用时间推进法模拟一维线性对流模型

% Simulation of a 1-D Linear Convection model by a time march (Finite ...Difference Method) % Numerical scheme used is a first order upwind in both space and time

%% %Specifying Parameters nx=50; %Number of steps in space(x) nt=50; %Number of time steps dt=0.01; %Width of each time step c=1.0; %Velocity of wave propagation dx=2/(nx-1); %Width of space step x=0:dx:2; %Range of x (0,2) and specifying the grid points u=zeros(1,nx); %Preallocating u un=zeros(1,nx); %Preallocating un sigma=abs(c)*dt/dx; %Courant-Freidrich-Lewy number

%% %Initial Conditions: A square wave for i=1:nx if ((0.75<=x(i))&&(x(i)<=1.25)) u(i)=2; else u(i)=1; end end

%% %Evaluating velocity profile for each time step i=2:nx-1; for it=0:nt un=u; h=plot(x,u); %plotting the velocity profile axis([0 2 0 3]) title({[1-D Linear Convection with {itc} = ,num2str(c), and CFL (sigma) = ,num2str(sigma)];[time(itt) = ,num2str(dt*it)]}) xlabel(Spatial co-ordinate (x) ightarrow) ylabel(Transport property profile (u) ightarrow) drawnow; refreshdata(h) pause(0.1) %Explicit method with F.D in time and B.D in space u(i)=un(i)-0.5*(sign(c)+1)*((c*dt*(un(i)-un(i-1)))/dx)... +0.5*(sign(c)-1)*((c*dt*(un(i+1)-un(i)))/dx); end

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