OpenFOAM A&H Field dimension

ZX-zha · November 28, 2023, 23:50

Hi everyone. As I know, in the SIMPLE algorithm:
$AU=H-\nabla p$
Through the volume integral, the field A should have a dimension of [1 0 -1 0 0 0 0]
But actually, the dimension of A is [1 -3 -1 0 0 0 0]
which means OpenFOAM cancels out the impact of the volume integral in some way. I'm curious about it.

Could anyone tell me the reason? Very thanks.

Tobermory · December 1, 2023, 12:11

The dimensions of P are [1 -1 -2 ...] and U are [0 1 -1 ...], so gradP is [1 -2 -2 ...] and gradP/U is [1 -3 -1 ...] which are the dimensions that you report for A, so all working as intended.

As for the volume integral - all terms in the equation are integrated over volume, so it has no impact (i.e. it divides through on each side of the equation).

November 28, 2023, 23:50	OpenFOAM A&H Field dimension	#1
ZX-zha New Member ZP zhao Join Date: Oct 2023 Location: China Posts: 7 Rep Power: 2	Hi everyone. As I know, in the SIMPLE algorithm: $AU=H-\nabla p$ Through the volume integral, the field A should have a dimension of [1 0 -1 0 0 0 0] But actually, the dimension of A is [1 -3 -1 0 0 0 0] which means OpenFOAM cancels out the impact of the volume integral in some way. I'm curious about it. Could anyone tell me the reason? Very thanks.

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December 1, 2023, 12:11		#2
Tobermory Senior Member Join Date: Apr 2020 Location: UK Posts: 668 Rep Power: 14	The dimensions of P are [1 -1 -2 ...] and U are [0 1 -1 ...], so gradP is [1 -2 -2 ...] and gradP/U is [1 -3 -1 ...] which are the dimensions that you report for A, so all working as intended. As for the volume integral - all terms in the equation are integrated over volume, so it has no impact (i.e. it divides through on each side of the equation).