精通ANSYSFLUENT13各种计算格式、加速算法以及VOF 模型 (仅供阅览)
For Scale-Resolving Simulations (SRS), specific discretization and solver settings are required to achieve optimal accuracy with minimal numerical effort.
The recommendations are based on incompressible, single phase flow without chemical reactions or other complex additional physics.
In most cases, this will mean that a higher effort needs to be invested into the coupling of the equations (e.g. lower time step, reduced under-relaxation, higher iteration count, smaller residuals), in order to avoid a de-coupling of different physical phenomena.
It is generally recommended to use the pressure-based solver, as it offers optimized schemes for resolving turbulence relative to the density based solver.
For Scale-Resolving Simulations, optimal numerics settings are essential for achieving accurate results in an acceptable time frame.Numerics settings therefore have to be chosen to provide an optimal balance between accuracy and robustness.
It is generally recommended to initialize the solution from a (reasonably) converged RANS simulation.
For Scale-Resolving Simulations, the resolution of the turbulent structures in time is essential for the success of the simulation. This is, to the largest extent, defined by the selected time step. As the SRS model is operating at the grid limit, you should select a time step that ensures a Courant-Friedrichs-Levy (CFL) number of
The recommendation of CFL =1 should be applied in the main SRS region in combination with a uniform isotropic grid.It is recommended to vary the time step for each type of application and explore its optimal value. This can substantially save on computing costs.In most transient cases, the CFL number should be set to 1e7with an explicit relaxation of 1.0.
The time derivative should be computed by the Second Order Implicit option
(压⼒速度分离算法4种，压⼒速度耦合算法1种，即coupled，其只能在pressure-based solver（压⼒基）求解器适⽤)。下⾯介绍五种算法的异同。 1.压⼒基压⼒速度分离算法: SIMPLE, SIMPLEC, PISO, Fractional Step (NIAT,FSM)
ANSYS FLUENT provides four segregated types of algorithms: SIMPLE, SIMPLEC, PISO, and (for time-dependant flows using the Non-Iterative Time Advancement option (NITA)) Fractional Step (FSM). These schemes are referred to as the pressure-based segregated algorithm. Steady-state calculations will generally use SIMPLE or SIMPLEC, while PISO is recommended for transient calculations. PISO may also be useful for steady-state and transient calculations on highly skewed meshes. Pressure-velocity coupling is relevant only for the pressure-based solver.
SIMPLE and SIMPLEC
SIMPLE is the default, but many problems will benefit from using SIMPLEC, particularly because of the increased under-relaxation that can be applied, as described below.
For relatively uncomplicated problems (laminar flows with no additional models activated) in which convergence is limited by the pressure-velocity coupling, you can often obtain a converged
solution more quickly using SIMPLEC.With SIMPLEC, the pressure-correction under-relaxation factor is generally set to 1.0, which aids in convergence speed-up. In some problems, however, incre
asing the pressure-correction under-relaxation to 1.0 can lead to instability due to high mesh skewness.For such cases, you will need to use one or more skewness correction schemes, use a slightly more conservative under-relaxation value (up to 0.7), or use the SIMPLE algorithm. For complicated flows involving turbulence and/or additional physical models, SIMPLEC will improve convergence only if it is being limited by the pressure-velocity coupling. Often it will be one of the additional modeling parameters that limits convergence; in this case, SIMPLE and SIMPLEC will give similar convergence rates.
非诚勿扰18期If you choose SIMPLEC under Pressure-Velocity Coupling, you must also set the Skewness Correction, whose default value is 0.
马尔康PISO
The Pressure-Implicit with Splitting of Operators (PISO) pressure-velocity coupling scheme, part of the SIMPLE family of algorithms, is based on the higher degree of the approximate relation between the corrections for pressure and velocity. One of the limitations of the SIMPLE and SIMPLEC algorithms is that new velocities and corresponding fluxes do not satisfy the momentum balance after the pressure-correction equation is solved. As a result, the calculation must be repeated until th
e balance is satisfied. To improve the efficiency of this calculation, the PISO algorithm performs two additional corrections: neighbor correction and skewness correction.
The main idea of the PISO algorithm is to move the repeated calculations required by SIMPLE and SIMPLEC inside the solution stage of the pressure-correction equation.[154]After one or more additional PISO loops, the corrected velocities satisfy the continuity and momentum equations more closely. This iterative process is called a momentum correction or “neighbor correction”. The PISO algor ithm takes a little more CPU time per solver iteration, but it can dramatically decrease the number of iterations required for convergence, especially for transient problems.This process, which is referred to as “skewness correction”, significantly reduce s convergence difficulties associated with highly distorted meshes. The PISO skewness correction allows ANSYS FLUENT to obtain a solution on a highly skewed mesh in approximately the same number of iterations as required for a more orthogonal mesh.[104]
[104] J. L. Ferzieger and M. Peric. Computational Methods for Fluid Dynamics. Springer-Verlag, Heidelberg. 1996.
[154] R. I. Issa. "Solution of Implicitly Discretized Fluid Flow Equations by Operator Splitting". J. Comput. Phys.. 62. 40–65. 1986.
The PISO algorithm with neighbor correction is highly recommended for all transient flow calculations, especially when you want to use a large time step.PISO can maintain a stable calculation with a larger time step and an under-relaxation factor of 1.0 for both momentum and pressure. For steady-state problems, PISO with neighbor correction does not provide any noticeable advantage over SIMPLE or SIMPLEC with optimal under-relaxation factors.
PISO with skewness correction is recommended for both steady-state and transient calculations on meshes with a high degree of distortion.When you use PISO neighbor correction, under-relaxation factors of 1.0 or near 1.0 are recommended for all equations. If you use just the PISO skewness correction for highly-distorted meshes (without neighbor correction), set the under-relaxation factors for momentum and pressure so that they sum to 1 (e.g., 0.3 for pressure
and 0.7 for momentum). If you use both PISO methods, follow the under-relaxation recommendations for PISO neighbor correction, above. For most problems, it is not necessary to disable the default coupling between neighbor and skewness corrections. For highly distorted meshes, however, disabling the default coupling between neighbor and skewness corrections is recommended.
If you choose PISO, the task page will expand to show the additional parameters for pressure-velocity coupling. By default, the number of iterations for Skewness Correction and Neighbor Correction are set to 1. If you want to use only Skewness Correction, then set the number of iterations for Neighbor Correction to 0. Likewise, if you want to use only Neighbor Correction, then set the number of iterations for Skewness Correction to 0. For most problems, you do not need to change the default iteration values. By default, the Skewness-Neighbor Coupling option is enabled to allow for a more economical, but a less robust variation of the PISO algorithm.
Fractional Step method
The Fractional Step method (FSM), described in Fractional-Step Method (FSM) in the Theory Guide, is available when you choose to use the NITA scheme (i.e., the Non-Iterative Time Advancement option in the Solution Methods task page). With the NITA scheme, the FSM is slightly less computationally expensive compared to the PISO algorithm. Whether you select FSM or PISO depends on the application. For some problems (e.g., simulations that use VOF), FSM could be less stable than PISO.In most cases, the default values for the solution methods are enough to set a robust convergence of the internal pressure correction sub-iterations due to skewness. Only very complex problems (e.g., moving deforming meshes, sliding interfaces, the VOF model) could require
a reduction of relaxation for pressure up to a value of 0.7 or 0.8.
2.Coupled（pressure-based coupled algorithm）
Selecting Coupled from the Pressure-Velocity Coupling drop-down list indicates that you are using the pressure-based coupled algorithm, described in Coupled Algorithm in the Theory Guide. This solver offers some advantages over the pressure-based segregated algorithm. The pressure-based coupled algorithm obtains a more robust and efficient single phase implementation for steady-state flows. （优点）It is not available for cases using the Eulerian multiphase, NITA, and periodic mass-flow boundary conditions.
If you choose Coupled, you will have to specify the Courant number in the Solution Controls task page, which is set at 200 by default. You will also specify the Explicit Relaxation Factors for Momentum and Pressure, which are set at 0.75 by default.
If high-order momentum discretization is used, you may need to decrease the explicit relaxation to 0.5. For cases with very skewed meshes, the run can be stabilized by further reduction of the explicit relaxation factor to 0.25. If ANSYS FLUENT immediately diverges in the AMG solver, then the CFL number is too high and should be reduced. Reducing the CFL number below 10 is not recommended
since it would be better to use the segregated algorithm for the pressure-velocity coupling（在这耦合算法下，CFL不推荐⼩于10，因为此时可⽤分离算法了）.
If you choose Coupled and enable the Pseudo Transient option, you will set the Pseudo
Transient Explicit Relaxation Factors in the Solution Controls task page.
VOF
The VOF model can model two or more immiscible fluids by solving a single set of momentum equations and tracking the volume fraction of each of the fluids throughout the domain. Typical applications include the prediction of jet breakup, the motion of large bubbles in a liquid, the motion of liquid after a dam break, and the steady or transient tracking of any liquid-gas interface.
You must use the pressure-based solver. The VOF model is not available with the density-based solver;All control volumes must be filled with either a single fluid phase or a combination of phases. The VOF model does not allow for void regions where no fluid of any type is present;Only one of the phases can be defined as a compressible ideal gas. There is no limitation on using compressible liquids using user-defined functions;Streamwise periodic flow (either specified mass flow rate or spe
cified pressure drop) cannot be modeled when the VOF model is used;The second-order implicit time-stepping formulation cannot be used with the VOF explicit scheme;When tracking particles in parallel, the DPM model cannot be used with the VOF model if the shared memory option is enabled (Parallel Processing for the Discrete Phase Model in the User's Guide). (Note that using the message passing option, when running in parallel, enables the compatibility of all multiphase flow models with the DPM model.)
The VOF formulation in ANSYS FLUENT is generally used to compute a time-dependent solution.A steady-state VOF calculation is sensible only when your solution is independent of the initial conditions and there are distinct inflow boundaries for the individual phases The VOF formulation relies on the fact that two or more fluids (or phases) are not interpenetrating.For each additional phase that you add to your model, a variable is introduced: the volume fraction of the phase in the computational cell. In each control volume, the volume fractions of all phases sum to unity. The fields for all variables and properties are shared by the phases and represent volume-averaged values, as long as the volume fraction of each of the phases is known at each location.Thus the variables and properties in any given cell are either purely representative of one of the phases, or representative of a mixture of the phases, depending upon the volume fraction values. In other words, if the fluid’s volume fraction in the cell is denoted as , then the following three conditions are possible:
5060lu: The cell is empty (of the fluid).
: The cell is full (of the fluid).
: The cell contains the interface between the fluid and one or more other fluids.
Based on the local value of , the appropriate properties and variables will be assigned to each control volume within the domain.
In the geometric reconstruction approach, the standard interpolation schemes that are used in ANSYS FLUENT are used to obtain the face fluxes whenever a cell is completely filled with one phase or another. When the cell is near the interface between two phases, the geometric reconstruction scheme is used.
Comparison:
The geometric reconstruction scheme represents the interface between fluids using a piecewise-linear approach. In ANSYS FLUENT this scheme is the most accurate and is applicable for general unstructured meshes.The geometric reconstruction scheme is generalized for unstructured meshes from the work of Youngs [432]. It assumes that the interface between two fluids has a linear slope wit
约翰-纳什hin each cell, and uses this linear shape for calculation of the advection of fluid through the cell faces. In the donor-acceptor approach, the standard interpolation schemes that are used in ANSYS FLUENT are used to obtain the face fluxes whenever a cell is completely filled with one phase or another. When the cell is near the interface between two phases, a “donor-acceptor” scheme is used to determine the amount of fluid advected through the face [144]. This scheme identifies one cell as a donor of an amount of fluid from one phase and another (neighbor) cell as the acceptor of that same amount of fluid, and is used to prevent numerical diffusion at the interface. The amount of fluid from one phase that can be convected across a cell boundary is limited by the minimum of two values: the filled volume in the donor cell or the free
volume in the acceptor cell.The compressive interface capturing scheme for arbitrary meshes (CICSAM), based on Ubbink’s work[388], is a high resolution differencing scheme. The CICSAM scheme is particularly suitable for flows with high ratios of viscosities between the phases. CICSAM is implemented in ANSYS FLUENT as an explicit scheme and offers the advantage of producing an interface that is almost as sharp as the geometric reconstruction scheme. The compressive scheme is a second order reconstruction scheme based on the slope limiter. The theory below is applicable to zonal discretization and the phase localized compressive scheme, which use the framework of the
compressive scheme.The BGM scheme is introduced to obtain sharp interfaces with the VOF model, comparable to that obtained by the Geometric Reconstruction scheme. Currently this scheme is available only with the steady state solver and cannot be used for transient problems. In the BGM scheme, discretization occurs in such a way so as to maximize the local value of the gradient, by maximizing the degree to which the face value is weighted towards the extrapolated downwind value [404].
[432] D. L. Youngs. "Time-Dependent Multi-Material Flow with Large Fluid Distortion". Numerical Methods for Fluid Dynamics. K. W. Morton and M. J. Baines, editorsAcademic Press. 1982.
进博会成果丰硕
The first step in this reconstruction scheme is calculating the position of the linear interface relative to the center of each partially-filled cell, based on information about the volume fraction and its derivatives in the cell. The second step is calculating the advecting amount of fluid through each face using the computed linear interface representation and information about the normal and tangential velocity distribution on the face. The third step is calculating the volume fraction in each cell using the balance of fluxes calculated during the previous step.
Important:
When the geometric reconstruction scheme is used, a time-dependent solution must be computed. Also, if you are using a conformal mesh (i.e., if the mesh node locations are identical at the boundaries where two subdomains meet), you must ensure that there are no two-sided (zero-thickness) walls within the domain. If there are, you will need to slit them, as described in Slitting Face Zones in the User's Guide.
For quad/hex meshes, you will also obtain better results using the second-order discretization, especially for complex flows.In summary, while the first-order discretization generally yields better convergence than the second-order scheme, it generally will yield less accurate results, especially on tri/tet meshes. See Convergence and Stability for information about controlling convergence.While the higher-order scheme may result in greater accuracy, it can also result in
convergence difficulties and instabilities at certain flow conditions. On the other hand, using a first-order scheme may not provide the desired accuracy. One approach to achieving improved accuracy while maintaining good stability is to use a discretization blending factor. This feature is available for both density-based and pressure-based solvers and can be invoked using the following text command:The QUICK and third-order MUSCL discretization schemes may provide better accuracy than the second-order scheme for rotating or swirling flows. The QUICK scheme is applicable to qua
drilateral or hexahedral meshes, while the MUSCL scheme is used on all types of meshes. Unlike the QUICK scheme which is applicable to structured hex meshes only, the MUSCL scheme is applicable to arbitrary meshes. Compared to the second-order upwind scheme, the third-order MUSCL has a potential to improve spatial accuracy for all types of meshes by reducing numerical diffusion, most significantly for complex three-dimensional flows, and it is available for all transport equations.In general, however, the second-order scheme is sufficient and the QUICK scheme will not provide significant improvements in accuracy.A power law scheme is also available, but it will generally yield the same accuracy as the first-order scheme.The bounded central differencing and central differencing schemes are available only when you are using the LES and DES turbulence models, and the central differencing scheme should be used only when the mesh spacing is fine enough so that the magnitude of the local Peclet number (see Equation 19–6 in the Theory Guide) is less than 1.A modified HRIC scheme (see Modified HRIC Scheme in the Theory Guide) is also available for VOF simulations using either the implicit or explicit formulation.Th e modified HRIC scheme provides improved accuracy for VOF calculations when compared to QUICK and second-order schemes, and is less computationally expensive than the Geo-Reconstruct scheme.
In the accurate solution of a real-life time-dependent CFD problem, it is important to make sure that t
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he solution converges at every time step to within the desired accuracy. Here the first few time steps will only come to a reasonably converged solution. This will save the time step size to the case file (the next time a case file is saved). This option (Frozen Flux Formulation) is only available for single-phase transient problems that use the segregated iterative solver and do not use a moving/deforming mesh model.
NITA基本思想：The idea underlying the non-iterative time-advancement (NITA) scheme is that, in order to preserve overall time accuracy, you do not really need to reduce the splitting error to zero, but only have to make it the same order as the truncation error. The NITA scheme, as seen in Figure 19.9, does not need the outer iterations, performing only a single outer iteration per time-step, which significantly speeds up transient simulations.
The non-iterative time advancement (NITA) scheme is often advantageous compared to the iterative schemes as it is less CPU intensive. Although smaller time steps must be used with NITA compared to the iterative schemes, the total CPU
expense is often smaller. If the NITA scheme leads to convergence difficulties, then the iterative schemes (e.g. PISO, SIMPLE) should be used instead.
It is best to select the Coupled pressure-velocity coupling scheme if you are using large time steps to solve your transient flow, or if you have a poor quality mesh.
Next, specify the desired Transient Formulation. The First Order Implicit formulation is sufficient for most problems. If you need improved accuracy, you can either use Second Order Implicit or Bounded Second Order Implicit. The Bounded Second Order Implicit formulation
would provide better stability, since time discretization would always ensure the bounds for variables, if available.Note that while the Bounded Second Order Implicit formulation provides the same accuracy as the Second Order Implicit formulation, it actually provides better stability. The Bounded Second Order Implicit formulation is available only for the pressure-based solver, and not for the density-based solver.
(optional) You can improve the convergence of the transient calculations by enabling the Extrapolate Variables option in the Run Calculation Task Page. This option instructs ANSYS FLUENT to predict the solution variable values for the next time step using a Taylor series expansion, and then inputs that predicted value as an initial guess for the inner iterations of the current time step. As a result, the absolute residual levels are lowered.
Note that the Extrapolate Variables option is not available if you are employing either the NITA scheme with the pressure-based solver or the explicit formulation with the density-based solver.Important:
If you use the Extrapolate V ariables option when modeling an incompressible flow with the density-based solver, it is recommended that you disable the extrapolation of pressure values. After you have enabled the Extrapolate Variables option, type the following text command in the console window:
> solve/set/extrapolate-eqn-vars/pressure
Extrapolate Pressure? [yes] no
Time
Max Iterations/Time Step: When ANSYS FLUENT solves the time-dependent equations using the implicit formulation, multiple iterations may be necessary at each time step. This parameter sets a maximum for the number of iterations per time step. If the convergence criteria are met before this number of iterations is performed, the solution will advance to the next time step.
Time Step Size: The time step size is the magnitude of . Since the ANSYS FLUENT formulation is fully implicit, there is no stability criterion that needs to be met in determining . However, to model transient phenomena properly, it is necessary to set at least one order of magnitude smaller than the smallest time constant in the system being modeled. A good way to judge the choice of is to observe the number of iterations ANSYS FLUENT needs to converge at each time step. The ideal number of iterations per time step is 5–10. If ANSYS FLUENT needs substantially more, the time step is too large. If ANSYS FLUENT needs only a few iterations per time step, should be increased. Frequently a time-dependent problem has a very fast “startup”transient that decays rapidly. Therefore, it is often wise to choose a conservatively small for the first 5–10 time steps. may then be gradually increased as the calculation proceeds.
For time-periodic calculations, you should choose the time step based on the time scale of the periodicity. For a rotor/stator model, for example, you might want 20 time steps between each blade passing. For vortex shedding, you might want 20 steps per period.
To verify that your choice for was proper after the calculation is complete, you can plot
contours of the Courant number within the domain. To do so, and Cell Courant Num
ber from the Contours of drop-down lists in the Contours dialog box. For a stable, efficient calculation, the Courant number should not exceed a value of 20–40 in most sensitive transient regions of the domain.
Time Stepping Method: By default, the size of the time step is fixed (as indicated by the selection of Fixed).
To have ANSYS FLUENT modify the size of the time step as the calculation proceeds, select Adaptive and click button to specify the parameters in the Adaptive Time Step Settings dialog box. See Adaptive Time Stepping for details.
For transient volume of fluid (VOF) calculations that use the explicit scheme of VOF, you can select the Variable time stepping method. The parameters set through button are in many ways the same as for the adaptive time stepping method, with the exception of specifying a global Courant number (see Variable Time Stepping).
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