Thomas algorithm - tridiagonal matrix

cesarjets · March 1, 2023, 19:29

Is there any other way to code and solve the tridiagonal matrix? the idea would be to try to get the plot shown. Matlab beginner, so, no sure how to do it. Any help will be greatly appreciated. Thanks

clear
cm=1/100;
delta = 1*cm;
nu=1e-6;
Uinf=1;
H=2*delta;
y=linspace(0,H,40);
u=Uinf*erf(3*y/delta);
dy=mean(diff(y));
dx=100*dy;
Q=nu*dx/Uinf/dy^2;
a=-Q;
c=-Q;
b=1+2*Q;
N=length(y)-2;
M = diag(b*ones(1,N)) + diag(c*ones(1,N-1),1) + diag(a*ones(1,N-1),-1);
%Constant Ue
Ue = @(x) Uinf;
u = u(2:end-1);
x=0;
uall=[0,u,Ue(x)];

LuckyTran · March 1, 2023, 23:31

If you are looking specifically for the tridiagonal matrix algorithm then:

Explained in detail on Wikipedia and you can interpret it as pseudo code. Actual VBA and C-variants also provided.

TDMA algorithm is a very popular shared repository on the Matlab exchange. You can just use it, it is licensed.

Note that you are not strictly limited to the tridiagonal matrix algorithm either. Any (more complicated and better) linear solver will do. For example, fsolve.

If the solution is unique (which is not always the case in CFD, but usually is when you are doing simple coding examples) then you can also use a computationally slow but semantically simple matrix division in matlab. That is, given A*x=b the solution found by solution=A\b. The left division will implicitly invoke the pseudo-inverse and in many cases still give the correct solution.

March 1, 2023, 19:29	Thomas algorithm - tridiagonal matrix	#1
cesarjets Member Join Date: Aug 2012 Posts: 41 Rep Power: 14	Is there any other way to code and solve the tridiagonal matrix? the idea would be to try to get the plot shown. Matlab beginner, so, no sure how to do it. Any help will be greatly appreciated. Thanks clear cm=1/100; delta = 1cm; nu=1e-6; Uinf=1; H=2delta; y=linspace(0,H,40); u=Uinferf(3y/delta); dy=mean(diff(y)); dx=100dy; Q=nudx/Uinf/dy^2; a=-Q; c=-Q; b=1+2Q; N=length(y)-2; M = diag(bones(1,N)) + diag(cones(1,N-1),1) + diag(aones(1,N-1),-1); %Constant Ue Ue = @(x) Uinf; u = u(2:end-1); x=0; uall=[0,u,Ue(x)];

Similar Threads
Thread	Thread Starter	Forum	Replies	Last Post
OpenFOAM version 1.6 details	lakeat	OpenFOAM Running, Solving & CFD	42	August 26, 2009 22:47
thomas algorithm	cvkeshav	Main CFD Forum	2	March 29, 2009 06:37
Block-Block tridiagonal matrix inverse	Abdulhafid Elfaghi	Main CFD Forum	3	September 16, 2007 03:55
Thomas Algorithm Testing	Out of Ideas	Main CFD Forum	3	February 8, 2001 23:45
Why Thomas Algorithm for tridiagonal systems?	Yogesh Talekar	Main CFD Forum	6	July 15, 1999 14:56

March 1, 2023, 23:31		#2
LuckyTran Senior Member Lucky Join Date: Apr 2011 Location: Orlando, FL USA Posts: 5,747 Rep Power: 66	If you are looking specifically for the tridiagonal matrix algorithm then: Explained in detail on Wikipedia and you can interpret it as pseudo code. Actual VBA and C-variants also provided. TDMA algorithm is a very popular shared repository on the Matlab exchange. You can just use it, it is licensed. Note that you are not strictly limited to the tridiagonal matrix algorithm either. Any (more complicated and better) linear solver will do. For example, fsolve. If the solution is unique (which is not always the case in CFD, but usually is when you are doing simple coding examples) then you can also use a computationally slow but semantically simple matrix division in matlab. That is, given A*x=b the solution found by solution=A\b. The left division will implicitly invoke the pseudo-inverse and in many cases still give the correct solution.