# Any desired level of accuracy in laminar flows?

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

 March 31, 2003, 03:58 Any desired level of accuracy in laminar flows? #1 gorka Guest   Posts: n/a Hi, In laminar flows in complex geometries (with recirculations, moving walls etc.) without any modelling requirement (neither combustion, phase change or multiphase), is it possible – by means of doing the mesh more and more fine - to achieve any desired level of accuracy of the results? In other words, can we do the overall numerical error as small as we want in the aforementioned case? Thanks in advance, Gorka

 March 31, 2003, 05:01 Re: Any desired level of accuracy in laminar flows #2 Jonas Larsson Guest   Posts: n/a There exists no error estimates for the Navier-Stokes equations, hence, it is not possible to in general say something about the accuracy. You can do grid refinenment studies etc. to make it likely that your results have a certain degree of accuracy. However, you can not prove this mathematically.

 April 1, 2003, 04:37 Re: Any desired level of accuracy in laminar flows #3 gorka Guest   Posts: n/a Thanks for your response Jonas, Actually I am looking for a more pragmatic answer. Lets suppose that we have to calculate an isothermal laminar flow in a very complex geometry with a good quality mesh and using a tested code that works with well-posed (consistent, conservative etc.) numerical schemes. Doing the mesh more and more fine, can we aspire to reduce the numerical error to the computer round off error, and then affirm that the results would be realistic without the need to compare with experimental data??? Thanks in advance, Gorka

 April 1, 2003, 04:45 Re: Any desired level of accuracy in laminar flows #4 Rami Guest   Posts: n/a Let us assume that the NS equations are exact (excluding, e.g., breakdown of continuity for small Knudsen No.). Then, if the discretization is CONSISTENT, it is converging to the differential equations in the limit of infinitely small cell size. Therefore, to my understanding, refining the grid will bring you closer to the exact solution (assuming, of course, that the BCs are correct, that the iterative solution is converged, etc). I agree that the error estimates are unavailable, but performing refinement study gives some insight on the grid dependence and the rate of convergence wrt to the grid size.

 April 1, 2003, 04:53 Re: Any desired level of accuracy in laminar flows #5 gorka Guest   Posts: n/a Thanks for your response Rami, Of course, you are right. To obtain realistic results the Boundary Conditions should be realistic too. Gorka

 April 1, 2003, 04:56 Re: Any desired level of accuracy in laminar flows #6 Jonas Larsson Guest   Posts: n/a You can never be 100% sure of how accurate your results are since there is no mathematical proof to rely on. However, for simple laminar flows experience says that you can be quite sure that a good CFD code will produce good results, especially if you perform a grid-refinement study. However, if the flow is complex with separations, unsteadiness etc. you are more likely to produce incorrect results. If the flow is nicely attached and steady I'd trust the results.

 April 1, 2003, 14:41 Re: Any desired level of accuracy in laminar flows #7 Ananda Himansu Guest   Posts: n/a Jonas and Rami are both right. A numerical scheme is one approach to proving existence of a solution. Mathematicians sometimes use a finite-difference scheme to provide a constructive proof of existence of a solution to simpler equations than the NS. In those cases, they are able to prove certain things about how the difference scheme will behave as one refines the mesh. For the NS equations, such proofs are not available. In general, one should not expect such proofs for steady-state solutions, except perhaps for trivial cases. However, numerical experiments such as Gorka contemplates verge on being heuristic "proofs" for any particular geometry and boundary conditions. One may not be able to mathematically prove in advance that the procedure will not blow up on the next finer mesh, or that the sequence of "steady-state" numerical solutions will converge with respect to mesh refinement. However, numerical experimentation with a consistent scheme on a sequence of increasingly fine meshes, gives one confidence that a solution exists, and that one is approaching it as the mesh is refined. Engineers must press on with a Platonic attitude, while mathematicians compete for one of the Clay Institute prizes!

 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 Blasius_Pohlhausen_Crocco Main CFD Forum 12 September 30, 2013 17:35 ganesh Main CFD Forum 0 February 29, 2008 06:32 jinwon park Main CFD Forum 0 February 26, 2008 17:26 Watt Main CFD Forum 0 June 10, 2004 03:48 Ian Castro Main CFD Forum 4 July 17, 2001 02:24

All times are GMT -4. The time now is 08:52.