Accuracy of the MUSCL 3rd-order differencing scheme.

JAndreotti · May 11, 2020, 18:46

I was reading up on the MUSCL 3rd-order/CD model that is available in STAR-CCM+ as I was intending on using it for some aerodynamic simulations and some questions have come up in my mind.

First off: the implementation STAR-CCM+ uses for this differencing scheme seems to switch to upwind differencing in regions where the Normalized-Variable Diagram value goes outside the range (0, 1). Given that UDS is first order accurate, is it possible for the MUSCL scheme to be overall less accurate than a second order upwind scheme due to it switching to a lower accuracy model in most of the domain? If it can become less accurate than LUDS is there anyway I can judge whether I'm losing accuracy by choosing MUSCL over LUDS? Are there any field functions that show whether MUSCL or UDS is being used in a particular cell?
The second question that came up was: Is it a problem to use MUSCL for one of the physics models and not for another? E.g. Setting the segregated flow solver to MUSCL and the k-eps solver to LUDS.
Thanks in advance for the help!

LuckyTran · May 11, 2020, 19:36

1) It isn't a hard switch but a soft switch using a limiter on the gradient/flux and/or linear blending. 2nd order upwind is also limited and does a very similar switch as MUSCL. Nearly all robust CFD codes do this because non-physical wiggles are a big no-no for engineering purposes. It's actually much more rare to see unlimited discretization schemes except for academic purposes.

Because it doesn't really switch to another discretiation, there isn't an accessible variable that shows you which cells have been limited and where. You can however dsicover it by turning on temporary storage in the solvers. Then you have access to the raw reconstruction gradients and their limited ones and you can do the comparison.

2) Yes, it's fairly common to use a mix and match of different discretization schemes.

May 11, 2020, 18:46	Accuracy of the MUSCL 3rd-order differencing scheme.	#1
JAndreotti New Member João V. M. Andreotti Join Date: May 2020 Posts: 2 Rep Power: 0	I was reading up on the MUSCL 3rd-order/CD model that is available in STAR-CCM+ as I was intending on using it for some aerodynamic simulations and some questions have come up in my mind. First off: the implementation STAR-CCM+ uses for this differencing scheme seems to switch to upwind differencing in regions where the Normalized-Variable Diagram value goes outside the range (0, 1). Given that UDS is first order accurate, is it possible for the MUSCL scheme to be overall less accurate than a second order upwind scheme due to it switching to a lower accuracy model in most of the domain? If it can become less accurate than LUDS is there anyway I can judge whether I'm losing accuracy by choosing MUSCL over LUDS? Are there any field functions that show whether MUSCL or UDS is being used in a particular cell? The second question that came up was: Is it a problem to use MUSCL for one of the physics models and not for another? E.g. Setting the segregated flow solver to MUSCL and the k-eps solver to LUDS. Thanks in advance for the help!

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May 11, 2020, 19:36		#2
LuckyTran Senior Member Lucky Join Date: Apr 2011 Location: Orlando, FL USA Posts: 5,754 Rep Power: 66	1) It isn't a hard switch but a soft switch using a limiter on the gradient/flux and/or linear blending. 2nd order upwind is also limited and does a very similar switch as MUSCL. Nearly all robust CFD codes do this because non-physical wiggles are a big no-no for engineering purposes. It's actually much more rare to see unlimited discretization schemes except for academic purposes. Because it doesn't really switch to another discretiation, there isn't an accessible variable that shows you which cells have been limited and where. You can however dsicover it by turning on temporary storage in the solvers. Then you have access to the raw reconstruction gradients and their limited ones and you can do the comparison. 2) Yes, it's fairly common to use a mix and match of different discretization schemes.