
[Sponsors] 
July 26, 2000, 12:56 
How to get BC for Psi in the computing domain?

#1 
Guest
Posts: n/a

July 26, 2000 Dear colleagues,
Notations ========= (x,y) Cartesian coordinates. (r,s) Curvilinear coordinates. P Stream Function P is defined as follow: u = dP/dy = dP/dr dr/dy + dP/ds ds/dy [1] v =dP/dx =dP/dr dr/dx  dP/ds ds/dx [2] Inlet Boundary condition ======================== For 0<y<ymax u(0,y)=1 v(0,y)=0 Now if I go to the computing domain, I have: 1=dP/dr dr/dy + dP/ds ds/dy 0=dP/dr dr/dx + dP/ds ds/dx Two equations with two unknowns: dP/dr and dP/ds Solving for dP/ds and integrating from s=0 to s>0 yields: P(r=0,s)= Int_{0}^{y(s)} [dr/dx] /[dr/dx ds/dy  dr/dy ds/dx] dy I have used my 2 BC, namely u=1 and v=0, to get a Dirichlet BC for the stream function P. I think it's the way to do it. Let's see now another boundary condition. Outlet Boundary condition ========================= For x=xmax and 0<y<ymax du/dx=0 dv/dx=0 In the computing domain I have: du/dr dr/dx + du/ds ds/dx=0 dv/dr dr/dx + dv/ds ds/dx=0 Using eqs [1] and [2] yields: [d^2P/dr^2 dr/dy + d^2P/drds ds/dy] dr/dx + [d^2P/drds dr/dy + d^2P/ds^2 ds/dy] ds/dx=0 [3] [d^2P/dr^2 dr/dx + d^2P/drds ds/dx] dr/dx + [d^2P/drds dr/dx + d^2P/ds^2 ds/dx] ds/dx=0 [4] From these two equations, how can I get my boundary condition for the sream function? I cannot isolate dP/ds from eqs [3] and [4]! Same remark applies when I have the following BC: du/dy=0 and v=0. It's a symmetry BC. Thank you so much in advance for replying to my question. My very best regards, Dr. Pierre Forges UAE University Mech. Eng. Dept. pforges@uaeu.ac.ae 

July 26, 2000, 20:10 
Re: How to get BC for Psi in the computing domain?

#2 
Guest
Posts: n/a

(1). The coordinate transformation is not done UNTIL the coordinate transformation factors are determined or specified. You are the one who must specify these coordinate transformation factors. (2). So, you can arbitrarily create a new coordinate transformation (just like a structured mesh) and have all nonzero transformation factors. (3). But, who would do thing like that. (4). If your original inlet condition is nice and clean in xy coordinate system, then keep the transformed coordinates exactly the same as the xy coordinates by specifying the proper transformation factors in that region. In simple sentense, no stretching and rotation in the inlet region when creating the new coordinates. In this way, the new is identical to the old. But you are still using the new one, except that the transformation factors in those regions are such that nothing has changed. (5). This is the way to create the new coordinates. If you do not follow this rule, you will end up with a general distorted mesh over the inlet, and will have to use interpolation method to specify the inlet conditions in the new coordinates. So, you have to generate the mesh (or the cew coordinates) to simply the work by specifying the transformation factors.(or how the mesh should be stretched or rotated). (6). In other words, in your message, you have not even finished your coordinate transformation, because the transformation factors are not specified yet. You are the one who must supply the values of ds/dx(at i,j), ds/dy(at i,j), dr/dx(at i,j), and dr/dy(at i,j). (if s=x at i=1, and r=y at i=1, then ds/dx=1 at i=1, dr/dy=1 at i=1. ds/dy=dr/dx=0. Or you can let s=const*x, r=const2*y, the ds/dy and dr/dx are still zeros.)


Thread Tools  
Display Modes  


Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Domain Imbalance  HMR  CFX  5  October 10, 2016 05:57 
Vertical Axis Wind Turbine Rotating Domain Problems  TWaung  CFX  4  May 1, 2012 03:14 
CFX domain comparison  Kiat110616  CFX  4  April 3, 2011 22:43 
CFX Solver Memory Error  mike  CFX  1  March 19, 2008 08:22 
BC for the stream function in the computing domain  Pierre Forges  Main CFD Forum  1  July 26, 2000 14:47 