Does OpenFOAM Have an Implicit Gradient?

SeanOpenfoam · October 8, 2020, 18:20

Dear all,

Hello! I'm new to CFD and OpenFOAM, but I've played around with creating and modifying the source code for a little bit, and I have a question about OpenFOAM's implicit schemes.

I've read on this forum that OpenFOAM does not have an implicit formulation for the gradient of a variable.

The explanation, as I understand it, is that under certain conditions, such as a uniform mesh, an implicit gradient formulation would produce a coefficient matrix with zeros on the diagonal. We can, by hand, write out a 1D mesh of a few cells and a single variable, discretize that variable, and see for ourselves how those zeros are produced.

However, everything I've seen so far is at least a couple of years old, and with OpenFOAM v8 now available, I'm wondering if anything has changed. I haven't seen a "grad" scheme listed under the FVM namespace in the c++ source guide, but perhaps I just missed something.

dlahaye · October 9, 2020, 04:43

Chapter 9 of the book Moukalled-Darwish-Mangani [1] does confirm explicit only.

Not sure where advanced linear algebra as e.g. [2] allows to by-pass the numerical linear algebra argument that you validly raise.

[1]: Moukalled, Manga and Darwish, The finite volume method in computational fluid dynamics, Springer 2015 , http://www.springer.com/gp/book/9783319168739

[2]: OpenFoam-PETSc interface: https://develop.openfoam.com/modules/external-solver

October 8, 2020, 18:20	Does OpenFOAM Have an Implicit Gradient?	#1
SeanOpenfoam New Member Sean Join Date: Nov 2014 Posts: 3 Rep Power: 12	Dear all, Hello! I'm new to CFD and OpenFOAM, but I've played around with creating and modifying the source code for a little bit, and I have a question about OpenFOAM's implicit schemes. I've read on this forum that OpenFOAM does not have an implicit formulation for the gradient of a variable. The explanation, as I understand it, is that under certain conditions, such as a uniform mesh, an implicit gradient formulation would produce a coefficient matrix with zeros on the diagonal. We can, by hand, write out a 1D mesh of a few cells and a single variable, discretize that variable, and see for ourselves how those zeros are produced. However, everything I've seen so far is at least a couple of years old, and with OpenFOAM v8 now available, I'm wondering if anything has changed. I haven't seen a "grad" scheme listed under the FVM namespace in the c++ source guide, but perhaps I just missed something.

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October 9, 2020, 04:43		#2
dlahaye Senior Member Domenico Lahaye Join Date: Dec 2013 Posts: 798 Blog Entries: 1 Rep Power: 17	Chapter 9 of the book Moukalled-Darwish-Mangani [1] does confirm explicit only. Not sure where advanced linear algebra as e.g. [2] allows to by-pass the numerical linear algebra argument that you validly raise. [1]: Moukalled, Manga and Darwish, The finite volume method in computational fluid dynamics, Springer 2015 , http://www.springer.com/gp/book/9783319168739 [2]: OpenFoam-PETSc interface: https://develop.openfoam.com/modules/external-solver