Outline
Using the Solver (solution procedure overview)
– Setting Solver Parameters
– Convergence
Definition
Monitoring
Stability
Accelerating Convergence
– Accuracy
Grid Independence
Grid Adaption
– Unsteady Flow Modeling (covered in a later lecture)
Unsteady-flow problem setup
Unsteady flow modeling options
– Summary
– Appendix
Solution Procedure Overview
Solution parameters
– Choosing the solver
– Discretization schemes
Initialization
Convergence
– Monitoring convergence
– Stability
Setting Under-relaxation
Setting Courant number
– Accelerating convergence
Accuracy
– Grid Independence
– Adaption
Available Solvers
There are two kinds of solvers available in FLUENT – Pressure based and Density based.
The pressure-based solvers take momentum and pressure (or pressure correction) as the primary variables.
– Pressure-velocity coupling algorithms are derived by reformatting the continuity equation
Two algorithms are available with the pressure-based solvers:
– Segregated solver – Solves for pressure correction and momentum sequentially.
– Coupled Solver (PBCS) – Solves pressure and momentum simultaneously.
Density-Based Coupled Solver
– Equations for continuity, momentum, energy and species (if required) are solved in vector form.
– Pressure is obtained through an equation of state.
– Additional scalar equations are solved in a segregated fashion.
The DBCS can be run either explicit or implicit.
– Implicit – Uses a point-implicit Gauss-Seidel / symmetric block Gauss-Seidel / ILU method to solve for variables.
– Explicit: uses a multi-step Runge-Kutta explicit time integration method
Choosing a Solver
The pressure-based solver is applicable for a wide range of flow regimes from low speed incompressible flow to high-speed compressible flow.
– Requires less memory (storage).
– Allows flexibility in the solution procedure.
The pressure-based coupled solver (PBCS) is applicable for most single phase flows, and yields superior performance to the standard pressure-based solver.
– Not available for multiphase (Eulerian), periodic mass-flow and NITA cases.
– Requires 1.5–2 times more memory than the segregated solver.
The density-based coupled solver (DBCS) is applicable when there is a strong coupling, or interdependence, between density, energy, momentum, and/or species.
– Examples: High speed compressible flow with combustion, hypersonic flows, shock interactions.
The implicit option is generally preferred over explicit since it has a very strict limit on time step size
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. (e.g.: propagation of high-Ma shock waves).
Discretization (Interpolation Methods)
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 first-order accurate.
– Power Law – More accurate than first-order for flows when Recell < 5 (typ. 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 mesh.
Interpolation Methods (Gradients)
Gradients of solution variables are required in order to evaluate diffusive fluxes, velocity derivatives, and for higher-order discretization schemes.
The gradients of solution variables at cell centers can be determined using three approaches:
– Green-Gauss Cell-Based – The default method; solution may have false diffusion (smearing of the solution fields).
– Green-Gauss Node-Based – More accurate; minimizes false diffusion; recommended for tri/tet meshes.
– Least-Squares Cell-Based – Recommended for polyhedral meshes; has the same accuracy and properties as Node-based Gradients.
Gradients of solution variables at faces computed using multi-dimensional Taylor series expansion.
Interpolation Methods for Pressure
Interpolation schemes for calculating cell-face pressures when using the segregated solver in FLUENT are available as follows:
– Standard – The default scheme; reduced accuracy for flows exhibiting large surface-normal pressure gradients near boundaries (but should not be used when steep pressure changes are present in the flow – PRESTO! scheme should be used instead.)
– PRESTO! – Use for highly swirling flows, flows involving steep pressure gradients (porous media, fan model, etc.), or in strongly curved domains
– Linear – Use when other options result in convergence difficulties or unphysical behavior
– Second-Order – Use for compressible flows; not to be used with porous media, jump, fans, etc. or VOF/Mixture multiphase models
– Body Force Weighted – Use when body forces are large, e.g., high Ra natural convection or highly swirling flows
http://www.cadfamily.com/html/Article/Introductory%20FLUENT%20Training-Solver%20Settings_863_1.htm
http://www.cadfamily.com/html/Article/Introductory%20FLUENT%20Training-Solver%20Settings_863_2.htm
http://www.cadfamily.com/html/Article/Introductory%20FLUENT%20Training-Solver%20Settings_863_3.htm
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