What is an updraft scheme in CFD
Hybrid Spatial Schemes for CFD: Are There Downsides to Mixing vs. Switching?
In addition to the additional computational costs involved in calculating both flows over a certain range, is there a disadvantage if two flow assessments for a hybrid scheme have to be mixed in a finite volume method? The flow assessment would look like this:
F.i + 12 = Λi + 12F.ci + 12+ (1 - Λi + 12) F.ui + 12
Depending on the application, the switch is based on a pressure and / or density gradient sensor. is a central scheme (McCormack, compact, ...) and is an updraft scheme like a flow difference division with a MUSCL reconstruction. Are there problems with numerical and conservative properties if I mix the two schemes with a continuous function for instead of simply switching between schemes with a value of 0 or 1?
The approach you used maintains conservation in both cases. There are other obvious approaches that are not conservative and can cause problems.
It is possible (and even likely) that you will lose an order of accuracy in the region you are switching when you investigate the local truncation error. Usually, however, this error is localized in such a way that the global error is still within the expected range. So, in my experience, you'll see essentially the same behavior whether you're using a hard switch or a transition area.
I have a manuscript on (more or less) this topic: Failure Analysis of Explicitly Partitioned Runge-Kutta Schemes for Conservation Laws.
I would be very interested to see what you see when you try the two approaches, if it is different from what I am suggesting.
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