Coupling Momentum and Continuity Increases CFD Robutness

The FLUENT computational fluiddynamics (CFD) solver has undergoneextensive development to extend itsrobustness and accuracy for a widerange of flow regimes. Since its initial release, the FLUENT solver has provided two basic solver algorithms:The first is a density-based coupledsolver (DBCS) that uses the solution ofthe coupled system of fluid dynamics equations (continuity, momentum andenergy); the second is a pressure-basedalgorithm that solves the equations in asegregated or uncoupled manner. Thesegregated pressure-based algorithmhas proven to be both robust and versatile, and has been utilized in concert with a wide range of physical models, including multiphase flows,conjugate heat transfer and combus-tion. However, there are applications inwhich the convergence rate of the segregated algorithm is not satisfactory,generally due to the need in these scenarios for coupling between the continuity and momentum equations.Situations in which equation couplingcan be an issue include rotating machin-ery flows and internal flows in complexgeometries.Coupling Momentum and ContinuityIncreasesCFD Robustness FLUENT technology introduces a pressure-based coupled solver to reduce computation time for low-speed compressible and incompressible flow applications.By Franklyn J. Kelecy, Applications Specialist, ANSYS, Inc.Figure 1.Flowchart illustrating FLUENT solver algorithmsInitializeSegregatedPressure-BasedSolverPBCSDBCSBegin LoopSolver?RepeatExit LoopCheck ConvergenceUpdate PropertiesSolve U-MomentumSolve EnergySolve SpeciesSolve TurbulenceSolve Other TransportEquations as RequiredSolve Mass &MomentumSolve Mass,Momentum,Energy &SpeciesSolve V-MomentumSolve W-MomentumSolve Mass Continuity;Update VelocityThe ANSYS CFX solver relies on a pressure-based coupled solverapproach to achieve robust conver-gence rates. ANSYS now offers asimilar pressure-based coupled solver(PBCS) for the first time with version6.3 of the FLUENT software. As itsname implies, the algorithm solves thecontinuity and momentum equations ina coupled fashion, thereby eliminatingtheapproximations associated with a

segregated solution approach wherethe momentum and continuity equa-tions are solved separately. Whilethese approximations do not affectsolution accuracy at convergence,they can hamper the convergence ratefor certain classes of problems. With the coupled approach,removing theapproximationsdue to isolating theequations permitsthe dependence ofthe momentum and continuity on each

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TIPS & TRICKSFigure 3.Solution controls for the pressure-based coupled solverotherto befelt more directly. Thisleads toa more rapid and monotonicconvergencerate and hencefastersolution times.In addition, the couplingleads to improved robustness such thaterrors associated with initial conditions,nonlinearities in the physical models,and stretched and skewed meshes donot affect the stability of the iterativesolution process as much as with segregated algorithms.The coupledalgorithmcanalso be used with awide range of physical models such asreacting flows, porous media, and manymultiphase models, including volume offluid (VOF) models.Algorithm OverviewA flowchart illustrating the pressure-based and density-based solveralgorithms is shown in Figure 1. This diagram depicts the process by whichthe pressure-based, segregated algo-rithm solves the momentum equations,for the unknown velocity componentsone at a time, as scalar equations andthen solves a separate equation formass continuity and pressure. The pressure solution is used to correct the velocities such that continuity is satisfied. When the flow equations arecoupled together, the coefficients that are computed for each equationFigure 2.Selection of solver algorithms reflected in theDefine󰀁Models󰀁Solver GUI (This panel was introducedas new in FLUENT 6.3.)contain dependent variables from theother equations. In the segregated algorithm, these variables are suppliedsimply by using previously computedvalues, which introduces a decouplingerror. The decoupling error can delayconvergence in cases in which strongpressure–velocity coupling exists.The pressure-based coupledsolver differs from the segregatedalgorithm in that the continuity andmomentum equations are solved in afully coupled fashion. That is, a singlematrix equation is solved in which thedependent variable is now a solutionvector containing the unknownvelocities and pressures. This is similar to the density-based implicitsolver, except that the density-basedsolver also includes the energy equation in the coupled system andemploys a different discretization ofthe flux terms, among other differ-ences. The tradeoff with respect tocomputational resources is that thePBCS requires about twice the memory per cell as the segregatedalgorithm. This is due to the storagerequired for the coupled (matrix)equations. In general, the storagerequirements are comparable to,though slightly less than, the density-based implicit algorithm.