non orthogonal 2d grid

Jauo · July 12, 2019, 09:41

Hey there
I have a nozzle like the image

the vertical grid is called r and the grid along each streamline is called m as a meridional grid

I dont know what to do to compute derivative of some parameter along m direcion with backward difference method...
i mean what should be the denominator ?

FMDenaro · July 12, 2019, 16:59

Just consider the transformation from the physical (csi,eta) to the computational domain (x,y). In your case csi=x, you have only to consider the transformation along the vertical direction given by the law eta(csi).

Jauo · July 13, 2019, 13:35

thanks
so you mean say for taking derivative of like function F along each stream line dFdm
will be (Fi-F(i-1))/(x(i)-x(i-1) ?

selig5576 · July 18, 2019, 16:40

From my experience with curvilinear grid (albeit still learning), you should calculate the metrics using central schemes. In this case

(F(i+1) - F(I-1))/(2*dx))

July 12, 2019, 09:41	non orthogonal 2d grid	#1
Jauo New Member hajo jllon Join Date: Jun 2019 Posts: 5 Rep Power: 6	Hey there I have a nozzle like the image the vertical grid is called r and the grid along each streamline is called m as a meridional grid I dont know what to do to compute derivative of some parameter along m direcion with backward difference method... i mean what should be the denominator ?

July 12, 2019, 16:59		#2
FMDenaro Senior Member Filippo Maria Denaro Join Date: Jul 2010 Posts: 6,772 Rep Power: 71	Just consider the transformation from the physical (csi,eta) to the computational domain (x,y). In your case csi=x, you have only to consider the transformation along the vertical direction given by the law eta(csi). Jauo likes this.

July 18, 2019, 16:40	Grid	#4
selig5576 Senior Member Selig Join Date: Jul 2016 Posts: 213 Rep Power: 10	From my experience with curvilinear grid (albeit still learning), you should calculate the metrics using central schemes. In this case (F(i+1) - F(I-1))/(2*dx))

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July 13, 2019, 13:35		#3
Jauo New Member hajo jllon Join Date: Jun 2019 Posts: 5 Rep Power: 6	thanks so you mean say for taking derivative of like function F along each stream line dFdm will be (Fi-F(i-1))/(x(i)-x(i-1) ?