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1、拟一维喷管流动的数值解法（MATLAB）代码数值计算代码%拟一维喷管流动的数值解%亚声速-超声速，非守恒形式function main()clear;clc;r=1.4; %绝热指数N=1001; %时间步长i=31; %网格数目L=3; %喷管长度C=0.5; %柯朗数dx=L/(i-1); %空间步长dt(N)=0; %时间步长x=linspace(0,L,i); %网格点横坐标A=1+2.2*(x-1.5).2; %喷管面积%赋值M(N,i)=0;T(N,i)=0;V(N,i)=0;%初始条件M(1,:)=1-0.3146*x;T(1,:)=1-0.2314*x;V(1,:)=(0.1+
2、1.09*x).*(1-0.2314*x).0.5;%按时间步长推进for k=1:N-1 %预估偏导数 M_t(1:i-1)=-V(k,1:i-1).*(M(k,2:i)-M(k,1:i-1)/dx-M(k,1:i-1).*(V(k,2:i)-V(k,1:i-1)/dx-M(k,1:i-1).*V(k,1:i-1).*log(A(2:i)./A(1:i-1)/dx; V_t(1:i-1)=-V(k,1:i-1).*(V(k,2:i)-V(k,1:i-1)/dx-1/r.*(T(k,2:i)-T(k,1:i-1)/dx+T(k,1:i-1)./M(k,1:i-1).*(M(k,2:i)-M(k
3、,1:i-1)/dx); T_t(1:i-1)=-V(k,1:i-1).*(T(k,2:i)-T(k,1:i-1)/dx-(r-1).*T(k,1:i-1).*(V(k,2:i)-V(k,1:i-1)/dx+V(k,1:i-1).*log(A(2:i)./A(1:i-1)/dx); %求取内部网格点处最小时间步长 t=C*dx./(V(k,2:i-1)+sqrt(T(k,2:i-1); dt(k)=min(t); %预估值 M1(1:i-1)=M(k,1:i-1)+M_t(1:i-1)*dt(k); V1(1:i-1)=V(k,1:i-1)+V_t(1:i-1)*dt(k); T1(1:i-1
4、)=T(k,1:i-1)+T_t(1:i-1)*dt(k); %校正偏导数 M_t_1(2:i-1)=-V1(2:i-1).*(M1(2:i-1)-M1(1:i-2)./dx-M1(2:i-1).*(V1(2:i-1)-V1(1:i-2)./dx-M1(2:i-1).*V1(2:i-1).*log(A(2:i-1)./A(1:i-2)./dx; V_t_1(2:i-1)=-V1(2:i-1).*(V1(2:i-1)-V1(1:i-2)./dx-1/r.*(T1(2:i-1)-T1(1:i-2)./dx+T1(2:i-1)./M1(2:i-1).*(M1(2:i-1)-M1(1:i-2)./dx
5、); T_t_1(2:i-1)=-V1(2:i-1).*(T1(2:i-1)-T1(1:i-2)./dx-(r-1).*T1(2:i-1).*(V1(2:i-1)-V1(1:i-2)./dx+V1(2:i-1).*log(A(2:i-1)./A(1:i-2)./dx); %偏导数平均值 M_t_av(2:i-1)=0.5*(M_t(2:i-1)+M_t_1(2:i-1); V_t_av(2:i-1)=0.5*(V_t(2:i-1)+V_t_1(2:i-1); T_t_av(2:i-1)=0.5*(T_t(2:i-1)+T_t_1(2:i-1); %内部网格点修正值 M(k+1,2:i-1)=M
6、(k,2:i-1)+M_t_av(2:i-1)*dt(k); V(k+1,2:i-1)=V(k,2:i-1)+V_t_av(2:i-1)*dt(k); T(k+1,2:i-1)=T(k,2:i-1)+T_t_av(2:i-1)*dt(k); %出口边界值 M(k+1,i)=2*M(k+1,i-1)-M(k+1,i-2); V(k+1,i)=2*V(k+1,i-1)-V(k+1,i-2); T(k+1,i)=2*T(k+1,i-1)-T(k+1,i-2); %入口边界值 M(k+1,1)=1; V(k+1,1)=2*V(k+1,2)-V(k+1,3); T(k+1,1)=1;endend图形处理
7、代码close all;a=1 51 101 151 201 701;plot(x,M(a(1),:).*A(:).*V(a(1),:),r-)hold onplot(x,M(a(2),:).*A(:).*V(a(2),:),m.-)plot(x,M(a(3),:).*A(:).*V(a(3),:),g*-)plot(x,M(a(4),:).*A(:).*V(a(4),:),co-)plot(x,M(a(5),:).*A(:).*V(a(5),:),bh-)plot(x,M(a(6),:).*A(:).*V(a(6),:),k-)axis equallegend(0dt,50dt,100dt,
8、150dt,200dt,700dt)figureax,h1,h2=plotyy(x,M(a(6),:),x,sqrt(M(a(6),:).(1-r)-1)*5),plot);set(h1,linestyle,-,marker,o,color,b); set(h2,linestyle,-,marker,*,color,r);set(ax,xtick,0:0.3:3)set(ax(1),ytick,0:0.1:1)set(ax(2),ytick,0:0.4:4)set(h1,linewidth,1.5)set(h2,linewidth,1.5)set(get(ax(1),xlabel),string,无量纲轴向距离(x)set(get(ax(1),ylabel),string,无量纲密度(M)set(get(ax(2),ylabel),string,马赫数(Ma)title(无量纲密度和马赫数定常分布数值解)legend(无量纲密度数值解,马赫数数值解)
