1.cpp
#include
#include "matlib.h"
#include
#include "function.h"
using namespace std;
void main(){
initM(MATCOM_VERSION);
cout<<"*********************TTM方法生翼形网格*********************"<
int IM,JM,NUM;
double omega,dx,dy;
cout<<"请输入ξ方向网格节点数IM";
cin>>IM;
cout<<"请输入η方向网格节点数IN";
cin>>JM;
cout<<"迭代方法： 1.点Gauss-Siedel迭代 2.线Gauss-Siedel迭代";
cout<<" 3.超松弛点Gauss-Siedel迭代 ";
cin>>NUM;
if (NUM==3)
{
cout<<"松弛因子:1<ω<2";
cin>>omega;
}
Mm time;
tic();
dx=2.0/(IM-1);
dy=2.0/(JM-1);
////////////////////////////////////////////////////////////////////////
/* 绘制初始网格 */
/////////////////////////////////////////////////////////////////////////
//绘制翼形；
Mm x,y;
x=colon(0,0.01,1);
y=zeros(1,x.size());
for (int i=1;i<=x.size(2);i++){
y.r(1,i)=valueAtX(x.r(1,i));
}
plot((CL(x),y,TM("-b"),x,-y,TM("-b")));
hold(TM("on"));
/////////////////////////////////////////////////////////////////////////
//绘制初始网格
double dsita;
dx=1.0/((IM+1)/2-1);
dsita=2.0*3.1415926/(IM-1);
x=zeros(IM,JM);
y=zeros(IM,JM);
for (i=1;i<=IM;i++)
{
double x0,y0,sita;
sita=dsita*(i-1);
x0=findRoot(sita);
if (sin(sita)>=0)
y0=valueAtX(x0);
else
y0=-valueAtX(x0);
x.r(i,1)=x0;
y.r(i,1)=y0;
x.r(i,JM)=0.5+2.5*cos(sita);
y.r(i,JM)=2.5*sin(sita);
x(i,c_p)=linspace(x.r(i,1),x.r(i,JM),JM-1);
y(i,c_p)=linspace(y.r(i,1),y.r(i,JM),JM-1);
}
plot((CL(x(c_p,colon(2,JM))),y(c_p,colon(2,JM)),
TM("-b"),transpose(x(colon(1,IM),c_p)),transpose(y(colon(1,IM),c_p)),TM("-b")));
axis(TM("equal"));
///////////////////////////////////////////////////////////////////////
Mm x_temp=ones(x.size(1),x.size(2)),y_temp=ones(x.size(1),x.size(2));
double err=10.0;
int k=0;
//////////////////////G--S点迭代
if (NUM==1||NUM==3)
{
while(err>1.0e-5)
{
x_temp(c_p,c_p)=x(c_p,c_p);
y_temp(c_p,c_p)=y(c_p,c_p);
Cacl_p(x,y,x_temp,y_temp,dx,dy,NUM,omega);
err=max(max(abs(x-x_temp)+abs(y-y_temp))).r(1,1);
k++;
}
}
if (NUM==2)
{
while(err>1.0e-5)
{
x_temp(c_p,c_p)=x(c_p,c_p);
y_temp(c_p,c_p)=y(c_p,c_p);
Cacl_l(x,y,x_temp,y_temp,dx,dy,NUM,omega);
err=max(max(abs(x-x_temp)+abs(y-y_temp))).r(1,1);
k++;
}
}
disp(k);
figure();
plot((CL(x(c_p,c_p)),y(c_p,c_p),
TM("-b"),transpose(x(colon(1,IM),c_p)),transpose(y(colon(1,IM),c_p)),TM("-b")));
axis(TM("equal"));
time=toc();
disp(time);
exitM();
}
*********************************************************************************************************************
function.cpp
#include
#include "matlib.h"
#include
#include "function.h"
using namespace std;
double valueAtX(doub
le x){
return 0.2969*sqrt(x)-0.1260*x-0.3516*pow(x,2)+0.2843*pow(x,3)-0.1015*pow(x,4);
}
double findRoot(double sita){
double x[3], y[3]; //x－进行二分法插值的三个点。y－对应的函数值
x[0]=0.5;
if (cos(sita)>0)
x[2]=1;
else
x[2]=0;
while (abs(x[0]-x[2])>1e-6)
{
x[1]=(x[0]+x[2])/2;
if (sin(sita)>=0)
y[2]=valueAtX(x[2])-tan(sita) * (x[2]-0.5),
y[1]=valueAtX(x[1])-tan(sita) * (x[1]-0.5),
y[0]=valueAtX(x[0])-tan(sita) * (x[0]-0.5);
else
y[2]=-valueAtX(x[2])-tan(sita) * (x[2]-0.5),
y[1]=-valueAtX(x[1])-tan(sita) * (x[1]-0.5),
y[0]=-valueAtX(x[0])-tan(sita) * (x[0]-0.5);
if (y[1]*y[0]<0)
x[2]=x[1];
else
x[0]=x[1];
}
return x[1];
}
void coefficence(double& a,double& b,double& c,double i,double j,Mm& x, Mm& y,double dx,double dy){
double x_yita,y_yita,x_yip,y_yip;
int i0=i,i1=i;
if (i0==1)
{
i0=x.size(1)-1;
}
else
i0=i-1;
if (i1==x.size(1))
{
i1=2;
}
else
i1=i+1;
x_yita=(x.r(i,j+1)-x.r(i,j-1))/(2*dy);
x_yip =(x.r(i1,j)-x.r(i0,j))/(2*dx);
y_yita=(y.r(i,j+1)-y.r(i,j-1))/(2*dy);
y_yip =(y.r(i1,j)-y.r(i0,j))/(2*dx);
a=pow(x_yita,2)+pow(y_yita,2);
b=x_yip*x_yita+y_yip*y_yita;
c=pow(x_yip,2)+pow(y_yip,2);
}
void Cacl_p(Mm& x,Mm& y ,Mm& x_temp,Mm& y_temp,double dx,double dy,int& NUM,double& omega){ //Gauss-Siedel点迭代。充分利用新值
double a,b,c;
for (int i=2;i<=x.size(1);i++)
{
for (int j=2;j<=x.size(2)-1;j++)
{
int i0=i-1,i1=i;
if (i1==x.size(1))
{
i1=2;
}
else
i1=i+1;
coefficence(a,b,c,i,j,x,y,dx,dy);
x.r(i,j)=(a/(dx*dx)*(x.r(i1,j)+x.r(i0,j)) - b/(2*dx*dy)*(x.r(i1,j+1)-x.r(i0,j+1)-
x.r(i1,j-1)+x.r(i0,j-1))+c/(dy*dy)*(x.r(i,j+1)+x.r(i,j-1)))/(2*a/(dx*dx)+2*c/(dy*dy));
y.r(i,j)=(a/(dx*dx)*(y.r(i1,j)+y.r(i0,j)) - b/(2*dx*dy)*(y.r(i1,j+1)-y.r(i0,j+1)-
y.r(i1,j-1)+y.r(i0,j-1))+c/(dy*dy)*(y.r(i,j+1)+y.r(i,j-1)))/(2*a/(dx*dx)+2*c/(dy*dy));
if (NUM==3) //超松弛法点迭代
{
x.r(i,j)=x_temp.r(i,j)+omega*(x.r(i,j)-x_temp.r(i,j));
y.r(i,j)=y_temp.r(i,j)+omega*(y.r(i,j)-y_temp.r(i,j));
}
}
}
x(1,c_p)=x(x.size(1),c_p);
y(1,c_p)=y(x.size(1),c_p);
}
void Cacl_l(Mm& x,Mm& y ,Mm& x_temp,Mm& y_temp,double dx,double dy,int NUM,double omega){
int JM=x.size(2),IM=x.size(1);
double a,b,c;
Mm A ,bx, by;
for (int i=2;i<=IM;i++)
{
Mm BX,BY;
A=diag(2*ones(1,JM-2))-diag(ones(1,JM-3),-1)-diag(ones(1,JM-3),1);
BX=zeros(JM-2,1),BY=zeros(JM-2,1);
for (int j=2;j<=JM-1;j++)
{
int i1=i;
if (i1==IM)
{
i1=2;
}
else
i1=i+1;
coefficence(a,b,c,i,j,x,y,dx,dy);
BX.r(j-1,1)=(4*a*dy*dy*(x.r(i1,j)+x.r(i-1,j))-2*b*dx*dy*(x.r(i1,j+1)-x.r(i-1,j+1)-x.r(i1,j-1)+x.r(i-1,j-1)))/(4*dx*dx*c);
BY.r(j-1,1)=(4*a*dy*dy*(y.r(i1,j)+y.r(i-1,j))-2*b*dx*dy*(y.r(i1,j+1)-y.r(i-1,j+1)-y.r(i1,j-1)+y.r(i-1,j-
1)))/(4*dx*dx*c);
A.r(j-1,j-1)=A.r(j-1,j-1)+pow(dy,2)/c*a/pow(dx,2)*2;
}
BX.r(1,1)=BX.r(1,1)+x.r(i,1);
BX.r(JM-2,1)=BX.r(JM-2,1)+x.r(i,JM);
BY.r(1,1)=BY.r(1,1)+y.r(i,1);
BY.r(JM-2,1)=BY.r(JM-2,1)+y.r(i,JM);
x(i,colon(2,JM-1))=mldivide(A,BX);
y(i,colon(2,JM-1))=mldivide(A,BY);
}
x(1,c_p)=x(IM,c_p);
y(1,c_p)=y(IM,c_p);
}
**************************************************************************************************************************
function.h
double valueAtX(double x); //计算翼形在对应点的函数值
//Mm bound(Mm& sita); //计算中心射线与边界的交点
double findRoot(double sita);
void coefficence(double& a,double& b,double& c,double i,double j,Mm& x, Mm& y,double dx,double dy);
void Cacl_p(Mm& x,Mm& y ,Mm& x_temp,Mm& y_temp,double dx,double dy,int& NUM,double& omega);
void Cacl_l(Mm& x,Mm& y ,Mm& x_temp,Mm& y_temp,double dx,double dy,int NUM,double omega);