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November 2, 2007, 13:48 
Pressure&Veloctiy Iteration in SOLA method

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Hi, I try to use SOLA method to solve NS equations without considering free surface. it suppose to be a simply coding work. But I cannot get the pressure right.
After the first step calculating a tentative veloctiy field, the pressure corrections by applying the tentative veloctiy field in continuity equation are applied. the equation i used is delp(p)=  D(ijk)/[∂D/∂p] . and then, use delp(p) to correct the velocity field until they are converged. Is there any trick for this classic method? since there is no free surface, the calculation should be quite straight forward. the BCs i used are noslip for velocity, and sysmetry for pressure. Any suggestion to improve the code? 

November 5, 2007, 12:24 
Re: Pressure&Veloctiy Iteration in SOLA method

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plz give more details what you mean about wrong pressure,
note that you should define a ref. pressure in one position and then talk about pressure. I already have used sola in cavity benchmark and i was well (althouth it was very slow to converge in high renolds, e.g. 1000) 

November 5, 2007, 15:37 
Re: Pressure&Veloctiy Iteration in SOLA method

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There are a couple of things you can do to speed things up. First, experiment some with alpha, the relaxation factor.
Second, the LANL folks who developed SOLAsurf learned long ago that there's no benefit with converging the pressure iteration beyond some minimum value  it just burns up more iterations. The rule of thumb is given in a publication that I can't find just now. If you need to document it, look at publications of C. W. Hirt in the 198085 time frame. The formula is 'optimum' epsilon (convergence criteria defined in the documentation) is about = 2.0e4 * V / D. V is a 'typical velocity' D is the minimum mesh dimension. Again, you'll need to do some experimentation. If you have a free surface, the code automatically sets the fluid pressure relative to the specified surface pressure. With no free surface, the changes in pressure determined by the iteration procedure are designed to satisfy continuity in every cell. To start the calculation, specify an initial pressure field, then allow that to be corrected in such a way that continuity is satisfied from time step to time step. Fixing the pressure in one cell destroys mass conservation in that cell  and slows down the convergence process. 

November 6, 2007, 00:16 
Re: Pressure&Veloctiy Iteration in SOLA method

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> Fixing the pressure in one cell destroys mass conservation in that cell  and slows down the convergence process.
It is not required to fix pressure during pressure relaxation, but it is sufficint to compute ur desirable pressure by post processing pressure, e.g., P_new = P_calc + P_ref. I suggest this issue to "Lang Yuan" because novice peoples usually has difficulty to interpret pressure, e.g. negative pressure is strang for them and they think that it is due to computation error. 

November 6, 2007, 07:41 
Re: Pressure&Veloctiy Iteration in SOLA method

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Thanks for your reply.
Take a simplest example to explain how i used. [constant veloctiy goes through a steight tube] . i set that initial conditons for pressure are all air pressure and set the inlet pressure to Air pressure as well and with constant velocity. outlet conditions are only set the same velocity with the inlet. Boundary condtion for pressure i used is symmetric, for velocity is noslip. during each iteration of pressure and velocity corretion, I applied the BCs in the calculation. the reuslts showed the velocity field is reasonable, but the pressure value decreased significantly(range 1e4 to 1e5), which is not right. I tried the classic lid driven cavity flow. the whole process cannot be converged. (different relaxation factors and alpha are tried). I double checked the iteration process of pressure and velocity correction. they are totally fit with the original method. So i get confused with the problem. Actually, I used SOLAVOF for a free surface problem before, it works well. Thanks very much, waiting for your comments. LY 

November 6, 2007, 07:50 
Re: Pressure&Veloctiy Iteration in SOLA method

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Thanks very much for both your comments.
I will try to read the paper and find more. Here For classic lid driven cavity flow problem, how do you set the initial condtions and boundary condtions for this problem? if you define three differnet types of cells: Wall, inlet and fluid. Cheers, LY 

November 6, 2007, 09:51 
Re: Pressure&Veloctiy Iteration in SOLA method

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Don't know what an 'inlet' bc is for a driven cavity. The fluid is sealed in the cavity so there's no inlet or outlet. That is, the velocity across the boundary is zero.
The standard noslip boundary (on the velocities parallel to the walls) is vtangent = 0. The condition is applied by setting the tangential velocity in the 'image' or 'ghost' cell. This is set by vghost =  vinterior. It's straightforward to extend this to vtangent = specifiedwallvelocity, which drives the circulating flow in the cavity. Use something like vghost = 2*vtangent  vinterior Be careful with this because it assumes a uniform mesh spacing at and near the wall. 

November 6, 2007, 10:25 
Re: Pressure&Veloctiy Iteration in SOLA method

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thanks! Otd.
what's the pressure boundary conditons used in this case? here inlet just means the moving lid which drives the flow. It should be correctted in this case as you said. 

November 6, 2007, 11:46 
Re: Pressure&Veloctiy Iteration in SOLA method

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at first a general comment:
you should first validate your code againts either exact solution or available benchmark. My suggestion: at first step lid deriven cavity is the best one, because it is very simple, particularly we do not have inlet/outlet conditions which are more problematic. Then i suggest to test flow in a channel with velosity inlet bc (not pressure). Regarding to lid driven cavity: pressure bc is homogeneousw newmann, i.e., grad P . n = 0 across all walls. in uniform grid FDM language is P_in = P_gost. Note that sola has difficulty to resolve corner vortexes when Renold is high, basically cell by cell pressure correction is not good method and works when pressure gradient is low, note that sola is almost exterminated nowadays, i stronly recommend to switch to projection method. also if you follow Los Alamos progress you see that they switch to projection method (ICCG solver) in NASAVOF code and betterly in Ripple code (if you need code in this context i could guide you, my personal code has this issue plus MAC plus PLIC VOF for interface resolution, i could share it with you), i do not think you can figure out Re=10000 results with formal sola algorithm. > how do you set the initial condtions and boundary is not important, i have used zero field condition. Bc is noslip in all walls except u velosity of lid. Finally i should say that in Sola algorithm a spesified pressure BC is a serious problem and is one of difficulty of thyis method. 

November 6, 2007, 12:21 
Re: Pressure&Veloctiy Iteration in SOLA method

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Thank you so much! rt!
i am trying to solve the lid moving case with Sola code first to test the code anyway. From your text, It is better for me to switch to another method. I am also thinking about it. I always foucs on SOLA and SIMPLE, know very little about other methods. Could you recommend some key papers? I suppose I will have lots of questions on these kinds of problems, could you please tell me your email or send me an email? so that i can contact with you easily. 

November 6, 2007, 16:12 
Re: Pressure&Veloctiy Iteration in SOLA method

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note that simple is not a good choice for unsteady cases (computationally expensive)
> Could you recommend some key papers? if you look for a book this one give you a good insight about projection method: M Griebel, T Dornseifer, T Neunhoeffer, Numerical simulation in fluid dynamics, 1998. Another good Ref. is Ripple manual it is online available, if u need it and do ont find it, give ur mail ID i will forward to u a copy, i do not remember it link. 

November 6, 2007, 16:44 
Re: Pressure&Veloctiy Iteration in SOLA method

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January 2, 2010, 07:40 

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