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SIMPLE method with explicit solver?

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Old   July 24, 2010, 18:07
Default SIMPLE method with explicit solver?
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I have a question about implementing the SIMPLE method using and explicit method for the momentum equations. All of the literature that I have found implies that the momentum equations for each direction be advanced implicitly, before solving the pressure correction equations and applying the velocity corrections. However, I would like to solve momentum equations using a direction split, explicit, monotone method. Is this a reasonable approach? Any help is greatly appreciated.

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Old   July 25, 2010, 00:09
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Related question:

Does anyone have a paper or lecture link that has a very basic and detailed explanation of the SIMPLE algorithm?
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Old   July 26, 2010, 07:45
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Refer the following book for SIMPLE algorith.

which will be very useful for the beginners.
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Old   July 27, 2010, 08:45
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I have also been trying to implement a very small general flow solver using the SIMPLE/pressure correction method. As simplicity is more important than performance at this stage of my project, I used MATLAB to program it. In the future, I plan to implement an immersed boundary test case to gain some experience with this method.

The code uses upwind and central differencing and is explicit in time. This seems to work quite well if the usual restrictions (CFL, Re etc) are upheld. One of the simplest ways to ensure convergence and stability of the simulation is of course to increase the amount of cells and decrease the time step. This has worked quite well, although the actual computation is of course slow.

One of the major problems I am experiencing are the boundary conditions of the simulation. Away from the boundaries, 4 neighboring cells are used to compute the pressure in the center cell enclosed. However, computing the pressure at the boundary cells is difficult because there are only 3 neighboring cells and the pressure is unknown, therefore rendering an implementation using ghost cells useless. Does anyone have a good solution to calculating the pressures at the boundaries?

BTW, a good book explaining the pressure correction method is also:

Numerical computation of internal and external flows by Charles Hirsch.
Unfortunately, he advocates using implicit methods, but the equations can be changed on paper without much ado.
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Old   July 30, 2010, 12:13
Default Projection Method
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When using explicit time discretization, the straightforward and natural treatment of the pressure is Chorin's Projection Method. Here the pressure is calculated after each timestep and then used to correct the velocities in order to achieve divergence-free velocities.
This method does not work for implicit time stepping, since all velocities are from the new time step. When the velocities are corrected with the pressure, they are divergence free, but the momentum equation is not fulfilled anymore. The solution to this problem is an iterative procedure, where the velocities and the pressure are solved several times in each timestep, so that the velocities fulfill both the continuity and the momentum equation. The SIMPLE algorithm is build upon this idea, except it does not solve for the pressure, but for the pressure correction.
Details can be found in the Ferziger & Peric book, chapter 7.


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Old   August 7, 2010, 13:44
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Thank you for your reply. It was extreamly helpful.

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Old   August 9, 2010, 06:08
Question SHIP FLOW help please
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i am using shipflow to model an amphibious tank.
i have made the model in SHIPFLOW design,
i made a reference plane and then i tried to generate a section group.
the section group is not being created.
it is giving the following error.

'INFO section calculation failure [boundary coincidence]'

someone please help me in this matter.
thank u very much
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explicit, implicit, monotone, simple

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