why div(grad) is not equal to laplacian

JasonWang3 · May 19, 2017, 05:57

Hi all

I did a test about div(grad(Ux)) and laplacian(Ux), but got different results. Why did it happen?

However, div(mesh.Sf()*snGrad(Ux)) is equal to laplacian(Ux).

I am looking for a way to calculate the second derivatives of Ux dux2dy2. I am not sure grad(grad(Ux).component(vector::Y))..component(vec tor::Y) is right or not.

JasonWang3 · May 19, 2017, 09:15

I test using icoFoam and 'cavity' in the tutorial.

Did anyone meet the same problem?

randolph · July 2, 2018, 12:46

Quote:

Originally Posted by JasonWang3

I test using icoFoam and 'cavity' in the tutorial.

Did anyone meet the same problem?

div(grad) is not equal to Laplacian in the discrete sense, although they are equal in the continuous domain. You can show this by comparing the D2 matrix with the D1*D1 matrix. I know this is true in FDM. I think also apply to FVM.

May 19, 2017, 05:57	why div(grad) is not equal to laplacian	#1
JasonWang3 Member Xinguang Wang Join Date: Feb 2015 Posts: 45 Rep Power: 11	Hi all I did a test about div(grad(Ux)) and laplacian(Ux), but got different results. Why did it happen? However, div(mesh.Sf()*snGrad(Ux)) is equal to laplacian(Ux). I am looking for a way to calculate the second derivatives of Ux dux2dy2. I am not sure grad(grad(Ux).component(vector::Y))..component(vec tor::Y) is right or not. amuzeshi likes this.

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May 19, 2017, 09:15		#2
JasonWang3 Member Xinguang Wang Join Date: Feb 2015 Posts: 45 Rep Power: 11	I test using icoFoam and 'cavity' in the tutorial. Did anyone meet the same problem?