
[Sponsors] 
Boundary condition: intermediate velocity for fractional time step method 

LinkBack  Thread Tools  Display Modes 
June 19, 2015, 18:37 
Boundary condition: intermediate velocity for fractional time step method

#1 
New Member
Rime
Join Date: Jun 2015
Posts: 28
Rep Power: 3 
Hi!
How to calculate u*=u_n+1 for the intermediate velocity u* 

June 20, 2015, 03:47 

#2 
Senior Member
Filippo Maria Denaro
Join Date: Jul 2010
Posts: 2,357
Rep Power: 28 
are you talking about the intermediate BC.s in the fractional time step method? The literature is full of paper about this issue, starting from the hystorical paper of Kim & Moin on JCP you can find many many studies and proposals. However, u_n+1 is the physical BC you have to know, a zeroorder approximation simply set it as u*. 

June 20, 2015, 07:25 

#3 
New Member
Rime
Join Date: Jun 2015
Posts: 28
Rep Power: 3 
Thank u for the reply.
yes for fractional time step method 

June 20, 2015, 14:24 

#4 
New Member
Rime
Join Date: Jun 2015
Posts: 28
Rep Power: 3 
I use FSM with free pressure
boundary : 1)n.u*=n.u_n+1 u*=u_n+1 => u*=u_n+dt*u_t =u_n+dt*(u*grad_u+(1/rho)*(mu*laplace(u)+grad_pression+F) is correct?? (depent to density rho) 2) t.u*=t.(u_n+1+(dt*grad_Phi) 3) for pressure: laplace(phi)=(rho/dt)*div u^* boundary n.grad_phi=0 4) and to calculate u_n+1 u_n+1=u*(dt/rho)*grad_phi No boundary conditions, ie I compute the velocity for interior and boundary points. PS: I am beginner in CFD I need your help Thank you 

June 20, 2015, 18:27 

#5 
Senior Member
Filippo Maria Denaro
Join Date: Jul 2010
Posts: 2,357
Rep Power: 28 
I think your process need a careful revision...
1) Are you using a second order implicit time integration in the momentum equation? 2) The pressure equation is nothing else but the continuity equation in which the Hodge decomposition is substituded. 3) You need to take care of the product Div Grad, I suggest not to write it as Laplacian for a correct setting of the Neuman BC.s 4) What books/papers are you studying for the FTS method? 

June 20, 2015, 18:48 

#6 
New Member
Rime
Join Date: Jun 2015
Posts: 28
Rep Power: 3 
for time discretisation I use Adams Bashforth and Crank Nicolson scheme.
[1] Application of a FractionalStep Method to Incompressible NavierStokes Equations J. KIM AND P. MOIN [2] David L. Brown, Ricardo Cortez,y and Michael L. Minionz Accurate Projection Methods for the Incompressible Navier–Stokes Equations [3]J.L. Guermond, P. Minev c, Jie Shen An overview of projection methods for incompressible flows and other paper for spatial discretisation (Radial basis function). 

June 21, 2015, 03:21 

#7  
Senior Member
Filippo Maria Denaro
Join Date: Jul 2010
Posts: 2,357
Rep Power: 28 
Quote:
Ok, therefore you solve the implicit scheme for v* using the BC.s v* = v_n+1 + dt Grad phi_n, right? Then you solve the elliptic equation Dic Grad phi_n+1 = Div q, wherein q is the source term. What's wrong with your results? 

June 21, 2015, 07:01 

#8 
New Member
Rime
Join Date: Jun 2015
Posts: 28
Rep Power: 3 
Thank you for the reply.
my result diverge and when I use steady boundary I get a false solution. 

June 21, 2015, 07:10 

#9 
Senior Member
Filippo Maria Denaro
Join Date: Jul 2010
Posts: 2,357
Rep Power: 28 

June 21, 2015, 07:16 

#10 
New Member
Rime
Join Date: Jun 2015
Posts: 28
Rep Power: 3 
I get div u around 0.04


June 21, 2015, 07:29 

#11 
Senior Member
Filippo Maria Denaro
Join Date: Jul 2010
Posts: 2,357
Rep Power: 28 

June 21, 2015, 07:42 

#12 
New Member
Rime
Join Date: Jun 2015
Posts: 28
Rep Power: 3 

June 21, 2015, 08:31 

#13 
Senior Member
Filippo Maria Denaro
Join Date: Jul 2010
Posts: 2,357
Rep Power: 28 

June 21, 2015, 08:36 

#14 
New Member
Rime
Join Date: Jun 2015
Posts: 28
Rep Power: 3 

June 21, 2015, 08:43 

#15 
Senior Member
Filippo Maria Denaro
Join Date: Jul 2010
Posts: 2,357
Rep Power: 28 

June 21, 2015, 09:19 

#16  
New Member
Rime
Join Date: Jun 2015
Posts: 28
Rep Power: 3 
Quote:
n.u^* = n.u_n+1 + n.grad_phi so n.grad_phi= n.(u^*  u_n+1^*) I look that in my code I consider that the velocity in the boundary equal to zero (therefore that is false) 

June 21, 2015, 11:58 

#17  
Senior Member
Filippo Maria Denaro
Join Date: Jul 2010
Posts: 2,357
Rep Power: 28 
Quote:
As you see, if you set in n.u^* = n.u_n+1 + n.grad_phi the BC.s : n.grad_phi=0 , you MUST set also n.u^* = n.u_n+1 therfore in computing the source term Div u^* you have to use the physical BC.s n.u_n+1. One you have fulfilled such constraints, you have the compatibility condition satisfied and the Poisson equation will converge. Finally, if you use a staggered secondo order discretization you should have the continuity equation satisfied up to machine precision 

June 21, 2015, 12:34 

#18  
New Member
Rime
Join Date: Jun 2015
Posts: 28
Rep Power: 3 
Quote:
n.u^* = n.u_n+1 <=> n.u^* = n.u_bc (bc=boundary condition) because I can't see the difference between u_n+1 and steady u_bc 

June 21, 2015, 12:37 

#19 
Senior Member
Filippo Maria Denaro
Join Date: Jul 2010
Posts: 2,357
Rep Power: 28 

June 21, 2015, 12:44 

#20 
New Member
Rime
Join Date: Jun 2015
Posts: 28
Rep Power: 3 

Thread Tools  
Display Modes  


Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Contribution a new utility: refine wall layer mesh based on yPlus field  lakeat  OpenFOAM Mesh Utilities  57  February 1, 2015 09:25 
Moving mesh  Niklas Wikstrom (Wikstrom)  OpenFOAM Running, Solving & CFD  122  June 15, 2014 06:20 
Help for the small implementation in turbulence model  shipman  OpenFOAM Programming & Development  25  March 19, 2014 11:08 
How to write k and epsilon before the abnormal end  xiuying  OpenFOAM Running, Solving & CFD  8  August 27, 2013 15:33 
Low Mixing time Problem  Mavier  CFX  5  April 29, 2013 00:00 