CFD Online Logo CFD Online URL
www.cfd-online.com
[Sponsors]
Home > Forums > General Forums > Main CFD Forum

Computational fluid dynamics problem (Matlab)

Register Blogs Members List Search Today's Posts Mark Forums Read

Reply
 
LinkBack Thread Tools Search this Thread Display Modes
Old   March 25, 2013, 13:05
Default Computational fluid dynamics problem (Matlab)
  #1
New Member
 
srikanth
Join Date: Mar 2013
Posts: 3
Rep Power: 13
srik is on a distinguished road
Hi,

While using the MIT18086_NAVIERSTOKES.m code I encountered a problem to which I need some guidance from to come up with a solution. I modified the MIT18086_NAVIERSTOKES.m code to suit my problem. But I'm unable to achieve the correct required result when the code is executed. I have explained my problem below.

A rectangular obstacle (a heat source) is placed in a rectangular domain of incompressible fluid flow. The rectangular obstacle is placed where its left boundary lying on the left boundary of the rectangular domain (obstacle moved to the left side). The top or bottom boundaries of the obstacle do not touch the rectangular domain boundary. This can be seen in the image attached.

I want to apply finite difference method to this problem. But I can't figure out the boundary conditions for the obstacle for the velocity components, temperature and also the outflow temperature condition. I have attached the modified code as well. Please be kind enough to help me out to sort this issue.

Thank you in advance.

The code is given below:
------------------------------------------------------------------------
Main code:

global Re Pr nx ny hx hy dt out
%==============================MAIN PROGRAM================================
Re = 50; % Reynolds number
Pr = 7; % Prandtl number
dt = 1e-2; % time step
tf = 8e-0; % final time
lx = 1; % width of box
ly = 1; % height of box
nx = 40; % number of x-gridpoints
ny = 40; % number of y-gridpoints
nsteps = 10; % number of steps with graphic output
in = 10; % number of cells for inflow
out = 12; % number of cells for outflow
RT = 30; % Room temperature
obl = 1; obr = 24; obb = 19; obt = 22; %defining the obstacle
%--------------------------------------------------------------------------
close all
nt = ceil(tf/dt); dt = tf/nt;
x = linspace(0,lx,nx+1); hx = lx/nx;
y = linspace(0,ly,ny+1); hy = ly/ny;
ax = avg(x); ay = avg(y);
%--------------------------------------------------------------------------
%Initial conditions
U0 = zeros(nx-1,ny); V0 = zeros(nx,ny-1);
%T = zeros(nx,ny)+RT;
%Boundary conditions
uN = x*0; vN = ax*0;
uS = x*0; vS = ax*0;
uW = [ay(1:end-in)*0 ay(end-in+1:end)*0+1]; vW = y*0;
uE = ay*0; vE = y*0;
%--------------------------------------------------------------------------
fprintf('initialization')
Lq = kron(speye(ny-1),K1(nx-1,hx,2))+kron(K1(ny-1,hy,2),speye(nx-1));
perq = symamd(Lq); Rq = chol(Lq(perq,perq)); Rqt = Rq';
figure('un', 'normalized', 'pos',[0.01 0.05 0.98 0.85])
fprintf(', time loop\n--20%%--40%%--60%%--80%%-100%%\n')

for k=1:nt
vS(1:out) = V0(1:out,1)'; %outflow B.C
uS(2:out+1) = U0(1:out,1)'; %outflow B.C
%calling Energy function
%T = Energy(U,uW,uE,V,vN,vS,T,TN,TS,TW,TE);
%calling Navierstokes function
[U,V] = Navierstokes(U0,uN,uS,uE,uW,V0,vN,vS,vW,vE);

V(obl:obr,obt) = V(obl:obr,obt)*0;
V(obl:obr,obb-1) = V(obl:obr,obb-1)*0;
U(obr,obb:obt) = U(obr,obb:obt)*0;
% U(obl-1,obb:obt) = U(obl-1,obb:obt)*0;
U(obl:obr-1,obb) = -U(obl:obr-1,obb-1);
U(obl:obr-1,obt) = -U(obl:obr-1,obt+1);
% V(obl,obb:obt-1) = -V(obl-1,obb:obt-1);
V(obr,obb:obt-1) = -V(obr+1,obb:obt-1);
U(obl:obr-1,obb:obt) = U(obl:obr-1,obb:obt)*0;
V(obl:obr,obb:obt-1) = V(obl:obr,obb:obt-1)*0;


%visualization
if floor(25*k/nt)>floor(25*(k-1)/nt), fprintf('.'), end
if k==1 | floor(nsteps*k/nt)>floor(nsteps*(k-1)/nt)
%stream function
rhs = reshape(diff(U')'/hy-diff(V)/hx,[],1);
q(perq) = Rq\(Rqt\rhs(perq));
Q = zeros(nx+1,ny+1);
Q(2:end-1,2:end-1) = reshape(q,nx-1,ny-1);
Q(obl:obr+1,obb:obt+1)=Q(obl:obr+1,obb:obt+1)*0;
clf, %contourf(avg(x),avg(y),P',20,'w-'),
hold on
contour(x,y,Q',20,'k-');
Ue = [uS' avg([uW;U;uE]')' uN'];
Ve = [vW;avg([vS' V vN']);vE];
Len = sqrt(Ue.^2+Ve.^2+eps);
quiver(x,y,(Ue./Len)',(Ve./Len)',.4,'b-')
% streamline((Ue./Len)',(Ve./Len)',2,4)
hold off, axis equal, axis([0 lx 0 ly])
% p = sort(p); caxis(p([8 end-7]))
title(sprintf('Re = %0.1g ,Pr = %0.1g ,t = %0.2g',Re,Pr,k*dt))
drawnow
end
U0=U; V0=V;
end
fprintf('\n')

----------------------------------------------------------------------
function 1:

function [Unew,Vnew,P] = Navierstokes(U,uN,uS,uE,uW,V,vN,vS,vW,vE)
% function NAVIERSTOKES
% Solves the incompressible Navier-Stokes equations in a
% rectangular domain with prescribed velocities along the
% boundary. The solution method is finite differencing on
% a staggered grid with impicit diffusion and a Chorin
% projection method for the projection.
%----------------------------------------------------------------------
global Re nx ny hx hy dt

Ubc = dt/Re*([2*uS(2:end-1)' zeros(nx-1,ny-2) 2*uN(2:end-1)']/hx^2+...
[uW;zeros(nx-3,ny);uE]/hy^2);
Vbc = dt/Re*([vS' zeros(nx,ny-3) vN']/hx^2+...
[2*vW(2:end-1);zeros(nx-2,ny-1);2*vE(2:end-1)]/hy^2);

Lp = kron(speye(ny),K1(nx,hx,1))+kron(K1(ny,hy,1),speye (nx));
Lp(1,1) = 3/2*Lp(1,1);
perp = symamd(Lp);Rp = chol(Lp(perp,perp)); Rpt = Rp';
Lu = speye((nx-1)*ny)+dt/Re*(kron(speye(ny),K1(nx-1,hx,2))+...
kron(K1(ny,hy,3),speye(nx-1)));
peru = symamd(Lu); Ru = chol(Lu(peru,peru)); Rut =Ru';
Lv = speye(nx*(ny-1))+dt/Re*(kron(speye(ny-1),K1(nx,hx,3))+...
kron(K1(ny-1,hy,2),speye(nx)));
perv = symamd(Lv); Rv = chol(Lv(perv,perv)); Rvt = Rv';

% treat nonlinear terms
gamma = min(1.2*dt*max(max(max(abs(U)))/hx,max(max(abs(V)))/hy),1);
Ue = [uW;U;uE]; Ue = [2*uS'-Ue(:,1) Ue 2*uN'-Ue(:,end)];
Ve = [vS' V vN']; Ve = [2*vW-Ve(1,:);Ve;2*vE-Ve(end,:)];
Ua = avg(Ue')'; Ud = diff(Ue')'/2;
Va = avg(Ve); Vd = diff(Ve)/2;
UVx = diff(Ua.*Va-gamma*abs(Ua).*Vd)/hx;
UVy = diff((Ua.*Va-gamma*Ud.*abs(Va))')'/hy;
Ua = avg(Ue(:,2:end-1)); Ud = diff(Ue(:,2:end-1))/2;
Va = avg(Ve(2:end-1,:)')'; Vd = diff(Ve(2:end-1,:)')'/2;
U2x = diff(Ua.^2-gamma*abs(Ua).*Ud)/hx;
V2y = diff((Va.^2-gamma*abs(Va).*Vd)')'/hy;
U = U-dt*(UVy(2:end-1,:)+U2x);
V = V-dt*(UVx(:,2:end-1)+V2y);

%implicit viscosity
rhs = reshape(U+Ubc,[],1);
u(peru) = Ru\(Rut\rhs(peru));
U = reshape(u,nx-1,ny);
rhs = reshape(V+Vbc,[],1);
v(perv) = Rv\(Rvt\rhs(perv));
V = reshape(v,nx,ny-1);

%pressure correction
rhs = reshape(diff([uW;U;uE])/hx+diff([vS' V vN']')'/hy,[],1);
p(perp) = -Rp\(Rpt\rhs(perp));
P = reshape(p,nx,ny);
U = U-diff(P)/hx;
V = V-diff(P')'/hy;

Unew = U;
Vnew = V;



-------------------------------------------------------------------
function 2:

function A = K1(n,h,a11)
%a11: Neumann=1, Dirichlet=2, Dirichlet mid=3
A = spdiags([-1 a11 0;ones(n-2,1)*[-1 2 -1];0 a11 -1],-1:1,n,n)/h^2;

--------------------------------------------------------------------
function 3:

function B = avg(A)
if size(A,1)==1, A = A'; end
B = (A(2:end,:)+A(1:end-1,:))/2;
if size(A,2)==1, B = B'; end

----------------------------------------------------------------------
function 4:

function Tnew = Energy(U,uW,uE,V,vN,vS,T,TN,TS,TW,TE)
%computes the temperature at each discretized point according
%to the velocity components using Energy equation
%--------------------------------------------------------------------------
global Re Pr nx ny hx hy dt

LT = speye(nx*ny)-dt/(Re*Pr)*(kron(speye(ny),K1(nx,hx,2))+...
kron(K1(ny,hy,2),speye(nx)));
gamma = min(1.2*dt*max(max(max(abs(U)))/hx,max(max(abs(V)))/hy),1);

Ue = [uW;U;uE]; Ve =[vS' V vN'];
Te = [2*TW-T(1,:); T; 2*TE-T(end,:)];
Ta = avg(Te); Td = diff(Te)/2;
UTx = diff(Ue.*Ta-gamma*abs(Ue).*Td)/hx;
Te = [2*TS'-T(:,1) T 2*TN'-T(:,end)];
Ta = avg(Te')'; Td = diff(Te')'/2;
VTy = diff((Ve.*Ta-gamma*abs(Ve).*Td)')'/hy;
T = reshape(T,[],1); Tx = reshape(UTx,[],1); Ty = reshape(VTy,[],1);
T1 = LT*T-(Tx+Ty)*dt;
Tnew = reshape(T1,nx,ny);
Attached Images
File Type: jpg untitled2.jpg (11.0 KB, 31 views)
srik is offline   Reply With Quote

Old   March 26, 2013, 08:49
Default
  #2
Senior Member
 
Jonas T. Holdeman, Jr.
Join Date: Mar 2009
Location: Knoxville, Tennessee
Posts: 128
Rep Power: 18
Jonas Holdeman is on a distinguished road
An observation: a lot of simulations use Pr=0.7, I haven't stopped to figure why, I have used it too, but I notice you set Pr=7.
Jonas Holdeman is offline   Reply With Quote

Old   March 26, 2013, 09:32
Default
  #3
New Member
 
srikanth
Join Date: Mar 2013
Posts: 3
Rep Power: 13
srik is on a distinguished road
I assumed that the fluid is water. And the Pr (prandl number) for water is 7.
srik is offline   Reply With Quote

Old   February 3, 2015, 11:56
Default how to create the obstacle geometry in matlab?
  #4
Member
 
amine
Join Date: Jun 2012
Posts: 65
Rep Power: 13
lbmagis is on a distinguished road
Hello,
I 'd like to know the program that create a square or rectangular obstacle in matlab???
Thank you
lbmagis is offline   Reply With Quote

Reply

Thread Tools Search this Thread
Search this Thread:

Advanced Search
Display Modes

Posting Rules
You may not post new threads
You may not post replies
You may not post attachments
You may not edit your posts

BB code is On
Smilies are On
[IMG] code is On
HTML code is Off
Trackbacks are Off
Pingbacks are On
Refbacks are On


Similar Threads
Thread Thread Starter Forum Replies Last Post
An error has occurred in cfx5solve: volo87 CFX 5 June 14, 2013 18:44
Terrible Mistake In Fluid Dynamics History Abhi Main CFD Forum 12 July 8, 2002 10:11
computational fluid dynamics Amy Moseley Main CFD Forum 10 July 1, 1999 09:46
Computational Fluid Dynamics software T Barron Main CFD Forum 5 December 1, 1998 08:43
CFD - Trends and Perspectives Jonas Larsson Main CFD Forum 16 August 7, 1998 17:27


All times are GMT -4. The time now is 07:16.