Lecture 2 Boundary Conditions & Solver Settings

Express Introductory Training in ANSYS Fluent

Dimitrios Sofialidis Technical Manager, SimTec Ltd.

Mechanical Engineer, PhD

PRACE Autumn School 2013 - Industry Oriented HPC Simulations, September 21-27, University of Ljubljana, Faculty of Mechanical Engineering, Ljubljana, Slovenia

Introduction to ANSYS Fluent

Lecture Theme: Part 1. The problem definition for allBoundary CFD simulations Conditions includes boundary conditions, cell zone conditions and material properties. The accuracy of the simulation results depends on defining these properly.

Learning Aims: You will learn: • How to define material properties. • The different boundary condition types in FLUENT and how to use them. • How to define cell zone conditions in FLUENT including solid zones and porous media. • How to specify well–posed boundary conditions.

Learning Objectives: You will know how to perform these essential steps in setting up a CFD analysis.

Lecture Theme: The problem definition for all CFD simulations includes boundary conditions, cell zone conditions and material properties. The accuracy of the simulation results depends on defining these properly.

Learning Objectives: You will know how to perform these essential steps in setting up a CFD analysis.

• FLUENT provides a standard database of materials and the ability to create a custom user–defined database.

• Your choice of physical models may require multiple materials and dictate which material properties must be defined. – Multiphase (multiple materials). – Combustion (multiple species). – Heat transfer (thermal conductivity). – Radiation (emissivity and absorptivity).

• Material properties can be customized as function of temperature, mass fraction or pressure (density). – Use of other solution variable(s) requires a User–Defined Function (UDF).

Introduction Material Properties Cell Zone Conditions Boundary Conditions Summary © 2012 ANSYS, Inc. September 19, 2013 5 Release 14.5 Materials Databases • FLUENT materials database – Provides access to a number of pre–defined fluid, solid and mixture materials. – Materials can be copied to the case file and edited if required.

• User–Defined material database – Custom databases can be created, accessed and modified from the standard materials panel in FLUENT

Introduction Material Properties Cell Zone Conditions Boundary Conditions Summary © 2012 ANSYS, Inc. September 19, 2013 6 Release 14.5 Fluid Density • For incompressible flow with  = constant. – Select constant for density. • Ideal gas properties – Incompressible flow,  = f(T). • Polynomial or piecewise–polynomial function of temperature.

• Incompressible ideal gas law ( = poperating/RT).

– Set poperating close to the mean pressure in the problem  see Slide 8.

– Compressible flow,  = f(p,T)

• Use ideal–gas for density ( = pabsolute/RT).

– For low–Mach–number flows, set poperating close to mean pressure of the problem to avoid round–off errors. – Use Floating Operating Pressure for unsteady flows with large, gradual changes in absolute pressure (segregated solver only).

Introduction Material Properties Cell Zone Conditions Boundary Conditions Summary © 2012 ANSYS, Inc. September 19, 2013 7 Release 14.5 Options for Defining Common Properties Density Viscosity – Constant. – Constant. – Incompressible Ideal Gas. – Temperature–Dependent1. – Ideal Gas. – Sutherland. – Real Gas (5 Built–in Models). – Power Law. – Temperature Dependent1. – Kinetic Theory. – Boussinesq. – Non–Newtonian (4 Built–in Models). – User–defined. – User–defined. Thermal Conductivity Specific Heat – Constant. – Constant. – Temperature–Dependent1. – Temperature–Dependent1. – Kinetic Theory. – User–defined. – User–defined. 1 Temperature–Dependent options include definition of properties as piecewise linear, polynomial or piecewise polynomial functions temperature.

Introduction Material Properties Cell Zone Conditions Boundary Conditions Summary © 2012 ANSYS, Inc. September 19, 2013 8 Release 14.5 Operating Pressure • Represents the absolute pressure datum from which all relative pressures are measured.

Pabsolute = Poperating + Prelative

– Pressures specified at boundary conditions and initial conditions are relative to the Operating Pressure. • Used to avoid problems with round–off errors which occur when the dynamic pressure differences in a fluid are small compared to the absolute pressure level.

Pref Pressure Pressure

Prel,max=100,001 Pa Prel,max=1 Pa

Prel,min=99,999 Pa Prel,min=-1 Pa

Pref Ex. 2: P = 100,000 Pa Ex. 1: Poperating= 0 Pa operating Introduction Material Properties Cell Zone Conditions Boundary Conditions Summary © 2012 ANSYS, Inc. September 19, 2013 9 Release 14.5 Cell Zones and Boundary Zones

• The mesh consists of a large number of finite volumes, or cells. • The cells are grouped into one or more cell zones. Boundary – For instance in a conjugate heat transfer Face calculation there may be one cell zone for the fluid region and a second cell zone for the solid material. • Each cell is bounded by a number of faces. Cell Simple 3D mesh • These faces are grouped into a number of face zones. Cell zone conditions are • Some of these faces are located on the applied to all cell zones. boundaries of the model. Boundary conditions are • The zones to which such faces belong are applied to all boundary zones. called boundary zones.

• A fluid cell zone, or more simply, a fluid zone, is a group of cells for which all active equations are solved.

e.g. A simulation of a copper heating coil in water e.g. To account for rotational motion, the rotor is will require a fluid zone and a solid zone Using placed in a rotating domain. The rotor fluid zone water properties, the equations of flow and heat will use equations in the rotating frame of transfer will be solved in the fluid zone Using reference. The stator fluid zone will use copper properties, only the heat transfer equation equations in the stationary frame of reference. will be solved in the solid zone.

• Fluid material selection is required – For multiple species or multiphase flows, the material is not shown Instead, the fluid zone consists of the mixture of the phases.

• Optional inputs – Frame/Mesh Motion. – Porous region. – Source terms. – Laminar region. – Fixed Values.

• A porous zone is a special type of fluid zone – Enable "Porous Zone" option in the "Fluid" panel. – Pressure loss in flow determined via user inputs of resistance coefficients to lumped parameter model.

• Used to model flow through porous media and other uniformly distributed flow resistances. – Packed beds. – Filter papers. – Perforated plates. – Flow distributors. – Tube banks.

• Inputs are directional viscous and inertial resistance coefficients.

• A solid zone is a group of cells for which only the heat conduction equation is solved. Flow equations are not solved.

– The only required input is the Material Name (defined in the Materials panel).

– Optional inputs allow you to set volumetric heat generation rate (Heat Source).

– Motion can be defined for a solid zone.

– Rotation axis must be specified if the solid zone is rotating or if rotationally periodic boundaries are adjacent to the solid zone.

• To define a problem that results in a unique solution, you must specify information on the dependent (flow) variables at the domain boundaries. As the governing equations are differential and their solution requires integration, the boundary conditions are the mathematical equivalent of the constant of integration, the value of which is required to gain a unique solution. – Specify fluxes of mass, momentum, energy, etc. into the domain.

• Poorly defined boundary conditions can have a significant impact on your solution (you are solving "another" problem).

• Defining boundary conditions involves: – Identifying types (e.g., inlets, walls, symmetry). – Identifying location. – Supplying required data depending on type, location and physical model.

• Choice depends on: – Geometry. – Availability of data. – Numerical considerations.

• External Boundaries • Internal Boundaries – General. – Fan. • Pressure Inlet. – Interior. • Pressure Outlet. – Porous Jump. – Radiator. – Incompressible . – Wall. • Velocity Inlet. outlet • Outflow (not recommended) . orifice – Compressible. wall • Mass Flow Inlet. • Pressure Far Field.

– Other. • Wall. • Symmetry. • Axis. • Periodic. plate – Special. plate-shadow • Inlet/Outlet Vent. • Intake/Exhaust Fan. inlet

• Zones and zone types are initially defined in the preprocessing phase.

• To change the boundary condition type for a zone: – Choose the zone name in the Zone list. – Select the type you wish to change it to in the Type pull-down list.

Introduction Material Properties Cell Zone Conditions Boundary Conditions Summary © 2012 ANSYS, Inc. September 19, 2013 18 Release 14.5 Setting Boundary Condition Data • Explicitly assign data in BC panels. – To set boundary conditions for particular zone: • Select "Boundary Conditions" in the project tree. • Choose the boundary name in the Zone list. • Click the "Edit…" button.

– Boundary condition data can be copied from one zone to another.

• Boundary conditions can also be defined by User–Defined Functions (UDFs) and profiles. – Profiles can be generated by: • Writing a profile from another CFD simulation. • Creating an appropriately formatted text file with boundary condition data. • See Lecture 11 for details of UDFs. • See Appendix for details of using profiles.

• Velocity Specification Method. – Magnitude, Normal to Boundary. – Components. – Magnitude and Direction. – Turbulence quantities (if applicable). – Thermal conditions (if applicable).

• Applies a uniform velocity profile at the boundary ,unless UDF or profile is used. • Velocity Magnitude input can be negative, implying that you can prescribe the exit velocity.

• Velocity inlets are intended for use in incompressible flows and are not recommended for compressible flows.

Introduction Material Properties Cell Zone Conditions Boundary Conditions Summary © 2012 ANSYS, Inc. September 19, 2013 20 Release 14.5 Pressure Outlet • Required information – Gauge Pressure (static) – static pressure of the environment into which the flow exits. • Specified pressure is ignored if flow is locally supersonic at the outlet.

– Backflow quantities – used as inlet conditions if/when backflow occurs (outlet acts like an inlet).

• Can be used as a "free" boundary in an external or unconfined flow. • Target Mass Flow Rate Option can be applied.

• Suitable for compressible and incompressible flows – Non-reflecting outlet boundary conditions (NRBC) are available for ideal gas (compressible) flow.

• In viscous flows, no–slip condition is applied at walls. – Shear stress can be applied. – Wall roughness can be defined for turbulent flows. • Modification of the Logarithmic Standard Wall Function.

• More information in moving zone and heat transfer presentation.

• Symmetry Boundary. – No inputs are required. – Flow field and geometry must be symmetric: • Zero normal velocity at symmetry plane. • Zero normal gradients of all variables at symmetry plane. • Must take care to correctly define symmetry boundary locations.

Symmetry Planes • Axis Boundary. – Used at the center line for 2d axisymmetric problems. – No user inputs required. – The axis boundary must coincide with the x–axis. Axis

• Used to reduce the overall mesh size.

• Flow field and geometry must contain either rotational or translational periodicity. – Rotational periodicity • ΔP = 0 across periodic planes. • Axis of rotation must be defined in fluid zone. Rotationally – Translational periodicity periodic • ΔP can be finite across periodic planes. planes. • Models fully developed conditions. • Specify either mean ΔP per period or net mass flow rate.

• Periodic boundaries can be either Flow conformal or non–conformal. Translationally – See next two slides. periodic planes.

2D Tube Heat Exchanger.

• Defined on the cell faces only: – Thickness of these internal faces is zero. – These internal faces provide means of introducing step changes in flow properties.

• Used to implement various physical models including: – Fans. – Radiators. – Porous–jump models. • Preferable over porous media for its better convergence behavior. – Interior walls.

• Fluent permits the use of non– conformal rotationally periodic BCs. • Non–conformal periodics do not require a matching mesh on the boundaries. – Coupling of the periodic zones is accomplished using the same algorithms employed in non–conformal interfaces. • Non–conformal periodic can now be created in the Create/Edit Mesh Interfaces GUI! – Select Periodic Boundary Condition option and choose the Type (Translational or Rotational). – Offset is computed automatically, but check this value to make sure it is evenly divisible into 360 deg!

• If possible, select inflow and outflow boundary locations and shapes such that flow either goes in or out normal to the boundaries. – Typically better convergence.

• Should not observe large gradients in direction normal to boundary. – Indicates incorrect set–up. – Move the boundary further upstream or downstream so it is located away from gradients.

• Minimize grid skewness near the boundary. – Introduction of an error.

Introduction Material Properties Cell Zone Conditions Boundary Conditions Summary © 2012 ANSYS, Inc. September 19, 2013 27 Release 14.5 Specifying Well Posed Boundary Conditions • Consider the following case which contains separate air and fuel supply pipes. Air • Three possible approaches in locating inlet boundaries: 1

1 Upstream of manifold. • Can use uniform profiles since natural profiles will develop in the supply pipes. 2 • Requires more elements. 3 2 Nozzle inlet plane. • Requires accurate velocity profile data for the air and fuel. 3 Nozzle outlet plane. Nozzle • Requires accurate velocity 1 Manifold box profile data and accurate profile data for the mixture fractions of air and fuel. Fuel

• When there is 1 Inlet and 1 Outlet:

– Most Robust: Velocity at inlet with static pressure at outlet (Velocity Inlet :: Pressure Outlet). • The inlet total pressure is an implicit result of the prediction.

– Robust: Mass flow rate at inlet with static pressure at outlet (Mass Flow Inlet :: Pressure Outlet). • The total pressure at the inlet will be adjusted to set the given mass flow.

– Sensitive to Initial Guess: Total pressure at inlet with static pressure at outlet (Pressure Inlet :: Pressure Outlet). • The system mass flow is part of the solution.

– Very Unreliable: • Total pressure or mass flow rate at inlet with Outflow boundary at outlet (Pressure Inlet :: Outflow or Mass Flow Inlet :: Outflow). – This combination should not be used, because the static pressure level is not fixed. – Mass Flow Inlet :: Outflow combination is ok if the density is constant. • Velocity at inlet and velocity at outlet – system is numerically unstable.

• Select Profiles in the Boundary Conditions panel (left figure). • After reading the profile, open the panel for the boundary where it is to be applied. • Select the arrow and scroll down in the drop–down list until the desired profile is reached (right figure). – The first three items in the list will usually be the coordinates of the profile variables – do not select these. • Profiles can be created from experimental data by creating an appropriately formatted file. – The file format details are in the User’s Guide. © 2012 ANSYS, Inc. September 19, 2013 30 Release 14.5

Introduction

Lecture Theme: Part 2. The problem definition for allSolver CFD simulations Settings includes boundary conditions, cell zone conditions and material properties. The accuracy of the simulation results depends on defining(Convergence these properly. & Accuracy)

Learning Objectives: You will know how to perform these essential steps in setting up a CFD analysis.

Lecture Theme: Fluent requires inputs (solver settings) which tell it how to calculate the solution. By introducing the concepts of accuracy, stability and convergence, the purpose of each setting can be understood. Emphasis will be placed on convergence, which is critical for the CFD simulation. Learning Aims: You will learn: How to choose the solver and the discretization schemes. How to initialize the solution. How to monitor and judge solution convergence and accuracy.

Learning Objectives: You will be able to choose appropriate solver settings for your CFD simulation and be able to monitor and judge solution convergence.

Introduction Solver Theory Initialization Convergence Summary © 2012 ANSYS, Inc. September 19, 2013 32 Release 14.5 Solution Procedure Overview • The sketch to the right shows the basic workflow for any simulation. • This lecture will look at all the items Set the solution parameters in the chart. – Solution parameters. Initialize the solution • Choosing the solver. • Discretization schemes. Enable the solution monitors of interest – Initialization. – Convergence. Modify solution Calculate a solution • Monitoring convergence. parameters or grid • Stability. – Setting Under–relaxation. Check for convergence – Setting Courant number. – Setting Pseudo–timestep. Yes No • Accelerating convergence. – Accuracy. • Higher Order Numerical Schemes. Check for accuracy No • Appropriateness of BCs. • Grid Independence. Yes • Adaption. Stop Introduction Solver Theory Initialization Convergence Summary © 2012 ANSYS, Inc. September 19, 2013 33 Release 14.5 Available Solvers

• There are two kinds of solvers available in Fluent. • Pressure–based. • Density–based. Pressure–Based Density–Based Segregated Coupled Coupled Implicit Coupled–Explicit

Solve U–Momentum

Solve V–Momentum Solve Mass, Solve Mass, Solve Mass Momentum, Momentum, Solve W–Momentum & Momentum Energy, Energy, Species Species Solve Mass Continuity; Update Velocity

Solve Energy

Solve Species

Solve Turbulence Equation(s)

Solve Other Transport Equations as required

• Pressure–based solvers. Pressure–Based

Segregated Coupled – Velocity field is obtained from the momentum equation. Solve U–Momentum

– Mass conservation (continuity) is achieved by Solve V–Momentum solving a pressure correction equation. Solve Mass • Pressure–velocity coupling algorithms are derived by Solve W–Momentum & Momentum reformatting the continuity equation. Solve Mass • The pressure equation is derived in such a way that Continuity; the velocity field, corrected by the pressure, satisfies Update Velocity continuity.

– Energy equation (where appropriate) is solved Solve Energy sequentially. Solve Species – Additional scalar equations are also solved in a segregated (sequential) fashion. Solve Turbulence Equation(s)

Solve Other Transport Equations as required

• Density–based Solvers (DBS). Density–Based

Coupled Implicit Coupled Explicit – The governing equations of continuity, momentum, and (where appropriate) energy and species transport are solved Solve Mass, Solve Mass, simultaneously (i.e., coupled together). Momentum, Momentum, Energy, Energy, – Additional scalar equations are solved in a Species Species segregated fashion.

– The density–based solver can be run implicit or explicit.

Solve Turbulence Equation(s)

Solve Other Transport Equations as required

• The pressure–based solver (segregated) is applicable for a wide range of flow regimes from low speed incompressible flow to high–speed compressible flow. – Requires less memory (storage) compared to coupled solvers. – Allows flexibility in the solution procedure – damping of all equations separately. – Examples: Good for the majority of day–to–day applications; for convergence issues switch to PBCS or DBCS.

• The pressure–based coupled solver is applicable for most flows, and yields superior performance to the standard (segregated) pressure–based solver.

– Requires 1.5–2 times more memory than the segregated solver. – Examples: More demanding applications where pressure–velocity coupling rules convergence, e.g. high inertia or body forces.

• Pressure–velocity coupling refers to the numerical algorithm which uses a combination of continuity and momentum equations to derive an equation for pressure correction when using the PBS.

• Five algorithms are available in Fluent.

– Semi–Implicit Method for Pressure–Linked Equations (SIMPLE). • The default scheme, robust (memory–efficient).

– Coupled. • Enable the Pressure–based coupled Solver (faster convergence than segregated).

– SIMPLE–Consistent (SIMPLEC). • Allows faster convergence than SIMPLE for simple problems (allow high under–relaxation factors) (e.g., laminar flows with no physical models employed).

– Pressure–Implicit with Splitting of Operators (PISO). • Useful for unsteady flow problems or for meshes containing cells with higher than average skewness.

– Fractional Step Method (FSM) for unsteady flows only. • Used with the NITA scheme; similar characteristics as PISO (used in LES for example).

• Implicit Under–Relaxation Factors (URFs) are used for SIMPLE, SIMPLEC, PISO. – The under–relaxation factor, α, is included to stabilize the iterative process for the pressure–based solver. – The final, converged solution is independent of the under–relaxation factor. • Only the number of iterations required for convergence is dependent (rate of convergence).

• Default settings are suitable for a wide range of problems. – You can reduce the values when necessary (to avoid divergence or convergence difficulties). – Appropriate settings are best learned from experience!

• Note : For the density–based solver, under–relaxation factors for equations outside the coupled set are modified as in the pressure–based solver. Introduction Solver Theory Initialization Convergence Summary © 2012 ANSYS, Inc. September 19, 2013 39 Release 14.5 Pressure–Based Coupled Solver

• Two main options to control convergence: – Piloted by Courant number: default =200. • Can be reduced for more complex physics to 10–50 (multiphase, combustion).

– Pseudo–transient (similar to CFX solver).

Pseudo–transient: Better convergence for meshes with

• Pseudo time step is determined from velocity and domain large aspect ratio size. cells. • User–specified: Characteristic physical time is chosen. Introduction Solver Theory Initialization Convergence Summary © 2012 ANSYS, Inc. September 19, 2013 40 Release 14.5 Pressure–Based Coupled Solver: Convergence

• Pressure based coupled solver with default settings. Rotating propeller 1500 rpm. SIMPLE: ~2250 iterations Coupled: ~120 iterations

– Approximately 2250 iterations of SIMPLE (default) in 3.5 hours. – Approximately 120 iterations of coupled 13 minutes.

• The density–based solver is applicable when there is a strong coupling, or interdependence, between density, energy, momentum, and/or species.

• Density–Based Coupled Implicit. – The implicit option is generally preferred over explicit since explicit has a very strict limit on time scale size (CFL constraint) as implicit does not have. – Examples: High speed compressible flow with combustion, hypersonic flows, shock interactions.

• Density–Based Coupled Explicit. – The explicit approach is used for cases where the characteristic time scale of the flow is on the same order as the acoustic time scale. – Example: propagation of high–Mach shock waves, shock tube problem.

• Field variables (stored at cell centers) must be interpolated to the faces of the control volumes.

• Interpolation schemes for the convection term:

– First–Order Upwind – Easiest to converge, only 1st–order accurate.

– Power Law – More accurate than first–order for flows when Recell < 5 (typically low Re flows).

– Second–Order Upwind – Uses larger stencils for 2nd order accuracy, essential with tri/tet mesh or when flow is not aligned with grid; convergence may be slower.

– Monotone Upstream–Centered Schemes for Conservation Laws (MUSCL) – Locally 3rd order convection discretization scheme for unstructured meshes; more accurate in predicting secondary flows, vortices, forces, etc.

– Quadratic Upwind Interpolation (QUICK) – Applies to quad/hex and hybrid meshes, useful for rotating/swirling flows, 3rd–order accurate on uniform Quad mesh.

Introduction Solver Theory Initialization Convergence Summary © 2012 ANSYS, Inc. September 19, 2013 43 Release 14.5 Effects of Discretization Flow is misaligned Theory RG with mesh. f f  fC0  b fC0 dr0 1 f f dr 0 fC1 0 fC0

1st–Order Upwind • If b = 0 we get the 1st–Order–Upwind convection scheme, Scheme i.e. no correction. b = 0. – This is robust but only 1st–Order accurate. – Sometimes useful for initial runs. 2nd–Order • If b = 1 we get the 2nd–Order–Upwind convection Scheme Scheme, i.e. with correction. b=1.00. – Additional Limiters must be added to guarantee the solution is bounded (fC0

QUICK • The QUICK Resolution scheme 'maximizes' b throughout Resolution the flow domain while keeping the solution bounded. Scheme.

• Interpolation schemes for the diffusive term:

– Always central–differenced & 2nd–order accuracy.

• Fluent requires that all solution variables be initialized before starting iterations. – A realistic initial guess improves solution stability and accelerates convergence. – In some cases a poor initial guess may cause the solver to fail during the first few iterations.

• Five ways to initialize the flow field.

– Standard initialization.

– Patch values.

– Hybrid initialization (solves potential equation).

– FMG initialization (solves Euler equations).

– Starting from a previous solution.

• Standard Initialization – Generally the user selects an inlet boundary under 'Compute from' to automatically fill the initialization values with the values that are specified at the inlet boundary.

• Patch values for individual variables in certain regions. – Free jet flows (high velocity for jet). – Combustion problems (high temperature region to initialize reaction). – Cell registers (created by marking the cells in the Adaption panel) can be used for patching values into various regions of the domain. – Multiphase flows (patch different phase volume fractions in one or more regions). Introduction Solver Theory Initialization Convergence Summary © 2012 ANSYS, Inc. September 19, 2013 47 Release 14.5 Hybrid Initialization

• The default initialization method. • This provides a quick approximation of the flow field, by a collection of methods. • It solves Laplace's equation to determine the velocity and pressure fields.

• All other variables, such as temperature, turbulence, species fractions, volume fractions, etc., will be automatically patched based on domain averaged values or a particular interpolation method.

• Full Multigrid (FMG) Initialization. – Can be used to create a better initialization of the flow field. • FMG Initialization is useful for complex flow problems involving large pressure and velocity gradients on large meshes. – FMG uses the Full Approximation Storage (FAS) Multigrid method to solve the flow problem on a sequence of coarser meshes. • Euler equations are solved with first–order accuracy on the coarse–level meshes.

• To enable FMG initialization, execute the TUI command. /solve/init/fmg–initialization • Settings can be accessed by the TUI command. /solve/init/set–fmg–initialization

• A previously calculated solution can be used as an initial condition when changes are made to the case setup. – Use solution interpolation to initialize a run (especially useful for starting fine–mesh cases when coarse–mesh solutions are available). – Once the solution is initialized, additional iterations always use the current data set as the starting point.

• Sometimes solving a simplified Actual Problem Initial Condition version of the problem first will Heat Transfer Isothermal provide a good initial guess for the Natural convection Low Rayleigh number real problem. Combustion / reacting flow Cold flow (no combustion) Turbulence Inviscid (Euler) solution

• The solver must perform enough iterations to achieve a converged solution • At convergence, the following should be satisfied: – All discrete conservation equations (momentum, energy, etc.) are obeyed in all cells to a specified tolerance (Residual). • The Residual measures the imbalance of the current numerical solution and is related but NOT EQUAL to the numerical error. – Overall mass, momentum, energy, and scalar balances are achieved. – Target quantities reach constant values (in steady state solver). • Integral: e.g. Pressure drop.

• Local: e.g. Velocity at specified position.

Efficiency

Residuals Isentropic

• Monitoring convergence using residual history: – Generally, a decrease in residuals by three orders of magnitude can be a sign of convergence (but not necessarily). – Scaled energy residual should decrease to 10–6 (for the pressure–based solver). – Scaled species residual may need to decrease to 10–5 to achieve species balance.

• Best practice is to also monitor quantitative variables to decide convergence: – Ensure that overall mass/heat/species conservation is satisfied. – Monitor other relevant key variables/physical quantities for confirmation.

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

• 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 defined surface. • These additional monitored quantities are important convergence indicators.

Introduction Solver Theory Initialization Convergence Summary © 2012 ANSYS, Inc. September 19, 2013 54 Release 14.5 Convergence Difficulties • Numerical instabilities can arise with an ill–posed problem, poor–quality mesh and/or inappropriate solver settings. – Exhibited as increasing (diverging) or 'stuck' residuals. – Diverging residuals imply increasing imbalance in conservation equations. – Unconverged results are very misleading! Continuity equation convergence • Troubleshooting. trouble affects convergence of – Ensure that the problem is well–posed. all equations. – Compute an initial solution using a first–order discretization scheme. – For the pressure–based solver, decrease underrelaxation factors for equations having 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! Introduction Solver Theory Initialization Convergence Summary © 2012 ANSYS, Inc. September 19, 2013 55 Release 14.5 Accelerating Convergence

• Convergence can be accelerated by:

– Supplying better initial conditions. • Starting from a previous solution (using file/interpolation when necessary).

– Gradually increasing under–relaxation factors or Courant number. • Excessively high values can lead to solution instability and convergence problems. • You should always save case and data files before continuing iterations. – Starting with a good quality mesh with appropriate mesh resolution. • The orthogonal quality reported in Mesh > Info > Quality should have a minimum value of .01 and an average value that is much higher.

• A converged solution is not necessarily an accurate solution.

– Accuracy depends on: • Order of the discretization schemes (2nd order schemes are recommended). • Mesh resolution. • Boundary Conditions. • Model limitations. • Geometry simplifications. • Precision of the solver (2d/3d or 2ddp/3ddp). • …

• Adapt grid in regions of large pressure gradient to better resolve the sudden pressure rise across the shock.

Large pressure gradient indicating a shock (poor resolution on coarse mesh).

Initial Mesh. Pressure Contours on Initial Mesh. Introduction Solver Theory Initialization Convergence Summary © 2012 ANSYS, Inc. September 19, 2013 58 Release 14.5 2D Planar Shell – Solution on Adapted Mesh

• Solution–based mesh adaption allows better resolution of the bow shock and expansion wave. Adapted cells in locations Mesh adaption yields much–improved of large pressure gradients. resolution of the bow shock.

• Serial.

• Local Parallel. – Shared Memory.

• Distributed Parallel. – Distributed Memory.

• Different communication methods are available (MPICH2, HP MPI, PVM). – See documentation 'When To Use MPI or PVM' for more details, but HP MPI is recommended in most cases. © 2012 ANSYS, Inc. September 19, 2013 60 Release 14.5 Running Simulations in Parallel [2]

• In the Fluent Launcher you can choose Parallel and set the Parameter.

• If you choose Distributed Memory, you have to specify the names of the computers which you want to connect. – You can specify the names directly. – You can specify a file which contains the names.

• For further information see Chapter 34 in User Guide.