[Tanmay.P]

I am new to CFD so pardon my stupid questions if they seem that way.

I was going through the Ansys Fluent Theory Manual recently along with some Udemy and Youtube Lectures to get started with CFD.

I have come across the Roe FDS scheme in Fluent Density Based Solver. It seemed like some sort of way to compute the face fluxes.

What I don't understand is why not just use simple upwind scheme to interpolate the variables from cell centro-ids to faces?

Since there is definitely something that I am missing. Why exactly was ROE-FDS introduced? How is it different from these discretization or face-interpolation schemes?
There is separate control for discretization schemes ( upwind, MUSCL, QUICK) as well under the same panel.

[Tanmay.P]

Okay since no one has replied anything,

I have still been working on finding answer resorting to multiple sources.

It seems more and more clear now,

Fundamentally to what I understood from these information pieces and discussion on Quora. This scheme is different than MUSCL and QUICK type discretization schemes which will still be used to interpolate values from cell centroids to faces. This ROE-FDS (approximate riemann solver) will be used when there is discontinuity at the boundary and needs to be captured (like in shocks) and that could be the reason why we see this formulation in DBS and not PBS.

I could be wrong but hopefully this will point any lost souls who come looking at this threads in a right direction.

Enclosing a few links below for reference which will make it more clear.

1) Comments and Christian's Answer to this quora question

2) This chimera CFD article on their implementation of these schemes

3) And ofcourse ANSYS Fluent's implementation theory


NOTE: if any of these information seems incorrect or needs a nudge in different direction to be 100% accurate, please do post a reply it would most definitely be helpful.

[danman155]

I actually can answer this one, as it was an important section from my Masters course in Finite-Volume Methods.

Fundamentally, the finite-volume method (which Fluent is) is looking to determine the fluxes across cell boundaries. This process can be separated into two steps: evaluating the face values on either side, and evaluating the flux given the two side values.

The spatial discretization scheme options you see farther down actually refer to the first step, while the flux type refers to the second.

As the main values stored are considered to be located in the center of the cell, a linear approximation is applied to each cell in order to determine the value at the cell face. This first-order vs second-order option is selecting whether to actually complete this extrapolation of the solution values from the cell to the face or not. The gradient options (Green-gauss vs Least squares) refers to *how* the linear approximation is calculated.

Once the face values on either side are determined (from the spatial reconstruction above), then the flux at the cell wall must be calculated. This is where the Flux Type comes in. As you have different solution values on either side of the face, this results in two different flux values. You could average the two sides, and which is what is used for the diffusion terms, but the convective terms are hyperbolic in nature and require upwinding. But this case is more complicated than basic scalar upwinding because you actually have multiple characteristic waves, potentially in different directions: what for example happens if the flow is moving left to right, but you have a shockwave moving right to left? This problem is particularly challenging as the Navier-Stokes eqn's are highly non-linear and the directions depend on the solution variables.

This problem is solved by what is known as the Reimann problem, which determines the characteristics which form from the discontinuous initial conditions. There are actually solvers which solve this problem exactly, but due to the non-linear nature of the problem, they all have to be iterative (which becomes extremely time consuming if you have to compute this iterative problem across every face, for every time evaluation of the residuals). As such, approximate methods were developed to solve the Reimann problem approximately, Roe-FDS and AUSM being two of them.

As such, the spatial discretization get you from the cell center *to* the face, while the flux type resolves the corresponding "upwinded" flux from that.

Hope that helps! Once you understand that, there's a lot of references online that can outline the exact method of implementation for all the various actual schemes..