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November 27, 2006, 09:49 |
lid-driven cavity using Matlab
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#1 |
Guest
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Does anyone happen to have a Matlab code for solving the 2-D lid-driven cavity problem in primitive variables (i.e. pressure and velocity)? I will be so grateful, if you would be able to share it.
Thanks a lot. |
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November 27, 2006, 10:38 |
Re: lid-driven cavity using Matlab
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#2 |
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does it have to be in primitive variables? It is not difficult at all using streamfuntion-vorticity, or streamfunction-velocity equations.
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November 27, 2006, 11:06 |
Re: lid-driven cavity using Matlab
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#3 |
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Thanks Andrew. In fact, I have already solved the problem using vorticity-streamfuntion formulation (which is quite easy), but I'm having some troubles implementing the SIMPLE algorithm (on staggered grid) for this problem in Matlab.
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November 28, 2006, 07:46 |
Re: lid-driven cavity using Matlab
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#4 |
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I have you tried using the SIMPLER method? Just out of curiousity, how are you defining the pressure in the cavity? I was reading that the SIMPLE method cannot be used in all situations. Can it be used here? You might need to incorporate the under-relaxation constant.
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August 24, 2009, 02:51 |
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#5 | |
New Member
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Quote:
the problem is, after the coding, i can't get the nice solution. i'm sorry to bother you all, but can you send me the code that's working because my code isn't. I just want to compare or to determine where is my code (matlab or fortran) went wrong. ok. my email: sesenangje@yahoo.com Thanx very much |
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August 24, 2009, 09:15 |
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#6 |
Senior Member
Jonas T. Holdeman, Jr.
Join Date: Mar 2009
Location: Knoxville, Tennessee
Posts: 128
Rep Power: 18 |
I have a Hermite FE code used in a paper to appear in IJNMF. It computes the velocity and the pressure as a function of the velocity.
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August 26, 2009, 00:48 |
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#7 | |
New Member
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Quote:
Thank you very very much |
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August 26, 2009, 13:02 |
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#8 |
Senior Member
Jonas T. Holdeman, Jr.
Join Date: Mar 2009
Location: Knoxville, Tennessee
Posts: 128
Rep Power: 18 |
Idris,
I will send the Matlab LDC code for one of the methods to you as attachments. A preprint of the paper describing the method can be found at http://webpages.charter.net/jtholdeman/RevIJNMFart1.pdf . |
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September 2, 2009, 04:30 |
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#9 |
New Member
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thanx guys,
i finally created the code myself. it's the matter of boundary condition. if the boundary condition is wrong, the solution also wrong. Actually my task is to solve vorticity-streamfunction equation of a lid driven cavity at steady state(using central finite difference). and not to forget,the relaxation scheme is needed when the reynolds number is very high (Re >1000) Anyway, many thanks to everybody, especially Jonas Holdeman. bye. |
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October 8, 2009, 06:16 |
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#10 |
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Join Date: Oct 2009
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can u please share the code....
thank you. |
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October 8, 2009, 23:28 |
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#11 |
New Member
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ok, here it is
clear all;clf;clc; re=100; % for higher reynolds number(>500-1000), use under relaxation rex=1; % underrelaxation, 0<rex<1 rexb=rex; nx=51; dx=1/(nx-1); %100x100 grid (101*101 nodes) ny=51; dy=1/(ny-1); fac=2*(1/dx^2+1/dy^2); Y=1; uo=1; nu=Y/(uo*re); % initial condition p(1:nx,1:ny)=0; o(1:nx,1:ny)=0; psi(1:nx,1:ny)=0; omega(1:nx,1:ny)=0; uact(1:nx,1:ny)=0; vact(1:nx,1:ny)=0; u(1:nx,1:ny)=0; v(1:nx,1:ny)=0; u(1:nx,ny)=1; for iteration =1:2000%iteration disp(['iteration= ',int2str(iteration)]) % stream function(internal nodes) for i=2nx-1) for j=2ny-1) pold(i,j)=p(i,j); f1=1/fac*(o(i,j)+(p(i+1,j)+p(i-1,j))/dx^2+(p(i,j+1) ... +p(i,j-1))/dy^2); p(i,j)=p(i,j)+rex*(f1-p(i,j)); end end % Vorticity (Boundary nodes) for j=1:ny fab=-2*p(2,j)/dx^2; %left side(AB) o(1,j)=o(1,j)+rexb*(fab-o(1,j)); fcd=-2*p(nx-1,j)/dx^2; %right side(CD) o(nx,j)=o(nx,j)+rexb*(fcd-o(nx,j)); end for i=1:nx fad=-2*p(i,2)/dy^2; %bottom side(AD) o(i,1)=o(i,1)+rexb*(fad-o(i,1)); fbc=-(2*p(i,ny-1)+2*uo*dy)/dy^2; %top side (BC) o(i,ny)=o(i,ny)+rexb*(fbc-o(i,ny)); end %vorticity internal nodes for i=2nx-1) for j=2ny-1) oold(i,j)=o(i,j); f2=1/fac*((o(i+1,j)+o(i-1,j))/dx^2+(o(i,j+1)+o(i,j-1))/dy^2 ... -re*(p(i,j+1)-p(i,j-1))*(o(i+1,j)-o(i-1,j))/(4*dx*dy)... +re*(p(i+1,j)-p(i-1,j))*(o(i,j+1)-o(i,j-1))/(4*dx*dy)); o(i,j)=o(i,j)+rex*(f2-o(i,j)); end end % Calculate the velocity (u and v) for i=2nx-1) for j=2ny-1) u(i,j)=(p(i,j+1)-p(i,j-1))/(2*dy); v(i,j)=-(p(i+1,j)-p(i-1,j))/(2*dx); end end % rearrange in cartesian coordinate %(which originally in matrix coordinate) for i=1:nx for j=1:ny k=i; l=j; psi(l,k)=p(i,j); omega(l,k)=o(i,j); uact(l,k)=u(i,j); vact(l,k)=v(i,j); end end figure(1)% Streamline plot with number Z = psi(1:ny,1:nx); X = linspace(0,1,size(Z,2)); Y = linspace(0,1,size(Z,1)); [c,h] = contour(X,Y,Z); axis equal axis([0 1 0 1]) drawnow end hope you can further developed these code by yourself. It's up to you what you are going to do about it :-) |
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October 9, 2009, 04:45 |
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#12 |
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thank you very much
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November 13, 2010, 04:55 |
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#13 |
Senior Member
KHB
Join Date: Aug 2010
Location: Singapore
Posts: 118
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Hi guys, I am a newbie in CFD thing. Currently I am trying to solve the same problem also.
I solved the problem using the stream function formulation, and now I'm trying to solve in in terms of primitive variable (u,v, and p) using projection method. First I tried using the most simple explicit projection method and it turns out the solution diverge, and I also used implicit projection method where the value of velocity field in each time step is iterated first and it still diverge. I don't know whats wrong with the code.. Have any of you tried to solve the problem using Projection method? |
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November 15, 2010, 14:29 |
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#14 |
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Marshall Ericson
Join Date: Nov 2010
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thank you very much for posting these codes. but these codes seem to have some problems. it doesnt give correct plot nor correct data. if you have any other simple matlab code for lid driven cavity problem that worked , i would be very grateful.
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November 16, 2010, 12:05 |
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#15 |
New Member
Tanay Deshpande
Join Date: Aug 2010
Posts: 20
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Hello All,
I'm trying to implement SIMPLE in Finite Volume method in driven-cavity flow using C++ in basic variables. Since the problem is steady state, I start out with u=0, v=0, p=0 for all interior nodes. This is causing the code to diverge away to infinity. For high viscosities, the divergence is less pronounced but u doesn't ever become negative in the results as it should. What may be the problem? Is it because I'm using unrelaxed pressure and velocity corrector equations? Thanks in advance. |
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May 15, 2011, 10:56 |
lid driven Cavity using FVM
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#16 |
New Member
ainal
Join Date: May 2011
Posts: 2
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hello ,
I am working on a CFD problem and developing a Matlab code for "Lid driven cavity " problem using finite volume method and Symmetric Couple Gauss Seidel Scheme but i have some confusion in writing the code in Matlab so can any one help me in this ... I shall be very grateful if anyone can share this |
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April 15, 2013, 00:15 |
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#17 |
New Member
TAMILNADU
Join Date: Apr 2013
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bro do u have any unsteady code for the same problem.. ??
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April 14, 2014, 06:23 |
Lid Driven Cavity using Staggered grid
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#18 |
New Member
sankha
Join Date: Mar 2014
Posts: 1
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Hi,
i have done LDC in collocated grid in stream function vorticity method...right now trying to do it in staggered grid in primitive variable method FDM....can somebody send me the code so that i can verify my results.. sm4fn@hotmail.com i'm using SIMPLE |
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July 21, 2014, 10:29 |
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#19 | |
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Bob Man
Join Date: Jul 2014
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Quote:
Can anyone explain why the boundary conditions for the vorticity are what they are? I mean what kind of approximation is that for the derivative of psi? Also what scheme is used for calculating the internal nodes of the vorticity? Thanks alot for the help |
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January 9, 2017, 04:09 |
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#20 |
New Member
Sumaira Mehmood
Join Date: Jan 2017
Posts: 1
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hi, guys
i need help how to find skin friction in 2-dimensional flow in lid driven cavity in matlab code kindly tell me its matlab command. i have already done but not get results. its my email address Sumaira_61554@yahoo.com |
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