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  • Convergence -- CFD Online Discussion Forums[7/16/2013 9:32:03 AM]

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    July 6, 2011, 07:54 Convergence #1

    Centurion2011Member Join Date: Jul 2011Posts: 39Rep Power: 7

    I see all kind of mistakes on these forums when dealing with convergence, so I willgive brief review of methods...

    At convergence, the following should be satisfied:

    All discrete conservation equations (momentum, energy, etc.) are obeyed inall cells to a specified tolerance OR the solution no longer changes withsubsequent iterations.Overall mass, momentum, energy, and scalar balances are achieved.Monitoring convergence using residual history:Generally, a decrease in residuals by three orders of magnitude indicates atleast qualitative convergence. At this point, the major flow features should beestablished.Scaled energy residual should decrease to 10-6 (for the pressure-basedsolver).Scaled species residual may need to decrease to 10-5 to achieve speciesbalance.Monitoring quantitative convergence:Monitor other relevant key variables/physical quantities for a confirmation.Ensure that overall mass/heat/species conservation is satisfied.

    In addition to residuals, you can also monitor lift, drag and moment coefficients.

    Relevant variables or functions (e.g. surface integrals) at a boundary or any definedsurface.

    In addition to monitoring residual and variable histories, you should also check foroverall heat and mass balances.

    The net flux imbalance (shown in the GUI as Net Results) should be less than 1%of the smallest flux through the domain boundary

    If solution monitors indicate that the solution is converged, but the solution is stillchanging or has a large mass/heat imbalance, this clearly indicates the solution isnot yet converged.

    In this case, you need to:


  • Convergence -- CFD Online Discussion Forums[7/16/2013 9:32:03 AM]

    Reduce values of Convergence Criterion or disable Check Convergence in theResidual Monitors panel.Continue iterations until the solution converges.

    Selecting None under Convergence Criterion disables convergence checking for allequations.

    Numerical instabilities can arise with an ill-posed problem, poor-quality meshand/or inappropriate solver settings.

    Exhibited as increasing (diverging) or stuck residuals.Diverging residuals imply increasing imbalance in conservation equations.Unconverged results are very misleading!


    Ensure that the problem is well-posed.Compute an initial solution using a first-order discretization scheme.For the pressure-based solver, decrease underrelaxation factors for equationshaving convergence problems.For the density-based solver, reduce the Courant number.Remesh or refine cells which have large aspect ratio or large skewness.Remember that you cannot improve cell skewness by using mesh adaption!

    Under-relaxation factor, a, is included to stabilize the iterative process for thepressure-based solver

    Use default under-relaxation factors to start a calculation.

    Decreasing under-relaxation for momentum often aids convergence.Default settings are suitable for a wide range of problems, you can reduce thevalues when necessary.Appropriate settings are best learned from experience!

    For the density-based solver, under-relaxation factors for equations outside thecoupled set are modified as in the pressure-based solver.

    A transient term is included in the density-based solver even for steady stateproblems.The Courant number defines the time step size.For density-based explicit solver:

    Stability constraints impose a maximum limit on the Courant number.Cannot be greater than 2(default value is 1).

    Reduce the Courant number when having difficulty converging.For density-based implicit solver:

    The Courant number is not limited by stability constraints.Default value is 5.

    Convergence can be accelerated by:

    Supplying better initial conditionsStarting from a previous solution (using file/interpolation when necessary)Gradually increasing under-relaxation factors or Courant numberExcessively high values can lead to solution instability convergence problemsYou should always save case and data files before continuing iterationsControlling MultiGrid solver settings (not generally recommended)

  • Convergence -- CFD Online Discussion Forums[7/16/2013 9:32:03 AM]

    Default settings provide a robust Multigrid setup and typically do not need tobe changed.

    A converged solution is not necessarily a correct one!

    Always inspect and evaluate the solution by using available data, physicalprinciples and so on.Use the second-order upwind discretization scheme for final results.Ensure that solution is grid-independent:Use adaption to modify the grid or create additional meshes for the grid-independence study

    If flow features do not seem reasonable:

    Reconsider physical models and boundary conditionsExamine mesh quality and possibly remesh the problemReconsider the choice of the boundaries location (or the domain): inadequatechoice of domain (especially the outlet boundary) can significantly impactsolution accuracy

    Numerical errors are associated with calculation of cell gradients and cell faceinterpolations.

    Ways to contain the numerical errors:

    Use higher-order discretization schemes (second-order upwind, MUSCL)Attempt to align grid with the flow to minimize the false diffusionRefine the meshSufficient mesh density is necessary to resolve salient features of flowInterpolation errors decrease with decreasing cell sizeMinimize variations in cell size in non-uniform meshesTruncation error is minimized in a uniform meshFLUENT provides capability to adapt mesh based on cell size variationMinimize cell skewness and aspect ratioIn general, avoid aspect ratios higher than 5:1 (but higher ratios are allowedin boundary layers)Optimal quad/hex cells have bounded angles of 90 degreesOptimal tri/tet cells are equilateral

    A grid-independent solution exists when the solution does not change when themesh is refined. Below is a systematic procedure for obtaining a grid-independent solution:

    Generate a new, finer mesh.Return to the meshing application and manually adjust the mesh.OR Use the solution-based adaption capability in FLUENT.VERY IMPORTANT: Save the case and data files first.Create adaption register(s) and adapt the mesh. Data from the original meshis interpolated onto the finer mesh. FLUENT offers dynamic mesh adaptionwhich automatically changes the mesh according to user-defined criteria.Continue calculations until convergence.Compare the results obtained on the different meshes.Repeat the procedure if necessary.

    To use a different mesh on a single problem, use the TUI commands file/write-bcand file/read-bc to facilitate the setup of a new problem.Better initialization can be obtained via interpolation from existing case/data byusing solution data interpolationA web-based training module is available to train users in replication of case setup

  • Convergence -- CFD Online Discussion Forums[7/16/2013 9:32:03 AM]

    and solution data interpolation.


    Solution procedure for both the pressure-based and density-based solvers isidentical.

    Calculate until you get a converged solutionObtain a second-order solution (recommended)Refine the mesh and recalculate until a grid-independent solution is obtained.

    All solvers provide tools for judging and improving convergence and ensuringstability.

    All solvers provide tools for checking and improving accuracy.

    Solution accuracy will depend on the appropriateness of the physical models thatyou choose and the boundary conditions that you specify.

    sorry for lengthy post... sometimes people are lazy when theory is involved...

    January 13, 2012, 11:18 #2

    ChipsgrottelNew Member Charles de LuzanJoin Date: Jun 2010Location: Cincinnati, OHPosts: 11Rep Power: 5


    Originally Posted by Centurion2011 A web-based training module is available to train users in replication ofcase setup and solution data interpolation.

    Hello, and thanks for this long post actually. But what is this web-based training module you are talking about please?Thank you in advance.

    January 18, 2012, 02:31 #3

    Centurion2011Member Join Date: Jul 2011Posts: 39Rep Power: 7

    There are training modules for Ansys, very useful. You can find them all over.

    for example:

    January 19, 2012, 11:53 #4

    wyldckat, Far, Julian K. and 32 others like this.

    ymanoj4 likes this.

    Chipsgrottel likes this.

  • Convergence -- CFD Online Discussion Forums[7/16/2013 9:32:03 AM]

    ChipsgrottelNew Member Charles de LuzanJoin Date: Jun 2010Location: Cincinnati, OHPosts: 11Rep Power: 5

    Thank you very much!I will spend some time on this.

    January 19, 2012, 11:58 Good post #5

    FarSuper Moderator

    Sijal Ahmed Memon( Date: Mar 2009Location: Islamabad PakistanPosts: 3,263Blog Entries: 5Rep Power: 32

    Make it blog and also ask Jola to add this in Fluent Section.

    __________________Best R