How to write Dot Product of Gradient and UDSI_G

goksue · January 3, 2022, 05:38

Hello!
I have to define the source term of the UDS Transport Equation as ∇. (f(T)∇T) where the function f is like a coefficient dependent on T and I already defined it. The problem is dot product of the gradient. How can I define a Gradient vector so that I can take the dot product?? Thank you so much !

LuckyTran · January 3, 2022, 05:57

The dot product is just notation, not an operator. What you have is the divergence operator (del dotted with the gradient) which is a Laplacian if you actually carried out the operator. But you shouldn't actually do this because this is FVM...

If you take this term and integrate it over the control volume you end up with surface integrals of gradients. So really your task is to find the gradients on the cell faces and add them all up.

January 3, 2022, 05:38	How to write Dot Product of Gradient and UDSI_G	#1
goksue New Member goksu Join Date: Jan 2022 Posts: 3 Rep Power: 4	Hello! I have to define the source term of the UDS Transport Equation as ∇. (f(T)∇T) where the function f is like a coefficient dependent on T and I already defined it. The problem is dot product of the gradient. How can I define a Gradient vector so that I can take the dot product?? Thank you so much !

January 3, 2022, 05:57		#2
LuckyTran Senior Member Lucky Join Date: Apr 2011 Location: Orlando, FL USA Posts: 5,668 Rep Power: 65	The dot product is just notation, not an operator. What you have is the divergence operator (del dotted with the gradient) which is a Laplacian if you actually carried out the operator. But you shouldn't actually do this because this is FVM... If you take this term and integrate it over the control volume you end up with surface integrals of gradients. So really your task is to find the gradients on the cell faces and add them all up.