Learning Forum

[shanmugapriyansv]

In ANSYS Fluent, when solving a transport equation involving a convective term of the form ∇·(ϕ𝐀), where ϕ is a scalar field and 𝐀 is a user-defined vector field (not the velocity field), how is this term discretized?

Specifically:

• Does Fluent expand ∇·(ϕ𝐀) as 𝐀·∇ϕ + ϕ∇·𝐀, or does it only compute 𝐀·∇ϕ?

• If 𝐀 is not the velocity field, is it sufficient to define the convective flux across a face as 𝐀·𝐧 (i.e., A·ds) in a UDF?

Thank you.

[SRP]

Hi,

You can check the discretization in the theory guide: 23.3.3. Evaluation of Gradients and Derivatives

I hope this helps.

[shanmugapriyansv]

Thank you sir, I have already learnt about discretization schemes in theory guide. I want to know something more in particular, like as I already mentioned, I want to know,

•  If Fluent expand ∇·(ϕ𝐀) as 𝐀·∇ϕ + ϕ∇·𝐀, or does it only compute 𝐀·∇ϕ? Because I have a equation in the form 𝐀·∇ϕ + ϕ∇·𝐀, if fluent expands and solves the convection term,  ∇·(ϕ𝐀) as 𝐀·∇ϕ + ϕ∇·𝐀, I can only solve the convection term as my whole equation, if fluent takes the convection term as only 𝐀·∇ϕ, then I have to introduce my ϕ∇·𝐀 as source term.

• Also, If 𝐀 is not the velocity field, is it sufficient to define the convective flux across a face as 𝐀·𝐧 (i.e., A·ds) or as phi*A.ds in a UDF?

Thank you. 

[SRP]

Hi,

Fluent scalar transport equations and most built-in convection handling use the conservative form.

If you formulate your equation in the non-conservative form and only provide A⋅∇ϕ to Fluent that computes only that gradient term, the ϕ∇⋅A term will be missing and must be provided as a source.

[shanmugapriyansv]

Thanks a lot sir, so, fluent will solve the conservative form which is ∇·(ϕ𝐀), that means it will solve for the expansion 𝐀·∇ϕ + ϕ∇·𝐀. Am I getting it right sir? Also, will it be sufficient for me to give 𝐀·𝐧 (i.e., A·ds) as my user defined convective flux to solve 𝐀·∇ϕ + ϕ∇·𝐀 ?