# Implicit method for Navier Stokes equations

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 January 6, 2012, 10:47 Implicit method for Navier Stokes equations #1 New Member   Vasiliy Join Date: Feb 2011 Posts: 9 Rep Power: 8 Hi All, I construct implicit solver for Navier Stokes equations. I use Roe method to calculate explicit fluxes. My question is about convective and viscous Jacobians in implicit part. I was told that some of such Jacobians can be excluded from large sparse matrix to accelerate convergence. It is not connected with technic where viscous Jacobian is changed with spectral radius. It looks like some of Jacobians are fully removed to accelerate convergence. Does anybody have information about such algorithms? Thanks

 January 6, 2012, 13:41 #2 Senior Member   Join Date: Jul 2009 Posts: 247 Rep Power: 12 Are you referring to something like this? http://www.sciencedirect.com/science...2199918190156X If so, try googling "pulliam diagonalized". Thomas Pulliam is the guy who has put a lot of developmental effort into such schemes. You should be able to find quite a bit of information on the internet.

 January 12, 2012, 08:43 Help please #4 New Member   Abhishek Chintagunta Join Date: Jan 2012 Posts: 2 Rep Power: 0 Hi Vasily, I am developing the same code for unstructured grids. Can you help me about the implementation of Boundary conditions ? (Any paper or book would do) I think I did not look properly. Thank you for your help. Sorry about asking a question for your question. Regards, Abhishek

 January 12, 2012, 09:05 Refer Yoon Jameson Paper #5 New Member   Vinayender Join Date: Jul 2009 Location: India Posts: 24 Rep Power: 10 Vasiliy , Please refer "AIAA 86 0105" "LU Implicit Schemes with Multiple Grids for the Euler Equations" by A.Jameson and S.Yoon Princeton Univ., Princeton, NJ Paper. for Implicit equation, of form (1/del_t - del_R/del_U) delt_U ) = R(U_n) Right hand side is imprortant because it is the governing physiscs and for steady problems LHS is just numerics. so its accuracy is not important. so for LHS you use only a very quick schems which refered in the paper said above......refer it __________________ Thanks , Vinayender

 January 12, 2012, 09:11 Abhishek #6 New Member   Vinayender Join Date: Jul 2009 Location: India Posts: 24 Rep Power: 10 Abhishek, if you are implementing a density based solver, you can refer "Computational Gas Dynamics " by Laney and also a book "Computational Fluid dynamics: principles and applications" by Jiri Blazek __________________ Thanks , Vinayender

 January 12, 2012, 09:32 #7 New Member   Abhishek Chintagunta Join Date: Jan 2012 Posts: 2 Rep Power: 0 Dear Vinay, I have already finished coding the entire Implicit algorithm for unstructured grids based on Roe scheme (upwind). But I am having a difficulty applying boundary conditions (to be specific calculating Convective Flux Jacobian at boundaries specifically Wall, Symmetry) in the implicit operator. I am trying to solve the system using a Newtons method. My code is based on an explicit code I previously developed. Any paper or book suggestion is highly appreciated. Kind Regards, Abhishek

 January 13, 2012, 01:45 Ghost Cell or Half Volume construction #8 New Member   Vinayender Join Date: Jul 2009 Location: India Posts: 24 Rep Power: 10 Hi Abhishek, There are few procedures to calculate the fluxes on wall (same with little different for symmetric bc) 1) construction of ghost cell 1) Construction of ghost cell, you can assume a ghost cell in the wall region of same volume jsut opposite to the real cell and define the properties of that cell as same values other than for velocities. velocity compenets can be calculated such that the net mass flux at the wall ( the interior face between real cell and ghost cell) is zero.. values of real cell at wall can be rho, p, temperature, u and v values of ghost cell at the wall can be rho, p, temperature, u_ghost and v_ghost u_ghost and v_ghost can be calculated using 2 relations. 1 is normal mass flux is zero and 2nd is wall tangential velocity is 0 for wall and tangential velocities a finite one for symmetric bc) Now flux at wall can be caculated at the face (which is between real and ghost cell) like you calculate for any other interior face...... __________________ Thanks , Vinayender

 January 13, 2012, 01:50 got wrong ? #9 New Member   Vinayender Join Date: Jul 2009 Location: India Posts: 24 Rep Power: 10 Hi Abhishek, i guess i got your question wrong.. let me get back to you __________________ Thanks , Vinayender

 December 3, 2012, 14:07 #10 New Member   Vasiliy Join Date: Feb 2011 Posts: 9 Rep Power: 8 Hi Everybody, Thanks for previous help. I have implemented Weiss and Smith precondition. It works fine for laminar flows but I have slow convergence for turbulent flows. It looks like there is method to improve convergence of turbulent flows. I saw it in some hard code results (Fluent for example). My current task is to minimize number of Navier-Stokes iterations. Does anybody know such methods? Thanks

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