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upwind schemes,zonal grids and LES
Hello everybody,
I am working on incompressible,turbulent channel flow simulations using dynamic LES. ( in the context of flow control). My aim is to enhance the near-wall resolution without making the simulation computation-intensive. I realise that zonal grids are a good solution. I have seen some papers which have reported using the QUICK scheme for the convective terms, and proceed using a fractional step algorithm with suitable 'intergrid' boundary treatments. My question is... can the LES subgrid-model be effective under such cirucmustances. I mean how does one ensure that the 'dissipative nature' of QUICK scheme doesn't destroy the effectiveness of the LES model ? Any references wherein people have used QUICK schemes coupled with LES ( is it correct to do so in the first place ?)..plus zonal grids..will be appreciated. Alternately I will be interested in knowing if there are any other 'oscillation supressing' schemes to handle the convective terms ...other than the QUICK scheme, all in the context of the zonal approach. I know that `spectral-elements' will do a fine job...but my main target is to modify an already existing code which employs a pseudospectral approach (conservative finite difference scheme along the wall normal and spectral along streamwise and spanwise. RK3 combined with crank-nicholson for time stepping.) coupled with the fractional step scheme. But then, I haven't heard much about combining spectral -elements with LES ( dynamic) either ! any suggestions ? Thanks Prabhu |

Re: upwind schemes,zonal grids and LES
(1) You talk about using upwind schemes in conjunction with LES: but you have to keep in my mind the dissipative nature of the higher order upwind schemes which causes spurious damping of the smaller scales. Central schemes don't offer numerical dissipation, and hence would be a better choice. (2) Using zonal grids is not the only solution to your problem. For LES, it would be better (in fact, easier) to use non-uniform grids in the wall-normal direction. In case of zonal grids, the exact conservation of the fluxes would be necessary at the intergrid boundary: this is something to take care of. (3) Using second-order central difference scheme would help retain the energy in the small scales; being energy conservative. And with slightly more fine grids, it would yield comparable results to the high-order upwind schemes. Besides, there is not much difference in the computational costs.
-Good luck, Mohit |

Re: upwind schemes,zonal grids and LES
Hello Mohit and the rest of the readers,
My priorities are two-fold. 1.) improve the near-wall resolution to better resolve the streaks and bursts.( in the channel) 2.) make the code more amenable to parallelisation. As a step towards improving the existing code..a zonal approach seems to address both the above issues in one shot. The only question is ....in the light of the intergrid- boundary treatments will the existing scheme survive. As I said earlier we do use a conservative second order CD scheme in the wall normal direction. ( we already employ a hyperbolic tangent, stretched grid.) The only alternative seems to be an `UPWIND' like method. But then this `seems' to conflict with the LES model. ('Seems' ..because I have not yet implemented the method)...Hence my question to this forum. I have little doubt that employing zonal grids will be less computation-intensive than treating the whole domain as a sigle zone. SO..zonal grids are here to stay. Only problem that needs to be addressed is ..how can all the three viz..intergrid-errors,upwinds ( if used as an alternative to central difference) and LES be made to coexist. Another point which may help you better appreciate my problem is ..we aim at going in for higher Reynolds number flows. SO...as we push the Reynolds number higher..zonal decomposition would make more sense than simple grid-stetching. I am going through Prof.R.L.Street's (Stanford) work in this regard ( ref: JFM 379,71-104,1999)). But my doubts remain. Thanks Prabhu |

Re: upwind schemes,zonal grids and LES
Hello Mohit and the rest of the readers,
My priorities are two-fold. 1.) improve the near-wall resolution to better resolve the streaks and bursts.( in the channel) 2.) make the code more amenable to parallelisation. As a step towards improving the existing code..a zonal approach seems to address both the above issues in one shot. The only question is ....in the light of the intergrid- boundary treatments will the existing scheme survive. As I said earlier we do use a conservative second order CD scheme in the wall normal direction. ( we already employ a hyperbolic tangent, stretched grid.) The only alternative seems to be an `UPWIND' like method. But then this `seems' to conflict with the LES model. ('Seems' ..because I have not yet implemented the method)...Hence my question to this forum. I have little doubt that employing zonal grids will be less computation-intensive than treating the whole domain as a sigle zone. SO..zonal grids are here to stay. Only problem that needs to be addressed is ..how can all the three viz..intergrid-errors,upwinds ( if used as an alternative to central difference) and LES be made to coexist. Another point which may help you better appreciate my problem is ..we aim at going in for higher Reynolds number flows. SO...as we push the Reynolds number higher..zonal decomposition would make more sense than simple grid-stetching. I am going through Prof.R.L.Street's (Stanford) work in this regard ( ref: JFM 379,71-104,1999)). But my doubts remain. Thanks Prabhu |

Re: upwind schemes,zonal grids and LES
Hi Prabhu,
Refer to the paper by A.W. Cook in J. Comp. Phys. (sept'99) "A consistent method for LES..." Clearly grid stretching introduces commutation errors which are second order in grid size and hence comparable to the SGS stresses you are modeling... therefore, you must have zonal grids free of commutation errors and the information between grids must be transferred consistently as described in Cook's paper. Prof. R.L. Street's work on LES is not free of commutation error... keep that in mind before making any inference... About upwind schemes... they have to be higher order accurate so that they are less dissipative ... read the paper by Sandip Ghosal on "Analysis of discretization errors in LES" which appeared in J. Comp. Phys. Central differencing schemes have some problems too.. I guess if you go through above stated papers you'll have some answer to your questions ( and off course.. a lot more questions too!!) take care Mayank |

Re: upwind schemes,zonal grids and LES
Thanks for the Reference to Cooks paper Mayank.
I have read through Sandip Ghosals elegant analysis of discretization errors in LES.. I would like to inform you that in our implementation of the dynamic LES model in the channel flow case, we calculate the parameter C ( the smagorinsky C )..by 'averaging over the planes' parallel to the walls. SO...the question of 'commutation errors' would arise only when we think of including the wall-normal averaging too. SO..far this has not been our main concern. This will definitely be the case when we plan to introduce grids with variable grid-spacing along spanwise/streamwise directions in order to resolve the structures...Ref: Kravachenko & Moins work with B-splines) So...my feeling is I needn't worry about this 'higher order' effect till the present issue of LES vs. 'zonal-boundary errors' as well as LES vs. upwinding errors are addressed. Ghoshal's work has not talked about these issues while analyzing LES errors. I shall be glad to receive inputs regarding other groups working in multidomain-LES issues ..( with respect to error analysis). Thanks Prabhu |

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