What's the definition of 'numerical boundary layer' and what's the physical mean of it? Thank you!!!

(1). numerical boundary layer is likely = numerical analysis of boundary layer flows, or = numerical boundary layer analysis. (2). So, numerical = numerical analysis.

it's wrong

One answer (perhaps not the only one) has to do with the error generated by poor numerical resolution of a boundary region.

Generally, the physical boundary layer thickness (flat plate theory) for a laminar flow is scaled by

delta / x = (nu / (x * U))^(0.5),

where delta is the boundary layer thickness, x is the distance from the leading edge of the plate, nu is the kinematic viscosity of the fluid, and U is the free stream velocity of the flow.

Of course, U * x / nu = Re, the Reynolds number for the flow.

These results above are not from CFD but from classical Fluid Mechanics. More info can be obtained from the texts by Schlichting (Boundary Layer Theory) or any of several modern books on convective heat transfer.

Now to CFD:

If the advection (or convection) terms in the NS equations are differenced using upwinding, an analysis of the numerical error due to the difference approximations will often show an error term of the form

ExtraVis = C| Rec |(Ur - Uc)

C is a constant based on upwinding parameters (zero for central differencing), Ur and Uc are the upstream and centered discrete velocities at the centers of computational cells, and

dx is the width of the computational cell parallel (not normal) to the solid boundary.

Rec is the "Cell Reynolds Number", U * dx / nu .

This analysis technique is detailed by C. W. Hirt, "Heuristic Stability Theory for Finite-Difference Equations," J. Comp. Physics, v. 8, p. 119 (1968).

The point is that ExtraVis, above, adds to the natural viscosity of the fluid in the difference equations due to the upwinding, generating a numerical viscosity. This can have the effect of artificially increasing the thickness of the COMPUTED boundary layer.

delnum / x = (nu*(1 + ExtraVis) / (x * U))^(0.5)

where delnum is the thickness of the numerical boundary layer.

The details of this analysis of course depend very much on the details of the differencing employed; this is just another demonstration that inadequate spatial resolution leads to errors in the computed flow.

I have heard the term numerical boundary layer before and its use differed from that explained in the previous post.

A boundary condition applied in a CFD calculation is not generally an exact physical boundary condition,it is some approximation. The distance from this boundary condition until the point at which the solution can be trusted is called the numerical boundary layer.

Han

In which context did you see the term "numerical boundary layer"?

Adrin Gharakhani

(1). I think, it is just something interesting.

Thank you, Adrin. I notice the term in the book 'Incompressible computational fluid dynamics' (G.E. Karniadakis, Orszag, Ronquist and Patera). This term appears in the context of estimation of error. I consider the above answer by Leo may be correct.

(1). The person who invented it is responsible for it. So, if he is still alive, why not e-mail him to get his direct comment. (2). Apprently, he is from FEM world.

I have used the term "numerical boundary layer" in my publications to denote a wall boundary layer model that mimimcs the physical phenomenon but as far as the characteristic length scales are concerned the numerical model is not exactly the same as in the physical world. So, this is a "numerical" and not "physical" boundary layer, since it solves the same physical boundary layer equations, but at a different length scale - say for thinner layers than physics would dictate.

Adrin Gharakhani

(1). Perhaps "wall layer", "modelled wall layer", or "pseudo wall layer" would be better than "numerical boundary layer". (2). The other way to do is to use "numerically induced boundary layer".

Unfortunately I have seen the term used in other contexts so it really is a sort of misused term that shouldn't be taken to have a general meaning ie it should be explicitly explained whenever it's used.

Agree. Strictly (or even loosely) speaking "numerical boundary layer" doesn't mean anything. And indeed, I usually put mine in quotes and explain (or refer to a publication that does) what I mean by the term.

Adrin Gharakhani