Coupled Flow Solvers Reference

For the Coupled Flow model, the conservation equations for continuity and momentum are solved in a coupled manner, that is, they are solved simultaneously as a vector of equations.

The velocity field is obtained from the momentum equations. From the continuity equation, the pressure is calculated and the density is evaluated from the equation of state. The coupled system of equations is solved by either the implicit or the explicit time-integration scheme.

The following solvers and solver options are available for the implicit scheme:

Coupled Implicit

AMG Linear Solver

Expert Initialization

Convergence Accelerator

The following solvers and solver options are available for the explicit scheme:

Coupled Explicit

Courant Number Ramp

Click on any link to see the available properties for each solver or solver option.

Coupled Implicit

The Coupled Implicit solver controls the solution update for the Coupled Flow model. If the Coupled Energy model and the Coupled or Segregated Species models are activated, the Coupled Implicit solver controls these models also. The solver is used for implicit spatial integration in both steady and unsteady analyses, using a coupled algebraic multi-grid method.

The following properties are available for the Coupled Implicit solver:

CFL Control Method

Specifies the method for controlling the CFL number in Eqn. (968) that controls the local time-step of the time-marching procedure.


Method	Corresponding Method Node
Automatic The default for steady time. Adjusts the CFL number in response to AMG solver convergence behavior to maintain the specified target number of cycles. It targets a balance between the cost of forming the linear system and the cost of solving it.	Automatic CFL Because the automatic CFL control number operates by interactions with the AMG solver, changes to AMG settings affect the CFL behavior. Any modification that makes the AMG solver do more work per cycle, and hence tends to solve the same linear system in fewer cycles, generally drives the CFL number higher. If your simulations require tighter AMG convergence tolerance, consider increasing the Target AMG Cycles. The default of 4 target cycles is based on default AMG settings and convergence tolerance of 0.1. If you must use a convergence tolerance of 0.01, you are advised to set Target AMG Cycles to 6 or 7. Has the following properties: Current CFL The present value of the CFL number. (Read only.) Initial CFL The CFL number value before automatic control begins. Minimum CFL The smallest allowed CFL number value. Maximum CFL The largest allowed CFL number value. Target AMG Cycles Controls the target number of AMG cycles when Automatic CFL is on. Because the CPU and GPU AMG solvers have different characteristics (such as convergence rates per cycle) on which the automatic CFL control number is based, this value is internally adjusted in GPU mode to match the characteristics of the GPU AMG solver. The target on the GPU is 50% higher than the CPU. Thus, for a default setting of 4, the applied target is 4 on the CPU and 6 on the GPU.
Constant Controls the CFL number by using a constant value. For unsteady flow, the default value is a CFL number of 50.0.	Constant CFL Specifies a Constant CFL number.
Expert Driver Activates the Expert Driver, an automatic convergence control for steady-state simulations.	Expert Driver CFL Has the following properties: Current CFL The present value of the CFL number. (Read only.) Target CFL The CFL number value when ramping ends. Initial CFL The CFL number value before the ramping begins. Ramp: Start Iteration Specifies the iteration at which ramping begins. Ramp: End Iteration Specifies the iteration at which ramping ends. CFL Recovery Rate When the AMG Linear Solver fails to converge, the CFL number is reduced. The Expert Driver can reduce the impact of this reduction by helping to recover the CFL number back to its desired ramp or target value. Specifies the rate of recovery to the desired value. Target AMG Cycles Controls CFL reduction. If the solver reduces the CFL number (when the AMG linear solver did not converge) and the number of AMG cycles (during the CFL recovery period) is larger than the specified optimal (or target) number of AMG cycles, the CFL number is additionally reduced (by 10% at a time).
Linear Ramp Controls the CFL number by using a linear ramp.	Linear Ramp CFL Has the following properties: Current CFL The present value of the CFL number. (Read only.) Target CFL The value of the CFL number when the ramping ends. Initial CFL The value of the CFL number before the ramping starts. Start Iteration Specifies the iteration on which to begin ramping, typically 1. End Iteration Specifies the iteration at which ramping ends, typically within the first 10–100 iterations.

Enhanced Dissipation

When On, significantly improves the convergence and robustness of the Coupled solver during the initial stages of a simulation. The increased numerical dissipation that it provides can lead to inaccuracies in the flow solution. Enhanced Dissipation is available for incompressible flows only. When the simulation reaches the iteration count set by Enhanced Dissipation Start Transition, the solver starts to reduce the amount of extra dissipation. The smooth non-linear reduction continues until the simulation reaches the iteration count set by Enhanced Dissipation End Transition. At this point, the extra dissipation is removed completely. The default is Off.

Enhanced Dissipation Start Transition

Sets the iteration at which the solver begins to reduce the amount of extra dissipation. The default value is 1.

Enhanced Dissipation End Transition

By the iteration set in this property, no extra dissipation is included. The default value is 100.

Explicit Relaxation Method

Explicit relaxation is a scaling factor that is used to relax all coupled flow corrections explicitly before they are applied to the flow solution, also known as a damped update. (See Eqn. (960).) This generally improves numerical stability and convergence, particularly when running at a high CFL number. For the unsteady solver, the default is None, as time-accurate integration usually provides sufficient stability. For the steady solver, the default is 0.3.


Method	Corresponding Method Node
Constant Controls explicit relaxation using a constant value.	Constant Relaxation Explicit Relaxation values should almost always be between 0.15 and 1.0. The default value of 0.3 generally provides a good balance between efficiency and robustness in conjunction with the typically high CFL number values of the automatic CFL method.
Line Search Controls explicit relaxation by performing a line search.	Line Search Automatically computes a value for the scaling factor by solving for the constrained minimization of the residual bounded between the Minimum Explicit Relaxation and Maximum Explicit Relaxation inputs. As this method incurs high computational cost, it is only performed once every N iterations, where N is the Update Frequency, unless a large residual increase is detected, in which case it executes automatically. For additional output on the automatic explicit relaxation factor calculation, you activate Verbose.
None No scaling factor is used. This is equivalent to an explicit relaxation factor of 1.	None.

Freeze Flow

When On, deactivates the flow solver solution update. The default is Off.

Pressure Reference Location

Provides a choice between using the automatic algorithm of Simcenter STAR-CCM+ for the pressure reference location or providing it manually. For more information, see Setting Reference Values.


Method	Corresponding Method Node
Automatic Selection Simcenter STAR-CCM+ sets the reference location at the cell that is next to the boundary face with the smallest X, Y, Z location in the domain.	None.
User Specified Allows to add one or more reference locations depending on the number of non-contiguous regions.	Pressure Reference Points Right-click this node to add a reference point. For each reference point, specifies the following properties: Point Coordinates: Specifies the geometric location of the pressure reference point in the selected coordinate system. Reference System: Specifies the coordinate system for defining the point coordinates. Enabled: When On, the solver uses the pressure reference point for finding the reference cell.

Reconstruction Frozen

When On, Simcenter STAR-CCM+ does not update reconstruction gradients with each iteration, but rather uses gradients from the last iteration in which they were updated. Activate Temporary Storage Retained in conjunction with this property. This property is Off by default.

Reconstruction Zeroed

When On, the solver sets reconstruction gradients to zero at the next iteration. This action means that face values used for upwinding (Eqn. (905)) and for computing cell gradients (Eqn. (917) and Eqn. (918)) become first-order estimates. This property is Off by default. If you turn this property Off after having it On, the solver recomputes the gradients on the next iteration.

Temporary Storage Retained

When On, Simcenter STAR-CCM+ retains additional field data that the solver generates during an iteration. The particular data retained depends on the solver, and becomes available as field functions during subsequent iterations. Off by default.

Unsteady Optimization Tolerance

The level of numerical optimization based on the reduction of the continuity residual. Allowed values range from 1 to 0. A value of 1 indicates the highest tolerance, thus enabling maximum optimization. A value of zero disables automatic numerical optimization. The default is 1 for new simulations, but 0 for simulations created before the introduction of this property, that is, created in Simcenter STAR-CCM+ 14.04 or earlier.

Velocity Correction Limiting

When On, the default, limits the maximum change in flow velocity allowed in a single iteration to a factor of 0.2. The On (Verbose) option reports the amount of limiting.

Expert Initialization

The grid-sequencing (GS) expert initialization performs the normal initialization followed by the computation of an approximate inviscid solution to the flow problem. It initializes flow variables (such as pressure, velocity, and temperature) and species (for mixtures of gases). GS is not available as an expert initialization method for simulation of heat conduction in solids.

During initialization, GS performs the following steps (this applies to initializing manually or starting a simulation run):

A series of coarse meshes is generated.
Normal initialization of the flow solution is performed on each of the coarse meshes.
Starting with the coarsest mesh:
- A number of iterations are run to compute an approximate solution on the current mesh.
- If either convergence or the maximum number of iterations is reached, the solution is interpolated on the next finer mesh and (unless the next mesh is the finest), the previous step is repeated.
The process stops when GS has reached the finest mesh level.

GS uses a full implicit incomplete-Newton solution algorithm to compute a first-order inviscid flow solution, which has the following advantages:

Increased robustness, due to the full implicit algorithm.
Faster convergence, due to relatively large CFL numbers that can be used.
Fully automatic coarse-mesh generation and solution.
An inviscid solution that is a much better approximation of the flow solution than that obtained through normal initialization.
Faster and more robust convergence of the flow solution, after GS initialization.


Method	Corresponding Method Node
None Deactivates grid sequencing.	None.
Grid Sequencing Activates grid sequencing.	Grid Sequencing Specifies the following properties: Maximum Grid Levels Number of coarse grid levels, created automatically, which the grid-sequencing (GS) algorithm uses to compute inviscid solutions, starting from the coarsest mesh. Maximum Iterations per Level Number of solver iterations that are performed during GS, to compute an approximate inviscid solution of the flow problem, on the current coarse mesh. Convergence Tolerance per Level Solution convergence criterion which, together with the maximum number of iterations per level, the solver uses to stop cycling on the current mesh level. CFL Number Courant-Friedrichs-Levy (CFL) number that the flow solver uses during the grid-sequencing initialization. This number can be different from the Courant number that the solver uses during iterations on the finest mesh (normal run).

Convergence Accelerator

The Continuity Convergence Accelerator (CCA) formulates and solves a pressure-correction equation using the Density-based/Riemann flux discretization. The solution of this additional equation provides updates for pressure, velocity, and other flow field variables in such a way that the overall and individual cell mass imbalances are minimized at each iteration.

For the Continuity Convergence Accelerator, you can set an Under-Relaxation Factor Ramp and AMG Linear Solver parameters.

Method

Corresponding Method Node

None

Deactivates the Continuity Convergence Accelerator.

None.

Continuity Convergence Accelerator

Activates the Continuity Convergence Accelerator.

Continuity Convergence Accelerator

Specifies the following properties:

Enhanced Stability Treatment

When On, activates the Bounded Velocity Corrections and the Enhanced Mass-Imbalance Calculations properties. Sets the AMG Acceleration Method to None. The default is Off.

Note	Switching from On back to Off does not restore the other properties to their defaults. They must be reset individually if required.

Verbose

When On, provides more output for this value while the simulation is running. This property is useful for debugging problems when they occur.

Convergence Accelerator Update Frequency

The iteration frequency at which the Continuity Convergence Accelerator is invoked. The default value is 1, meaning that the Continuity Convergence Accelerator is invoked at each iteration.

Under-Relaxation Factor

ω

in Eqn. (974). The default value is 0.1.

CCA Start Iteration, CCA Cutoff Iteration

Automatically activates and deactivates the Continuity Convergence Accelerator at the respective iteration.

Frozen

When On, prevents the Continuity Convergence Accelerator from updating the solution while iterating.

Bounded Velocity Corrections

When On, makes bounded velocity corrections and therefore limits the pressure correction gradient in the formula for velocity correction, Eqn. (976). This ensures that velocity corrections are “smooth,” providing bounded velocity updates.

Enhanced Mass-Imbalance Calculations

When On, calculates the final cell mass balances in step 6 of the Continuity Convergence Accelerator Algorithm using the Riemann solver fluxes depending on the flux scheme (see Eqn. (956) or Eqn. (959)). This option is more accurate, at the expense of computational cost. When Off, only corrects the mass flux. See Eqn. (936). This option is sufficient in most cases and is the default.

Minimum Pressure-Correction Scaling

Minimum value for additional pressure-correction scaling in the presence of strong initial transients, large pressure changes, or rotational motion. The default is 0.1

Pressure Reference Location

Provides a choice between using the automatic algorithm of Simcenter STAR-CCM+ for the reference location or providing it manually.


Method	Corresponding Method Node
Automatic Selection Simcenter STAR-CCM+ sets the reference location at the cell that is next to the boundary face with the smallest X, Y, Z location in the domain.	None.
User Specified Allows to add one or more reference locations depending on the number of non-contiguous regions.	Pressure Reference Points For each reference point, the following properties are available: Point Coordinates: Specifies the coordinates of the pressure reference point. Reference System: Specifies the coordinate system for the point coordinates. Enabled: When On, the pressure reference point is used.

Coupled Explicit

The Coupled Explicit solver controls the solution update for the Coupled Flow model and the Coupled Energy model. It is used for explicit integration using a Runge-Kutta multi-stage time-stepping scheme.

The following properties are available for the Coupled Explicit solver:

Courant Number: Controls the local time-step at each iteration according to Eqn. (960). The default Courant number is 1 for both unsteady and steady flows. However, for steady analysis, a value of 2 can often be used with two residual smoothing iterations. This restriction is much more severe than the implicit spatial integration scheme, although much less storage is required for the same size problem.
Dissipation-stage Flags: Indicates the stages of the multi-stage scheme on which dissipation (and viscous fluxes if appropriate) is evaluated. The number of these flags must be the same as the number of stages in the multi-stage coefficients.
Freeze Flow: As for Coupled Implicit.
Multi-stage Coefficients: Sets the multi-stage coefficient values, see Eqn. (960). The number of values in the vector indicates the number of stages.
Pressure Reference Location: As for Coupled Implicit.
Reconstruction Frozen: As for Coupled Implicit.
Reconstruction Zeroed: As for Coupled Implicit.
Residual Smoothing: When On, activates residual smoothing. Residual smoothing is a mechanism for increasing the explicit time-step size by removing the high-wave number oscillations from the residuals. This approach helps widen the stability margin and allows slightly larger Courant numbers to be used.; Residual smoothing can be employed along with the explicit spatial integration scheme.; For more information, see Residual Smoothing.
Residual Smoothing Iterations: Sets the number of residual smoothing iterations using Eqn. (963).
Residual Smoothing Underrelaxation: Sets the residual smoothing under-relaxation factor $ε$ , see Eqn. (962). The default value is 0.5.
Temporary Storage Retained: As for Coupled Implicit.

Courant Number Ramp

The Courant Number (CFL) Ramp provides a linear ramping of the CFL number to help the solution converge.


Method	Corresponding Method Node
No Ramp Leaves off ramp calculation.	None.
Linear Ramp Activates linear ramp value calculation.	Linear Ramp Specifies the following properties: Start Iteration: Specifies the iteration on which to begin ramping, typically 1. End Iteration: Specifies the iteration on which to stop ramping. Initial Value: Specifies the Courant number value before ramping starts.

Example: If the specified Courant Number is 1, Start Iteration is 100, End Iteration is 1000, and Initial Value is 0.1, then Simcenter STAR-CCM+ uses a Courant number of 0.1 for iterations before 100, a Courant number of 1 for iterations after 1000, and the Courant number grows linearly between those two values.