The following lines of codes implements 1D diffusion equation on 10 m long rod with fixed temperature at right boundary and right boundary temperature varying with time.(adsbygoogle = window.adsbygoogle || []).push({});

My question is how can I implement a symmetry boundary condition. I mean the temperature calculated for 9th node is assigned to 10th node? Also I want to know how can I implement infinite boundary condition?Code (Text):xsize = 10; % Model size, m

xnum = 10; % Number of nodes

xstp = xsize/(xnum-1); % Grid step

tnum = 504; % number of timesteps

kappa = 833.33; % k/rhocp; % Thermal diffusivity, m^2/s

dt = 300; % Timestep

x = 0:xstp:xsize; %Creating vector for nodal point positions

tlbc = sin(linspace(0.1,2.9,tnum)); % left boundary condition

%Define initial temperature profile

tback = 0; % background temperature, K

for i=1:1:xnum

% Background profile

t0imp(i) = tback; % profile for implicit solving

end

end

% Time cycle

timesum=0; % Elapsed time

for t=1:1:tnum

% Matrix of coefficients initialization for implicit solving

L = sparse(xnum,xnum);

% Vector of right part initialization for implicit solving

R = zeros(xnum,1);

% Implicit solving of 1D temperature equation: dT/dt=kappa*d2T/dx2

% Composing matrix of coefficients L()

% and vector (column) of right parts R()

% First point: T=tback

L(1,1) = 1;

R(1,1) = tlbc(t);

% Intermediate points

for i=2:1:xnum-1

% dT/dt=kappa*d2T/dx2

% Tnew(i)/dt-kappa*(Tnew(i-1)-2*Tnew(i)+Tnew(i+1))/dx^2=Told(i)/dt

%%% Eq 10.6

L(i,i-1) = -kappa/xstp^2;

L(i,i) = 1/dt+2*kappa/xstp^2;

L(i,i+1) = -kappa/xstp^2;

R(i,1) = t0imp(i)/dt;

end

% Last point:T=tback

L(xnum,xnum) = 1;

R(xnum,1) = tback;

% Obtaining solution for implicit temperature profile

t1imp = L\R;

end

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# Implementing symmetry boundary condition for the diffusion equation

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