Simple Heat Equation solver

Version 1.0.0.3 (5.51 MB) by michio
Simple Heat Equation solver using finite difference method
3.7K Downloads
Updated 18 Mar 2023

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

Cite As

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

MATLAB Release Compatibility
Created with R2016a
Compatible with any release
Platform Compatibility
Windows macOS Linux

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Version Published Release Notes
1.0.0.3

reflect markdown on File Exchange

1.0.0.2

Move to GitHub

1.0.0.1

Added a screenshot

1.0.0.0

To view or report issues in this GitHub add-on, visit the GitHub Repository.
To view or report issues in this GitHub add-on, visit the GitHub Repository.