Simple Heat Equation solver

版本 1.0.0.3 (5.5 MB) 作者: michio
Simple Heat Equation solver using finite difference method
5.0
(2)
3.7K 次下载
更新时间 2023/3/18
在 GitHub 上查看许可证

Finite differences for the 2D heat equation

Open in MATLAB Online View Simple Heat Equation solver on File Exchange

Implementation of a simple numerical schemes for the heat equation.

Applying the second-order centered differences to approximate the spatial derivatives,

Neumann boundary condition is employed for no-heat flux, thus please note that the grid location is staggered. Once the right hand side is obtained, the equation can be solved by the ODE suite. Here we use ode15s. Copyright 2015-2016 The MathWorks, Inc.

image_0.png

Problem Setup

N = 50; % Number of grid in x,y-direction
L = 4*pi; % Domain size

% Grid point
x = linspace(0,L,N);
y = linspace(0,L,N);
% Make it staggered.
x = (x(1:end-1)+x(2:end))/2;
y = (y(1:end-1)+y(2:end))/2;
[X,Y] = meshgrid(x,y);

Initial Condition

% Let's use MATLAB logo.
% A variable u0 is defined at the center of each grid cell
% thus the number of grid point is N-1.
u0(:,:) = peaks(N-1);

% Plot it
handle_surf = surf(X,Y,u0);
handle_axes = gca;
handle_axes.ZLim = [-10,10];
handle_axes.CLim = [-10,10];
title('Evolution of MATLAB Logo by Heat equation');

figure_0.png




Simulation


dx = x(2)-x(1); % spatial grid size
alpha = 2; % coefficient
tspan = linspace(0,1,40);
[t,u] = ode15s(@(t,x)getRHS(x,alpha,dx,N),tspan,u0(:));



Visualize


Tn = length(t);
u = reshape(u,Tn,N-1,N-1);

filename = 'heat.gif';
for ii=1:Tn
    Z = u(ii,:,:);
    Z = squeeze(Z);
    handle_surf.ZData = Z;
    drawnow;
    frame = getframe(gcf);
    im = frame2im(frame);
    [A,map] = rgb2ind(im,256);
    if ii==1
        imwrite(A,map,filename,'gif','LoopCount',Inf,'DelayTime',0.05);
    else
        imwrite(A,map,filename,'gif','WriteMode','append','DelayTime',0.05);
    end
end


figure_1.png


Copyright 2015-2016 The MathWorks, Inc.
View Simple Heat Equation solver on File Exchange



        


          

    

      引用格式
    

        

    michio (2024). Simple Heat Equation solver (https://github.com/mathworks/Simple-Heat-Equation-solver), GitHub.
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