Plot along line from. PDE solution

Question

John McGrath 2025-4-4

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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/2175998-plot-along-line-from-pde-solution

编辑： Torsten 2025-4-11

The code below solves a 1-D, transient heat transfer problem set up as in general PDE format. The solution is plotted in color across the domain from 0 to 0.1 after 10 seconds have elapsed. What is the best way to plot the temperature across the length of this domain at this final time?

Thanks

clear all;

%% Create transient thermal model

thermalmodel = createpde(1);

R1= [3,4,0,0.1,0.1,0,0,0,1,1]';

gd= [R1];

sf= 'R1';

ns = char('R1');

ns = ns';

dl = decsg(gd,sf,ns);

%% Create & plot geometry

geometryFromEdges(thermalmodel,dl);

pdegplot(thermalmodel,"EdgeLabels","on","FaceLabels","on")

xlim([0 0.1])

ylim([-1 1])

% axis equal

%% Generate and plot mesh

generateMesh(thermalmodel)

ans =

FEMesh with properties: Nodes: [2x361 double] Elements: [6x152 double] MaxElementSize: 0.0402 MinElementSize: 0.0201 MeshGradation: 1.5000 GeometricOrder: 'quadratic'

figure

pdemesh(thermalmodel)

title("Mesh with Quadratic Triangular Elements")

%% Apply BCs

% Edge 4 is left edge; Edge 2 is right side

applyBoundaryCondition(thermalmodel, "dirichlet",Edge=[4],u=100);

applyBoundaryCondition(thermalmodel, "dirichlet",Edge=[2],u=20);

%% Apply thermal properties [copper]

rho= 8933 %

rho = 8933

cp= 385 %

cp = 385

rhocp= rho*cp %

rhocp = 3439205

k= 401 % W/mK

k = 401

%% Define uniform volumetric heat generation rate

Qgen= 0 % W/m3

Qgen = 0

%% Define coefficients for generic Governing Equation to be solved

m= 0

m = 0

a= 0

a = 0

d= rhocp

d = 3439205

c= [k]

c = 401

f= [Qgen]

f = 0

specifyCoefficients(thermalmodel, m=0, d=rhocp, c=k, a=0, f=f);

%% Apply initial condition

setInitialConditions(thermalmodel, 20);

%% Define time limits

tlist= 0: 1: 10;

thermalresults= solvepde(thermalmodel, tlist);

% Plot results

sol = thermalresults.NodalSolution;

subplot(2,2,1)

pdeplot(thermalmodel,"XYData",sol(:,11), ...

"Contour","on",...

"ColorMap","jet")

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John McGrath 2025-4-5

编辑：Walter Roberson 2025-4-5

在 MATLAB Online 中打开

Hi Torsten

Thanks for your suggestion. I tried the plotAlongLine approach that you pointed me to for my problem. Matlab comes back with a message saying it doesn’t recognize p.

I’m actually interested in 2D problems. I thought that by simplifying to a 1D problem I would learn what I wanted to know to apply to 2D cases. It’s probably best to go directly to the type of 2D problem that I’m interested in to ask for your help for plotting along a defined line. Below I include code for a 2D transient problem. It produces a color-coded temperature field at a specified time. I would like to be able to plot the temperature along a line at the specified time. For example, from (0,3) to (6,3). I would also like for the program to define temperature at a specific location and the specific time. For example, T=T(4,3) within the temperature field produced by my program. Thank you in advance.

john

clear all;

thermalmodel = createpde();

R1= [3,4,0,3,3,0,0,0,10,10]';

R2= [3,4,3,6,6,3,-5,-5,5,5]';

gd= [R1 R2];

sf= 'R1+R2';

ns = char('R1','R2');

ns = ns';

dl = decsg(gd,sf,ns);

geometryFromEdges(thermalmodel,dl);

pdegplot(thermalmodel,"EdgeLabels","on","FaceLabels","on")

xlim([-1 7])

ylim([-6 11])

axis equal

%% Generate and plot mesh

generateMesh(thermalmodel);

figure

pdemesh(thermalmodel)

title("Mesh with Quadratic Triangular Elements")

%% Apply BCs

% Edge 3 is left edge; Edge 5 is right side; edge 8 is middle; Edges 2 & 6 top; Edges 1 & 4 bottom

% Edges 7 & 9 offset vertical edges

applyBoundaryCondition(thermalmodel, "dirichlet",Edge=[3],u=100);

applyBoundaryCondition(thermalmodel, "dirichlet",Edge=[5],u=20);

%% Apply thermal properties in first region

rho1= 1 %

rho1 = 1

cp1= 1 %

cp1 = 1

rhocp1= rho1*cp1 %

rhocp1 = 1

k1= 1 % W/mK

k1 = 1

%% Apply thermal properties in second region

rho2= 10 %

rho2 = 10

cp2= 10 %

cp2 = 10

rhocp2= rho2*cp2 %

rhocp2 = 100

k2= 10 % W/mK

k2 = 10

%% Define uniform volumetric heat generation rate

Qgen= 0 % W/m3 [1e12]

Qgen = 0

%% Define coefficients for generic Governing Equation to be solved

f= [Qgen]

f = 0

specifyCoefficients(thermalmodel, m=0, d=rhocp1, c=k1, a=0, f=f, Face=1);

specifyCoefficients(thermalmodel, m=0, d=rhocp2, c=k2, a=0, f=f, Face=2);

coeffs= thermalmodel.EquationCoefficients;

findCoefficients(coeffs, Face=1)

ans =

CoefficientAssignment with properties: RegionType: 'face' RegionID: 1 m: 0 d: 1 c: 1 a: 0 f: 0

findCoefficients(coeffs, Face=2)

ans =

CoefficientAssignment with properties: RegionType: 'face' RegionID: 2 m: 0 d: 100 c: 10 a: 0 f: 0

%% Apply initial condition

setInitialConditions(thermalmodel, 20);

%% Define time limits

tlist = 0:1:50;

%% Solve

thermalresults= solvepde(thermalmodel, tlist);

% Plot results

sol = thermalresults.NodalSolution;

subplot(2,2,1)

pdeplot(thermalmodel,"XYData",sol(:,50), ...

"Contour","on",...

"ColorMap","jet")

Torsten 2025-4-8

在 MATLAB Online 中打开

You only have to add the call to "plotAlongLine" and the function itself at the end of your code:

clear all;

thermalmodel = createpde();

R1= [3,4,0,3,3,0,0,0,10,10]';

R2= [3,4,3,6,6,3,-5,-5,5,5]';

gd= [R1 R2];

sf= 'R1+R2';

ns = char('R1','R2');

ns = ns';

dl = decsg(gd,sf,ns);

geometryFromEdges(thermalmodel,dl);

pdegplot(thermalmodel,"EdgeLabels","on","FaceLabels","on")

xlim([-1 7])

ylim([-6 11])

axis equal

%% Generate and plot mesh

generateMesh(thermalmodel);

figure

pdemesh(thermalmodel)

title("Mesh with Quadratic Triangular Elements")

%% Apply BCs

% Edge 3 is left edge; Edge 5 is right side; edge 8 is middle; Edges 2 & 6 top; Edges 1 & 4 bottom

% Edges 7 & 9 offset vertical edges

applyBoundaryCondition(thermalmodel, "dirichlet",Edge=[3],u=100);

applyBoundaryCondition(thermalmodel, "dirichlet",Edge=[5],u=20);

%% Apply thermal properties in first region

rho1= 1 %

rho1 = 1

cp1= 1 %

cp1 = 1

rhocp1= rho1*cp1 %

rhocp1 = 1

k1= 1 % W/mK

k1 = 1

%% Apply thermal properties in second region

rho2= 10 %

rho2 = 10

cp2= 10 %

cp2 = 10

rhocp2= rho2*cp2 %

rhocp2 = 100

k2= 10 % W/mK

k2 = 10

%% Define uniform volumetric heat generation rate

Qgen= 0 % W/m3 [1e12]

Qgen = 0

%% Define coefficients for generic Governing Equation to be solved

f= [Qgen]

f = 0

specifyCoefficients(thermalmodel, m=0, d=rhocp1, c=k1, a=0, f=f, Face=1);

specifyCoefficients(thermalmodel, m=0, d=rhocp2, c=k2, a=0, f=f, Face=2);

coeffs= thermalmodel.EquationCoefficients;

findCoefficients(coeffs, Face=1)

ans =

CoefficientAssignment with properties: RegionType: 'face' RegionID: 1 m: 0 d: 1 c: 1 a: 0 f: 0

findCoefficients(coeffs, Face=2)

ans =

CoefficientAssignment with properties: RegionType: 'face' RegionID: 2 m: 0 d: 100 c: 10 a: 0 f: 0

%% Apply initial condition

setInitialConditions(thermalmodel, 20);

%% Define time limits

tlist = 0:1:50;

%% Solve

thermalresults= solvepde(thermalmodel, tlist);

% Plot results

sol = thermalresults.NodalSolution;

subplot(2,2,1)

pdeplot(thermalmodel,"XYData",sol(:,50), ...

"Contour","on",...

"ColorMap","jet")

plotAlongLine(thermalresults.Mesh.Nodes, thermalresults.NodalSolution(:,50), [0,.5], [6,.5], 50);

function plotAlongLine(p, u, xy1, xy2, numpts)

x = linspace(xy1(1),xy2(1),numpts);

y = linspace(xy1(2),xy2(2),numpts);

F = TriScatteredInterp(p(1,:)', p(2,:)', u);

uxy = F(x,y);

figure; plot(x, uxy);

end

John McGrath 2025-4-11

What is Octave?

thanks for your continued support

Torsten 2025-4-11

编辑：Torsten 2025-4-11

What is Octave?

https://octave.org/

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Answer 1

Karanjot 2025-4-8

0
链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/2175998-plot-along-line-from-pde-solution#answer_1563317

在 MATLAB Online 中打开

Hi John,

In response to your latest comment, MATLAB returns the following error,as 'plotAlongLine' is not a standard function that is part of MATLAB. It's a custom function defined by another user.

Unrecognized function or variable 'plotAlongLine'.

In order to resolve the error, you may copy the function definition into your codebase, from the link attached below:

function plotAlongLine(p, u, xy1, xy2, numpts)
x = linspace(xy1(1),xy2(1),numpts);
y = linspace(xy1(2),xy2(2),numpts);
F = TriScatteredInterp(p(1,:)', p(2,:)', u);
uxy = F(x,y);
figure; plot(x, uxy);
end

https://www.mathworks.com/matlabcentral/answers/52403-plot-solution-of-pde-toolbox-on-a-line-or-submanifold#answer_64119

As also suggested by Torsten, Feel free to go through the following beginner courses on MATLAB basics:

https://matlabacademy.mathworks.com/?page=1&fq=get-started-with-matlab&sort=featured

I hope this helps!

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John McGrath 2025-4-8

Hi Karanjot,

Thank you very much for your suggestions. I have completed some of these courses and will continue to work on them.

I tried to implement your suggestion for code- but unsuccessfully. Furthermore, when I searched for documentation regarding the TriScatteredInterp function, the MatLab documentation indicates that this function is not recommended and that the function scatteredInterpolant should be used instead. [The original code taht incldued this functoin dates abck to 2012 or something like that.

I initially defined my heat transfer model in terms of a thermal model. I ran into problems when I tried to implement time-varying convective boundary conditions. I was told that to avoid that issue, I should define my heat transfer problem as a general pde problem- which is what I am trying to do now.

I recognize that I do not understand the details of how my pde solution for the temperatures [1D or 2D] [steady or transient] are mapped onto the grid that is generated by the generateMesh function. I therefore don't have a clear picture of how to query the vectors or matrices that are being generated so as to produce values at defined locations or to produce desired plots.

Thanks again

john

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Plot along line from. PDE solution

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Plot along line from. PDE solution

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