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Step 5: Solution

Now we will be dealing with the Solution section of FLUENT. Let's first specify the discretization method.

Solution > Solution Methods
Under Spatial Discretization, change Momentum, Turbulent Kinetic Energy, Turbulent Dissipation Rate, Energy to Second Order Upwind discretization method.
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Now let's us set the convergence criteria.

Solution > Monitors > Residuals - Print, Plot > Edit...

Enter convergence criteria of 1e6 for continuity, x-velocity, y-velocity, k and epsilon. Click OK to close the window.
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https://confluence.cornell.edu/download/attachments/111221575/monitor.png

Numerical Solution

Let's get FLUENT to solve our nonlinear BVP. It'll introduce discretization and linearization errors in the process, as discussed in the Pre-Analysis step. We'll check the level of numerical errors later in the Verification & Validation step. There are lots of knobs in the Solution menu that you can twiddle to improve your numerical solution to the BVP. We'll not mess with most of these since the default settings yield an adequate numerical solution for our problem. We could get a slight improvement in accuracy by fiddling various knobs which we'll refrain from doing here.

Solution > Methods

The FLUENT solver converts our BVP to a set of algebraic equations through a process called discretization. We'll use second-order discretization for which the error is of the order of the square of the mesh spacing. This is more accurate (albeit less stable) than first-order discretization where the error is of the order of the mesh spacing.  Choose Second-Order Upwind for all equations as shown below. Set Pressure-Velocity Coupling to SIMPLE if it is not by default.

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To set the convergence criterion identified in the flowchart above , select:

Solution > Monitors > Residual

We see that we need to provide a convergence criterion for each PDE that is being solved. The solver will stop iterating when mass, momentum, energy, k and epsilon imbalances (called residuals) fall below the convergence tolerance. We'll use a residual tolerance of 10^-6 for all six PDE's being solved. FLUENT will consider the iterations have converged when all six residuals have fallen below this tolerance. Set the residuals tolerance as shown in the figure below. Make sure to scroll down and set the tolerance for k and epsilon equations also. 

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Also make sure Plot box is checked as shown above. This will help you monitor how/whether the solution is proceeding to convergence as the iterations are carried out. Click OK.

Next, we set the initial guess indicated in the flowchart. The initial guess can be entered using:

Solution > Initialization

We need to provide FLUENT with an initial guess for the flow variables (velocity, pressure etc.) to start the iterations. For this example, we know the conditions at the inlet of the pipe (except for pressure which is set to zero gauge by default). Initialize the entire flowfield to the specified values at the inlet: First, select Standard Initialization, then under  
At this point, everything is set up properly. We just need to give an initial condition for FLUENT to start the calculation. 
Solution > Solution Initialization
Under Compute from, select Inlet and click Initialize.  
Now we can solve for a solution. 

To prevent the computer from iterating indefinitely, we need to set an iterations limit.

Solution > Run Calculation 
Enter 500 for Number of Iterations and click Calculate. Note that 500 is the maximum number of iterations we want the solver to carry out. You will see a window message saying Calculating the solution... Wait for FLUENT to finish the calculation. By the end of 500 iterations, all residuals converged to less than 1e6 except for continuity equation. Let's leave that for now and continue to check . Our solution converges in about 350 - 400  iterations. So the solver will stop the iterations before it reaches the maximum number of iterations specified (500). You should see a residual plot on screen as the computation is being performed. It should look something like below. At this point, we have a reasonable solution to the set of algebraic equations generated from the BVP using discretization. 

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Save project and exit FLUENT:

File > Save Project 

File > Close Fluent for our results and see if they make sense. Close FLUENT and return to Workbench.

Go to Step 6: ResultsSee and rate the complete Learning ModuleNumerical Results

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