|
[Sponsors] |
Boundary Conditions Of Discrete Adjoint Method For 2D NS Equations |
![]() |
|
LinkBack | Thread Tools | Search this Thread | Display Modes |
![]() |
![]() |
#1 |
New Member
Ashkaari
Join Date: May 2014
Posts: 5
Rep Power: 12 ![]() |
Hello everyone, I've been working on the adjoint based grid adaptation for viscous flow.But my adjoint solver doesn't work out well.
![]() Here is the problem, back in the flow solver, no-slip and isothermal wall conditions were applied. At wall,u=v=0,E=ρT/(γ-1)=Kρ. And the residuals of momentum and energy equations were all zeroed out(R2=R3=0). The adjoint equations is, (әR/әW)Tψ=әI/әW. ψ=[ψ1,ψ2,ψ3,ψ4] is the adjoint solution. (әR/әW)T is the transposed Jacobian with W=[ρ,ρu,ρv,E], I is an output function like lift or drag coefficient. For a wall node i, by hand differentiation: әR1/әW=[0,nx,ny,0], әR2/әW=әR3/әW=[0,0,0,0], әR4/әW=K*әR1/әW. The transposed Jacobian becomes [0,0,0,0;nx,0,0,Knx;ny,0,0,Kny;0,0,0,0]. According to David Venditti, ψ2,ψ3 can still be known via special treatment. However, since the first and last row of jacobian matrix is zero vector, I can not get ψ1,ψ4 . There must be something wrong in the above deduction, could you kindly point it out for me? Many Thanks. Last edited by Ashkaari; May 30, 2014 at 03:50. |
|
![]() |
![]() |
![]() |
![]() |
#2 |
New Member
Ashkaari
Join Date: May 2014
Posts: 5
Rep Power: 12 ![]() |
The flow and adjoint solver utilize a median-dual finite volume scheme.
According to Oliver Amoignon, discretization of the adjoint equations become: [(әR/әW)Tψ]i=∑(әRij/әWi)T*(ψj-ψi)/2+(әRib/әWi)ψi, and j stands for nodes share the same edge with node i. Rib will only be used for boundary nodes. For simplicity,artificial dissipation is not taken into consideration. Rij=(fc,fv)*(nx,ny). (nx,ny) is the outward normal vector on edge ij. The notation fc,fv stand for the convective and visous terms of node i. |
|
![]() |
![]() |
![]() |
![]() |
#3 | |
Super Moderator
Francisco Palacios
Join Date: Jan 2013
Location: Long Beach, CA
Posts: 404
Rep Power: 15 ![]() |
Quote:
Cheers, Francisco |
||
![]() |
![]() |
![]() |
![]() |
#4 |
New Member
Ashkaari
Join Date: May 2014
Posts: 5
Rep Power: 12 ![]() |
I believe I have solved this problem. To my knowledge, the continuous adjoint method was applied in SU2, thank you all the same.
|
|
![]() |
![]() |
![]() |
![]() |
#5 |
Member
Tommy Chen
Join Date: Mar 2011
Location: University of Michigan
Posts: 96
Rep Power: 15 ![]() |
||
![]() |
![]() |
![]() |
Tags |
adjoint solver, boundary condition, jacobian matrix |
|
|
![]() |
||||
Thread | Thread Starter | Forum | Replies | Last Post |
ribbed channel / simpleFoam / boundary conditions | beeo | OpenFOAM Pre-Processing | 20 | July 17, 2013 08:39 |
Error finding variable "THERMX" | sunilpatil | CFX | 8 | April 26, 2013 07:00 |
Euler Equations Boundary Conditions | Christian87 | Main CFD Forum | 0 | April 5, 2013 13:51 |
Method for solving the adjoint equations | fumiya | Main CFD Forum | 1 | June 13, 2011 00:18 |
A question about discrete adjoint method | Thomas | Main CFD Forum | 3 | August 9, 2006 12:37 |