# Crank-Nicolson scheme

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

 November 17, 2011, 07:38 Crank-Nicolson scheme #1 New Member   Join Date: Nov 2009 Posts: 17 Rep Power: 7 Hi Foamers, I'm trying to implement a second order solver for incomresssible flows which uses Crank-Nicolson (CN) method for the diffusive term and Adams-Bashfort method for the convective term. I am confused about how CN method is implemented in OpenFOAM, as I don't see any coefficient like 1/2 on the convective and viscous term. How can you apply CN scheme without using these coefficients? As far as I see it is only covered by ddt(U) term. Best, Asim

 November 17, 2011, 09:12 #2 New Member   Join Date: Nov 2009 Posts: 17 Rep Power: 7 The intention for implementing a second order solver is that PisoFOAM is only FIRST order accurate in time whatever scheme you use for time discretization. The reason for this is the explicit treatment of the flux phi in the convective term. They limit the accuracy in time to first order and this is not preferred in turbulent flow simulations. I don't understand why nobody cares about this, and I read a lot of papers Openfoam users claiming they have second order accuracy. It confuses me a lot. Am I missing something?

 November 25, 2011, 09:33 #3 Senior Member   Francois Join Date: Jun 2010 Posts: 107 Rep Power: 7 Dear Asim, I don't think it's the explicit treatment of the flux in the convective terms which reduces the order of the pisoFoam algorithm. In fact, even by doing everything explicitly you should be able to retrieve second order accuracy. It will however impact stability as your time integration is no longer purely implicit. But I think (and I've also heard via-via from developpers) that the main issue comes from the Rhie-Chow flux correction ddtPhiCorr in: Code: ```phi = (fvc::interpolate(U) & mesh.Sf()) + fvc::ddtPhiCorr(rAU, U, phi);``` Why nobody seems to care, I don't know.. I do! But apparently the fix of ddtPhiCorr is not trivial.. And as for the second order claim in papers.. Well.. A 'small' distortion of the truth perhaps? Kind regards, Francois

 Tags crank nicolson, incompressible flows

 Thread Tools Display Modes Linear Mode

 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 OffTrackbacks are On Pingbacks are On Refbacks are On Forum Rules

 Similar Threads Thread Thread Starter Forum Replies Last Post msrinath80 OpenFOAM Running, Solving & CFD 6 November 14, 2010 14:59 Cyp OpenFOAM 3 July 19, 2010 07:58 And OpenFOAM 0 November 19, 2009 08:11 msrinath80 OpenFOAM Running, Solving & CFD 0 December 12, 2006 23:41 ! Main CFD Forum 0 September 5, 2005 12:52

All times are GMT -4. The time now is 20:38.