e3;
yc[4]=14e3;
L[4]=11e3;W[4]=11e3;
Kbx[4]=kxbg*25;
Kby[4]=kybg*25;
for(i=0;i<nb;i++)
{
xlb[i]=xc[i]-L[i]*0.5;
xrb[i]=xc[i]+L[i]*0.5;
ytb[i]=yc[i]-W[i]*0.5;
ybb[i]=yc[i]+W[i]*0.5;
//printf("%f\t%f\t%f\t%f\t\%f\t\%f\n",xlb[i],xrb[i],ytb[i],ybb[i],Kbx[i],Kby[i]);
}
//Specific storage uniform......
double ss=1;
double Ss[ynum][xnum],Kx[ynum][xnum],Ky[ynum][xnum],Q[ynum][xnum];
double v1[ynum][xnum],v1x[ynum][xnum],v1y[ynum][xnum];
for (i=0;i<ynum;i++)
{
for(j=0;j<xnum;j++)
{
h0[i][j]=0;
h1[i][j]=0;
Ss[i][j]=ss;
Kx[i][j]=kxbg;
Ky[i][j]=kybg;
Q[i][j]=0;
v1[0][0]=v1x[0][0]=v1y[0][0]=0;
}
}
//set the K for different block
for(r=0;r<nb;r++)
{
for(i=0;i<ynum;i++)
{
for(j=0;j<xnum;j++)
{
if((y[i]<=ybb[r])&&(y[i]>=ytb[r])&&(x[j]>=xlb[r])&&(x[j]<=xrb[r]))
{
Kx[i][j]=Kbx[r];
Ky[i][j]=Kby[r];
}
}
}
//printf("%d\t",r);
}
//diffusivity for computing time step
double kappax=Max(&Kx[0][0])/Min(&Ss[0][0]);
double kappay=Max(&Ky[0][0])/Min(&Ss[0][0]);
double kappa=Max1(kappax,kappay);
//time step limit, [book]introduction to numerical geodynamic modelling p134, equation (10.4)
double dtexp=100*100.0/(3*kappa);
//time step
double dt=1.0*dtexp;
double time=0;
int it;
for(it=1;it<=maxtnum;it++)
{
solver(dx,dy,dt,h0p,h1p,&Kx[0][0],&Ky[0][0],&Ss[0][0],&Q[0][0],xlS,xrS,v0,&x[0]);
//h0p=h1p;
flow(dx,dy,&h1[0][0],&Kx[0][0],&Ky[0][0],&v1x[0][0],&v1y[0][0],&v1[0][0]);
for(i=0;i<ynum;i++)
for(j=0;j<xnum;j++)
h0[i][j]=h1[i][j];
time=time+dt;
}
//calculate the min of head and v1 for reference
/*double min_h,min_v1;
min_h=Min(&h1[0][0]);
min_v1=Min(&v1[0][0]);
printf("%g\n%g\n",min_h,min_v1);*/
FILE *fp1,*fp2;
FILE *fp3,*fp4;
FILE *fp5,*fp6,*fp7,*fp8;
fp1=fopen("head_h1.txt","w");
fp2=fopen("v1.txt","w");
fp3=fopen("v1x.txt","w");
fp4=fopen("v1y.txt","w");
fp5=fopen("Kx.txt","w");
fp6=fopen("Ky.txt","w");
fp7=fopen("xy.txt","w"); //storage x and y grid step
fp8=fopen("paramaters.txt","w");
for(i=0;i<ynum;i++)
{
for(j=0;j<xnum;j++)
{
//sometimes, if the results are to small (like 1e-100), we should be careful when write the result to file. maybe we can try %g
fprintf(fp1,"%.100lf\t",h1[i][j]); //%15.10lf
fprintf(fp2,"%.100lf\t",v1[i][j]);
fprintf(fp3,"%.100lf\t",v1x[i][j]);
fprintf(fp4,"%.100lf\t",v1y[i][j]);
fprintf(fp5,"%f\t",Kx[i][j]);
fprintf(fp6,"%f\t",Ky[i][j]);
}
fprintf(fp1,"\n");
fprintf(fp2,"\n");
fprintf(fp3,"\n");
fprintf(fp4,"\n");
fprintf(fp5,"\n");
fprintf(fp6,"\n");
}
for(i=0;i<ynum;i++)
fprintf(fp7,"%f\t",y[i]);
fprintf(fp7,"\n");
for(j=0;j<xnum;j++)
fprintf(fp7,"%f\t",x[j]);
fprintf(fp8,"%lf\t%lf\t%d\t%d\t%d\t%lf",xsize,ysize,xnum,ynum,it-1,time);
fclose(fp1);
fclose(fp2);
fclose(fp3);
fclose(fp4);
fclose(fp5);
fclose(fp6);
fclose(fp7);
fclose(fp8);
//plot the results in matlab
}