拟一维喷管流动的数值解法(MATLAB)代码

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functionmain()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+1.09*x).*(1-0.2314*x).^0.5;%按时间步长推进fork=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,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)=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);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(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图形处理代码closeall;a=[151101151201701];plot(x,M(a(1),:).*A(:)'.*V(a(1),:),'r--')holdonplot(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-')axisequallegend('0dt','50dt','100dt','150dt','200dt','700dt')figure[ax,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')