[sanjiiv]

hi scholars,
can any one say which is used for appropriate solution of a problem,in fluent
in gradient ,
green gauss nodal method for what ?
green gauss cell method for what?
least square cell method for what?
then the order selection for pressure and momentum selection for
which order need to select for solution for different problem
whether first,second, third ,quick and power law..

[LuckyTran]

It is highly problem dependent. But for a typical weakly compressible (incompressible or weakly compressible flows) the following is generally true: Note that the best method depends on whether you want highest accuracy or cheapest computation or some optimal in-between.

Least Squares & Green Gauss Node Based are the most accurate (least squares is slightly cheaper than Node based). Green Gauss Cell Based is least accurate but much cheaper than the other two.

The pressure interpolation scheme is applicable only to the pressure based solver. The density based solver does its own thing.

The linear pressure scheme is the absolute worst.

The second order pressure scheme, whenever it is available is generally the best. However, it is not accurate for flows with (strong) body forces and the PRESTO scheme is then the preferred scheme. The body force weighted scheme is great when the body forces are known a priori. The standard scheme uses a momentum-based weighting scheme to compute the pressure, but Second Order and Presto are generally much better unless there are stability issues.

For advective fluxes:
First order upwind is the least accurate in terms of order, but generally the most stable. The reason Fluent defaults to 1st order for some variables is because these equations are prone to numerical instabilities.

Second order upwind is much more accurate than 1st order, but has stability issues. Note however, that a 1st order scheme can have better absolute accuracy than a 2nd order scheme. The order of convergence for a 2nd order scheme is obtained via a loss of absolute accuracy (higher order of accuracy but errors are caused by numerical wiggles).

QUICK is 3rd order accurate for face values and 2nd order accurate for cell values on a hexahedral grid. For non-hexahedral cells, Fluent will use the second order scheme even if QUICK is selected (it will use QUICK for hexahedral cells and second order for non-hexahedral cells if both are present in the same mesh). In general the accuracy of QUICK is similar or slightly better than 2nd order upwind.

The power law scheme uses the exact power law solution to the advection-diffusion equation to interpolate values. It would be exact on an advection-diffusion problem, but Navier-Stokes is more complicated than simple advection-diffusion. The power law scheme has some niche utility; but in general, the power-law scheme is only slightly better than 1st order and not as accurate as second order and other schemes when all types of flow scenarios are considered.

The Third order MUSCL scheme can be interpreted as a generalization of the QUICK scheme for arbitrary grids (QUICK only works for hexahedral grids). The drawback is the gradient limiter doesn't work for MUSCL, and this scheme is prone to more pronounced overshoots and undershoots (these limiters do work for second order and QUICK). The scheme itself has the potential to better than 2nd order upwind and more usable than QUICK, but the implementation in Fluent needs a better limiter before you can use the MUSCL scheme for general cases.

QUICK and MUSCL schemes should really only be used by veterans. To use these schemes properly also requires a high quality grid, so some serious commitments are needed to get reasonable results with these two schemes. There's just very little gain for the cost in effort. They generally blow up in your face for a beginner. Beginners usually have all sorts of other issues to worry about though, like specifying the correct boundary and initial conditions. For beginners, I recommend to stick to defaults until they've learned how to use Fluent for many different types of problems before playing with these things. For beginners I would recommend 1st order on everything (because it's stable) or to use the defaults. Once they are familiar with how to setup a problem and solve it. The only setting I would recommend changing for beginners is switching from 1st to 2nd order upwind for all variables. Usually the simulation blows up at this point.

[sanjiiv]

Thank you very much sir, for your detailed reply for my question....

[randolph]

Originally Posted by LuckyTran

It is highly problem dependent. But for a typical weakly compressible (incompressible or weakly compressible flows) the following is generally true: Note that the best method depends on whether you want highest accuracy or cheapest computation or some optimal in-between.

Least Squares & Green Gauss Node Based are the most accurate (least squares is slightly cheaper than Node based). Green Gauss Cell Based is least accurate but much cheaper than the other two.

The pressure interpolation scheme is applicable only to the pressure based solver. The density based solver does its own thing.

The linear pressure scheme is the absolute worst.

The second order pressure scheme, whenever it is available is generally the best. However, it is not accurate for flows with (strong) body forces and the PRESTO scheme is then the preferred scheme. The body force weighted scheme is great when the body forces are known a priori. The standard scheme uses a momentum-based weighting scheme to compute the pressure, but Second Order and Presto are generally much better unless there are stability issues.

For advective fluxes:
First order upwind is the least accurate in terms of order, but generally the most stable. The reason Fluent defaults to 1st order for some variables is because these equations are prone to numerical instabilities.

Second order upwind is much more accurate than 1st order, but has stability issues. Note however, that a 1st order scheme can have better absolute accuracy than a 2nd order scheme. The order of convergence for a 2nd order scheme is obtained via a loss of absolute accuracy (higher order of accuracy but errors are caused by numerical wiggles).

QUICK is 3rd order accurate for face values and 2nd order accurate for cell values on a hexahedral grid. For non-hexahedral cells, Fluent will use the second order scheme even if QUICK is selected (it will use QUICK for hexahedral cells and second order for non-hexahedral cells if both are present in the same mesh). In general the accuracy of QUICK is similar or slightly better than 2nd order upwind.

The power law scheme uses the exact power law solution to the advection-diffusion equation to interpolate values. It would be exact on an advection-diffusion problem, but Navier-Stokes is more complicated than simple advection-diffusion. The power law scheme has some niche utility; but in general, the power-law scheme is only slightly better than 1st order and not as accurate as second order and other schemes when all types of flow scenarios are considered.

The Third order MUSCL scheme can be interpreted as a generalization of the QUICK scheme for arbitrary grids (QUICK only works for hexahedral grids). The drawback is the gradient limiter doesn't work for MUSCL, and this scheme is prone to more pronounced overshoots and undershoots (these limiters do work for second order and QUICK). The scheme itself has the potential to better than 2nd order upwind and more usable than QUICK, but the implementation in Fluent needs a better limiter before you can use the MUSCL scheme for general cases.

QUICK and MUSCL schemes should really only be used by veterans. To use these schemes properly also requires a high quality grid, so some serious commitments are needed to get reasonable results with these two schemes. There's just very little gain for the cost in effort. They generally blow up in your face for a beginner. Beginners usually have all sorts of other issues to worry about though, like specifying the correct boundary and initial conditions. For beginners, I recommend to stick to defaults until they've learned how to use Fluent for many different types of problems before playing with these things. For beginners I would recommend 1st order on everything (because it's stable) or to use the defaults. Once they are familiar with how to setup a problem and solve it. The only setting I would recommend changing for beginners is switching from 1st to 2nd order upwind for all variables. Usually the simulation blows up at this point.

______________
"Second order upwind is much more accurate than 1st order, but has stability issues. Note however, that a 1st order scheme can have better absolute accuracy than a 2nd order scheme. The order of convergence for a 2nd order scheme is obtained via a loss of absolute accuracy (higher order of accuracy but errors are caused by numerical wiggles)."

hi,

Just curiosity. In what case have you observed that the 1st order has better absolute accuracy than a 2nd order scheme? And how do you define the absolute accuracy? Compared with experiment result?

[LuckyTran]

For example when a higher order scheme diverges I consider it as having no accuracy. If the 1st order scheme converges to something, then I consider it as having some accuracy. Something vs nothing. See also Godunov's theorem.

Unbounded higher order schemes produce overshoots and undershoots which are completely non-physical. That might as well be considered no accuracy since it violates the very conservation laws we are using. Of course no one really uses unbounded schemes, but that just proves the point.

[randolph]

Originally Posted by LuckyTran

For example when a higher order scheme diverges I consider it as having no accuracy. If the 1st order scheme converges to something, then I consider it as having some accuracy. Something vs nothing. See also Godunov's theorem.

I agree. If there is no stability, there is no need talking about the accuracy.

In my personal experience, when the second-order blows up (no accuracy to speak), the "converged" result from the first-order is nothing useful neither (too diffusive, and quite often very misleading).

[Mike97]

Originally Posted by LuckyTran

It is highly problem dependent. But for a typical weakly compressible (incompressible or weakly compressible flows) the following is generally true: Note that the best method depends on whether you want highest accuracy or cheapest computation or some optimal in-between.

Least Squares & Green Gauss Node Based are the most accurate (least squares is slightly cheaper than Node based). Green Gauss Cell Based is least accurate but much cheaper than the other two.

The pressure interpolation scheme is applicable only to the pressure based solver. The density based solver does its own thing.

The linear pressure scheme is the absolute worst.

The second order pressure scheme, whenever it is available is generally the best. However, it is not accurate for flows with (strong) body forces and the PRESTO scheme is then the preferred scheme. The body force weighted scheme is great when the body forces are known a priori. The standard scheme uses a momentum-based weighting scheme to compute the pressure, but Second Order and Presto are generally much better unless there are stability issues.

For advective fluxes:
First order upwind is the least accurate in terms of order, but generally the most stable. The reason Fluent defaults to 1st order for some variables is because these equations are prone to numerical instabilities.

Second order upwind is much more accurate than 1st order, but has stability issues. Note however, that a 1st order scheme can have better absolute accuracy than a 2nd order scheme. The order of convergence for a 2nd order scheme is obtained via a loss of absolute accuracy (higher order of accuracy but errors are caused by numerical wiggles).

QUICK is 3rd order accurate for face values and 2nd order accurate for cell values on a hexahedral grid. For non-hexahedral cells, Fluent will use the second order scheme even if QUICK is selected (it will use QUICK for hexahedral cells and second order for non-hexahedral cells if both are present in the same mesh). In general the accuracy of QUICK is similar or slightly better than 2nd order upwind.

The power law scheme uses the exact power law solution to the advection-diffusion equation to interpolate values. It would be exact on an advection-diffusion problem, but Navier-Stokes is more complicated than simple advection-diffusion. The power law scheme has some niche utility; but in general, the power-law scheme is only slightly better than 1st order and not as accurate as second order and other schemes when all types of flow scenarios are considered.

The Third order MUSCL scheme can be interpreted as a generalization of the QUICK scheme for arbitrary grids (QUICK only works for hexahedral grids). The drawback is the gradient limiter doesn't work for MUSCL, and this scheme is prone to more pronounced overshoots and undershoots (these limiters do work for second order and QUICK). The scheme itself has the potential to better than 2nd order upwind and more usable than QUICK, but the implementation in Fluent needs a better limiter before you can use the MUSCL scheme for general cases.

QUICK and MUSCL schemes should really only be used by veterans. To use these schemes properly also requires a high quality grid, so some serious commitments are needed to get reasonable results with these two schemes. There's just very little gain for the cost in effort. They generally blow up in your face for a beginner. Beginners usually have all sorts of other issues to worry about though, like specifying the correct boundary and initial conditions. For beginners, I recommend to stick to defaults until they've learned how to use Fluent for many different types of problems before playing with these things. For beginners I would recommend 1st order on everything (because it's stable) or to use the defaults. Once they are familiar with how to setup a problem and solve it. The only setting I would recommend changing for beginners is switching from 1st to 2nd order upwind for all variables. Usually the simulation blows up at this point.

Hi,
i think you can answer my question!


I am simulating a flow over an airfoil (NACA 0015) using the SST-Transition turbulence model. My mesh is a double O-Grid in wich the external is structured and the internal unstructured, then i have 30 structured layer on growing up from the airfoil with a growth factor of 1.1. In FLUENT i ste Pressure-Based solver.

If i use a different scheme from the Fisrt-Upwind for the momentum equation, lift and drag values change a lot from one iteration to another. Also, the leading edge separation bubble is bigger, i have recirculation zones on the pressure side and every bubble consists of many vortex in sequence.



Do you think that the results i got from the higher-order scheme is correct or is unphysical? What discretization scheme i have to use?



Thank you.