Fluent Software Training TRN Solver Settings. Fluent Inc. 2/23/01

Transcription

1 Solver Settings E1

2 Using the Solver Setting Solver Parameters Convergence Definition Monitoring Stability Accelerating Convergence Accuracy Grid Indeendence Adation Aendix: Background Finite Volume Method Exlicit vs. Imlicit Segregated vs. Couled Transient Solutions Outline E2

3 Solution Procedure Overview Solution Parameters Set the solution arameters Choosing the Solver Discretization Schemes Initialize the solution Initialization Convergence Enable the solution monitors of interest Monitoring Convergence Stability Setting Under-relaxation Calculate a solution Modify solution arameters or grid Setting Courant number Check for convergence Accelerating Convergence Accuracy Yes Check for accuracy No Grid Indeendence Adation Yes Sto No E3

4 Choosing a Solver Choices are Couled-Imlicit, Couled-Exlicit, or Segregated (imlicit) The Couled solvers are recommended if a strong inter-deendence exists between density, energy, momentum, and/or secies. e.g., high seed comressible flow or finite-rate reaction modeled flows. In general, the Couled-Imlicit solver is recommended over the couled-exlicit solver. Time required: Imlicit solver runs roughly twice as fast. Memory required: Imlicit solver requires roughly twice as much memory as couledexlicit or segregated-imlicit solvers! (Performance varies.) The Couled-Exlicit solver should only be used for unsteady flows when the characteristic time scale of roblem is on same order as that of the acoustics. e.g., tracking transient shock wave The Segregated (imlicit) solver is referred in all other cases. Lower memory requirements than couled-imlicit solver. Segregated aroach rovides flexibility in solution rocedure. E4

5 Discretization (Interolation Methods) Fluent Software Training Field variables (stored at cell centers) must be interolated to the faces of the control volumes in the FVM: ( ρφ ) t+ t ( ρφ ) t t V + faces ρ f φ f V f A f = faces Γ f ( φ), f A f + S V φ FLUENT offers a number of interolation schemes: First-Order Uwind Scheme easiest to converge, only first order accurate. Power Law Scheme more accurate than first-order for flows when Re cell < 5 (ty. low Re flows). Second-Order Uwind Scheme uses larger stencil for 2nd order accuracy, essential with tri/tet mesh or when flow is not aligned with grid; slower convergence Quadratic Uwind Interolation (QUICK) alies to quad/hex mesh, useful for rotating/swirling flows, 3rd order accurate on uniform mesh. E5

6 Interolation Methods for Pressure Additional interolation otions are available for calculating face ressure when using the segregated solver. FLUENT interolation schemes for Face Pressure: Standard Linear default scheme; reduced accuracy for flows exhibiting large surface-normal ressure gradients near boundaries. useful only when other otions result in convergence difficulties or unhysical behavior. Second-Order use for comressible flows or when PRESTO! cannot be alied. Body Force Weighted use when body forces are large, e.g., high Ra natural convection or highly swirling flows. PRESTO! alies to quad/hex cells; use on highly swirling flows, flows involving orous media, or strongly curved domains. E6

7 Pressure-Velocity Couling Pressure-Velocity Couling refers to the way mass continuity is accounted for when using the segregated solver. Three methods available: SIMPLE default scheme, robust SIMPLEC PISO Allows faster convergence for simle roblems (e.g., laminar flows with no hysical models emloyed). useful for unsteady flow roblems or for meshes containing cells with higher than average skew. E7

8 Initialization Iterative rocedure requires that all solution variables be initialized before calculating a solution. Solve Initialize Initialize... Realistic guesses imroves solution stability and accelerates convergence. In some cases, correct initial guess is required: Examle: high temerature region to initiate chemical reaction. Patch values for individual variables in certain regions. Solve Initialize Patch... Free jet flows (atch high velocity for jet) Combustion roblems (atch high temerature for ignition) E8

9 Convergence Preliminaries: Residuals Transort equation for φ can be resented in simle form: Coefficients a, a nb tyically deend uon the solution. Coefficients udated each iteration. At the start of each iteration, the above equality will not hold. The imbalance is called the residual, R, where: R = a φ + a φ a φ + a φ = nb nb nb nb nb b nb b R should become negligible as iterations increase. The residuals that you monitor are summed over all cells: By default, the monitored residuals are scaled. You can also normalize the residuals. R = Residuals monitored for the couled solver are based on the rms value of the time rate of change of the conserved variable. Only for couled equations; additional scalar equations use segregated definition. cells R E9

10 Convergence At convergence: All discrete conservation equations (momentum, energy, etc.) are obeyed in all cells to a secified tolerance. Solution no longer changes with more iterations. Overall mass, momentum, energy, and scalar balances are obtained. Monitoring convergence with residuals: Generally, a decrease in residuals by 3 orders of magnitude indicates at least qualitative convergence. Major flow features established. Scaled energy residual must decrease to 10-6 for segregated solver. Scaled secies residual may need to decrease to 10-5 to achieve secies balance. Monitoring quantitative convergence: Monitor other variables for changes. Ensure that roerty conservation is satisfied. E10

11 Convergence Monitors: Residuals Residual lots show when the residual values have reached the secified tolerance. Solve Monitors Residual... All equations converged E11

12 Convergence Monitors: Forces/Surfaces In addition to residuals, you can also monitor: Lift, drag, or moment Solve Monitors Force... Variables or functions (e.g., surface integrals) at a boundary or any defined surface: Solve Monitors Surface... E12

13 Checking for Proerty Conservation In addition to monitoring residual and variable histories, you should also check for overall heat and mass balances. Net imbalance should be less than 0.1% of net flux through domain. Reort Fluxes... E13

14 Decreasing the Convergence Tolerance If your monitors indicate that the solution is converged, but the solution is still changing or has a large mass/heat imbalance: Reduce Convergence Criterion or disable Check Convergence. Then calculate until solution converges to the new tolerance. E14

15 Convergence Difficulties Numerical instabilities can arise with an ill-osed roblem, oor quality mesh, and/or inaroriate solver settings. Exhibited as increasing (diverging) or stuck residuals. Diverging residuals imly increasing imbalance in conservation equations. Unconverged results can be misleading! Troubleshooting: Ensure roblem is well osed. Comute an initial solution with a first-order discretization scheme. Decrease under-relaxation for equations having convergence trouble (segregated). Reduce Courant number (couled). Re-mesh or refine grid with high asect ratio or highly skewed cells. Continuity equation convergence trouble affects convergence of all equations. E15

16 Modifying Under-relaxation Factors Under-relaxation factor, α, is included to stabilize the iterative rocess for the segregated solver. φ = φ, old + α φ Use default under-relaxation factors to start a calculation. Solve Controls Solution... Decreasing under-relaxation for momentum often aids convergence. Default settings are aggressive but suitable for wide range of roblems. Aroriate settings best learned from exerience. For couled solvers, under-relaxation factors for equations outside couled set are modified as in segregated solver. E16

17 Modifying the Courant Number Courant number defines a time ste size for steady-state roblems. A transient term is included in the couled solver even for steady state roblems. For couled-exlicit solver: Stability constraints imose a maximum limit on Courant number. Cannot be greater than 2. Default value is 1. Reduce Courant number when having difficulty converging. For couled-imlicit solver: Courant number is not limited by stability constraints. t = (CFL) x u Default is set to 5. E17

18 Accelerating Convergence Convergence can be accelerated by: Sulying good initial conditions Starting from a revious solution. Increasing under-relaxation factors or Courant number Excessively high values can lead to instabilities. Recommend saving case and data files before continuing iterations. Controlling multigrid solver settings. Default settings define robust Multigrid solver and tyically do not need to be changed. E18

19 Starting from a Previous Solution Previous solution can be used as an initial condition when changes are made to roblem definition. Once initialized, additional iterations uses current data set as starting oint. Actual Problem flow with heat transfer natural convection combustion turbulent flow Initial Condition isothermal solution lower Ra solution cold flow solution Euler solution E19

20 Multigrid The Multigrid solver accelerates convergence by using solution on coarse mesh as starting oint for solution on finer mesh. Influence of boundaries and far-away oints are more easily transmitted to interior of coarse mesh than on fine mesh. Coarse mesh defined from original mesh. fine (original) mesh Multile coarse mesh levels can be created. AMG- coarse mesh emulated algebraically. FAS- cell coalescing defines new grid. a couled-exlicit solver otion Final solution is for original mesh. Multigrid oerates automatically in the background. Accelerates convergence for roblems with: Large number of cells Large cell asect ratios, e.g., x/ y > 20 Large differences in thermal conductivity solution transfer coarse mesh E20

21 Accuracy A converged solution is not necessarily an accurate one. Solve using 2nd order discretization. Ensure that solution is grid-indeendent. Use adation to modify grid. If flow features do not seem reasonable: Reconsider hysical models and boundary conditions. Examine grid and re-mesh. E21

22 Mesh Quality and Solution Accuracy Numerical errors are associated with calculation of cell gradients and cell face interolations. These errors can be contained: Use higher order discretization schemes. Attemt to align grid with flow. Refine the mesh. Sufficient mesh density is necessary to resolve salient features of flow. Interolation errors decrease with decreasing cell size. Minimize variations in cell size. Truncation error is minimized in a uniform mesh. Fluent rovides caability to adat mesh based on cell size variation. Minimize cell skewness and asect ratio. In general, avoid asect ratios higher than 5:1. Otimal quad/hex cells have bounded angles of 90 degrees Otimal tri/tet cells are equilateral. E22

23 Determining Grid Indeendence When solution no longer changes with further grid refinement, you have a grid-indeendent solution. Procedure: Obtain new grid: Adat Save original mesh before adating. If you know where large gradients are exected, concentrate the original grid in that region, e.g., boundary layer. Adat grid. Data from original grid is automatically interolated to finer grid. file reread-grid and File Interolate... Imort new mesh and initialize with old solution. Continue calculation to convergence. Comare results obtained w/different grids. Reeat adation/calculation rocedure if necessary. E23

24 Unsteady Flow Problems Transient solutions are ossible with both segregated and couled solvers. Solver iterates to convergence at each time level, then advances automatically. Solution Initialization rovides initial condition, must be realistic. For segregated solver: Time ste size, t, is inut in Iterate anel. t should be small enough to resolve time deendent features and to ensure convergence within 20 iterations. May need to start solution with small t. Number of time stes, N, is also required. N* t = total simulated time. Use TUI command it # to iterate without advancing time ste. For Couled Solver, Courant number defines in ractice: global time ste size for couled exlicit solver. seudo-time ste size for couled imlicit solver. E24

25 Summary Solution rocedure for the segregated and couled solvers is the same: Calculate until you get a converged solution. Obtain second-order solution (recommended). Refine grid and recalculate until grid-indeendent solution is obtained. All solvers rovide tools for judging and imroving convergence and ensuring stability. All solvers rovide tools for checking and imroving accuracy. Solution accuracy will deend on the aroriateness of the hysical models that you choose and the boundary conditions that you secify. E25

26 Aendix Background Finite Volume Method Exlicit vs. Imlicit Segregated vs. Couled Transient Solutions E26

27 Background: Finite Volume Method - 1 FLUENT solvers are based on the finite volume method. Domain is discretized into a finite set of control volumes or cells. General transort equation for mass, momentum, energy, etc. is alied to each cell and discretized. For cell, t V ρφdv + A ρφv da = A Γ φ da + S φ dv unsteady convection diffusion generation Eqn. continuity f 1 x-mom. u y-mom. v energy h control volume Fluid region of ie flow discretized into finite set of control volumes (mesh). All equations are solved to render flow field. E27

28 Background: Finite Volume Method - 2 Each transort equation is discretized into algebraic form. For cell, ( ρφ ) t+ t t ( ρφ ) t V + faces ρ f φ f face f cell adjacent cells, nb Discretized equations require information at cell centers and faces. Field data (material roerties, velocities, etc.) are stored at cell centers. Face values can be exressed in terms of local and adjacent cell values. Discretization accuracy deends uon stencil size. The discretized equation can be exressed simly as: V f A a φ + a φ = b f = faces nb Γ f ( φ) Equation is written out for every control volume in domain resulting in an equation set. nb nb, f A f + S V φ E28

29 Background: Linearization Equation sets are solved iteratively. Coefficients a and a nb are tyically functions of solution variables (nonlinear and couled). Coefficients are written to use values of solution variables from revious iteration. Linearization: removing coefficients deendencies on φ. De-couling: removing coefficients deendencies on other solution variables. Coefficients are udated with each iteration. For a given iteration, coefficients are constant. φ can either be solved exlicitly or imlicitly. a φ + a φ = b nb nb nb E29

30 Background: Exlicit vs. Imlicit Assumtions are made about the knowledge of φ nb : Exlicit linearization - unknown value in each cell comuted from relations that include only existing values (φ nb assumed known from revious iteration). φ solved exlicitly using Runge-Kutta scheme. Imlicit linearization - φ and φ nb are assumed unknown and are solved using linear equation techniques. Equations that are imlicitly linearized tend to have less restrictive stability requirements. The equation set is solved simultaneously using a second iterative loo (e.g., oint Gauss-Seidel). E30

31 Background: Couled vs. Segregated Segregated Solver If the only unknowns in a given equation are assumed to be for a single variable, then the equation set can be solved without regard for the solution of other variables. coefficients a and a nb are scalars. Couled Solver If more than one variable is unknown in each equation, and each variable is defined by its own transort equation, then the equation set is couled together. coefficients a and a nb are N eq x N eq matrices a φ + a φ = b φ is a vector of the deendent variables, {, u, v, w, T, Y} T nb nb nb E31

32 Background: Segregated Solver In the segregated solver, each equation is solved searately. The continuity equation takes the form of a ressure correction equation as art of SIMPLE algorithm. Under-relaxation factors are included in the discretized equations. Included to imrove stability of iterative rocess. Under-relaxation factor, α, in effect, limits change in variable from one iteration to next: φ = φ, old + α φ Udate roerties. Solve momentum equations (u, v, w velocity). Solve ressure-correction (continuity) equation. Udate ressure, face mass flow rate. Solve energy, secies, turbulence, and other scalar equations. No Converged? Yes Sto E32

33 Background: Couled Solver Continuity, momentum, energy, and secies are solved simultaneously in the couled solver. Equations are modified to resolve comressible and incomressible flow. Transient term is always included. Steady-state solution is formed as time increases and transients tend to zero. For steady-state roblem, time ste is defined by Courant number. Stability issues limit maximum time ste size for exlicit solver but not for imlicit solver. CFL) x t = where u Solve continuity, momentum, energy, and secies equations simultaneously. Solve turbulence and other scalar equations. No Udate roerties. Converged? Yes Sto ( CFL = Courant-Friedrichs-Lewy-number u = aroriate velocity scale x = grid sacing E33

34 Background: Segregated/Transient Transient solutions are ossible with both segregated and couled solvers. 1st- and 2nd-order time imlicit discretizations (Euler) available for couled and segregated solvers. Procedure: Iterate to convergence at each time level, then advance in time. 2nd order time-exlicit discretization also available for couled-exlicit solver. For segregated solver: Time ste size, t, is inut in Iterate anel. t should be small enough to resolve time deendent features. Number of time stes, N, is also required. N* t equals total simulated time. Generally, use t small enough to ensure convergence within 20 iterations. Note: Use TUI command it # to iterate further without advancing time ste. E34

35 Background: Couled/Transient If imlicit scheme is selected, two transient terms are included in discretization. Physical-time transient Physical-time derivative term is discretized imlicitly (1st or 2nd order). Time ste size, t, defined as with segregated solver. Pseudo-time transient At each hysical-time level, a seudo-time transient is driven to zero through a series of inner iterations (dual time steing). Pseudo-time derivative term is discretized: exlicitly in couled-exlicit solver. imlicitly in couled-imlicit solver. Courant number defines seudo-time ste size, τ. For exlicit time steing, hysical-time derivative is discretized exlicitly. Otion only available with couled-exlicit solver Physical-time ste size is defined by Courant number. Same time ste size is used throughout domain (global time steing). E35