[Tommy Chen]

Just as the question

I have been always confused about these terms.
What eactly are the 'point implicit' and 'line implicit' solver ?

Why someone has told me that the source term in the turbulence model can be treated as explict while the mean flow is treated as implicit.
What makes me more confused is that he said that the turbulence model could be treated as 'point implicit', I think I understand pretty well about the implicit cfd solver, however, what is the 'point and line implicit' eactly ?

Thanks ~~~

[mprinkey]

Originally Posted by Tommy Chen

Just as the question

I have been always confused about these terms.
What eactly are the 'point implicit' and 'line implicit' solver ?

Why someone has told me that the source term in the turbulence model can be treated as explict while the mean flow is treated as implicit.
What makes me more confused is that he said that the turbulence model could be treated as 'point implicit', I think I understand pretty well about the implicit cfd solver, however, what is the 'point and line implicit' eactly ?

Thanks ~~~

Point implicit generally means that you solve for an unknowns (or a group of unknowns) that are all located in a single computational cell. The size of the system will be from 1 to a few degrees of freedom.

Line implicit generally applies to structured finite volume/difference formulations where you have a clear axis directions. You take the couplings along that direction as implicit and all of the terms coupling along other directions as explicit. This gives you "lines" of coupled equations. For linear systems, these can be solved efficiently with (block) Thomas algorithms (aka tri-diagonal solvers).

Point implicit comes up in reacting flows, sometimes in multiphase flows with strong inter-phase heat or momentum transfer. Line implicit schemes can be used for direction smoothing (solving wall normal behavior in boundary layers) or operator splitting (making quick approximate work of the viscous/diffusion terms in fractional-step methods). They are also part of the ADI scheme that has various uses.

These are all different from segregated schemes (that solve full field implicit updates one variable at a time) or coupled schemes (that linearize with Picard or Newton or false timestepping) to solve full field values of all fields at the same time.

Most of the differences in various CFD techniques come down to how we choose to retain or lag coupling among neighbor cells and the various field variables. If you run into a case were convergence is slow or unstable, it is worth reviewing what lagging assumptions have been made and considered which might be causing the stiffness or instability.

[Tommy Chen]

Originally Posted by mprinkey

Point implicit generally means that you solve for an unknowns (or a group of unknowns) that are all located in a single computational cell. The size of the system will be from 1 to a few degrees of freedom.

Line implicit generally applies to structured finite volume/difference formulations where you have a clear axis directions. You take the couplings along that direction as implicit and all of the terms coupling along other directions as explicit. This gives you "lines" of coupled equations. For linear systems, these can be solved efficiently with (block) Thomas algorithms (aka tri-diagonal solvers).

Point implicit comes up in reacting flows, sometimes in multiphase flows with strong inter-phase heat or momentum transfer. Line implicit schemes can be used for direction smoothing (solving wall normal behavior in boundary layers) or operator splitting (making quick approximate work of the viscous/diffusion terms in fractional-step methods). They are also part of the ADI scheme that has various uses.

These are all different from segregated schemes (that solve full field implicit updates one variable at a time) or coupled schemes (that linearize with Picard or Newton or false timestepping) to solve full field values of all fields at the same time.

Most of the differences in various CFD techniques come down to how we choose to retain or lag coupling among neighbor cells and the various field variables. If you run into a case were convergence is slow or unstable, it is worth reviewing what lagging assumptions have been made and considered which might be causing the stiffness or instability.

Thank you so much for the answer ~
It is so helpful!

Could you list some classical papers that could help me understand it further if I may ask for . Thanks