[D.B]

Hi All,
I am trying to understand the order of accuracy of various terms in OpenFOAM. I have one question the answer of which I haven't found in the threads already posted on this forum.

I want to understand about the order of accuracy of the boundary conditions in OpenFoam. On the first instance I am getting the impression that the BC's are always first order accurate irrespective of what numerical schemes are used.

The programmers guide of openfoam v3.0.0 states the usage of fixed value and fixed gradients BC's as follows :

BC_application.jpeg

It seems from this that the gradients are first order accurate when a fixedvalue BC is used and when fixedGradient BC is used, the value only affects the last cell centre value directly, which should make it first order accurate.

Can anyone please tell me if this is a correct conclusion to draw from this ?

Cheers,

[hjasak]

Boundary conditions are implemented consistently with the volumetric discretisation: second order accurate.

I think your problem starts from
(mis)understanding what bc information actually brings.

If you wish to test it, do a mesh refinement study and check the order of accuracy.

Hrv

[D.B]

Hi Hrvoje,
Thanks for the quick reply. Apologies for my (mis)understanding. I guess I have misunderstood the formulations given in eqns 2.38 and 2.40 where the face normal gradient is expressed as

 (∇φ)f  = φ b − φ P
             |d|

Which seemed like a first order approximation for the derivative, I am sure I have missed some other steps in my basics which would be making it second order accurate. If you have any inputs it would be helpful in improving my understanding.

Thanks,

[D.B]

Hi,
Can anyone please clear my doubt ? Am I mistaken ? or the example given in the guide is just for representation purposes and the fixedvalue and fixedGradient are implemented differently depending on the schemes ?

Cheers,

[anishtain4]

I think you are correct, the implementation is first order. however this does not affect the solution. Having a first order BC (as many other commercial software also have, specially when it comes to unstructured grid) does not reduce the order of accuracy of solutions.

[santiagomarquezd]

Hi, discretize this equation

div(nu grad(T)) = Q

with nu and Q constants and zero Dirichlet BC's at both sides of 1D problem. It has exact solution which is a parabola. With a pure second order discretization this problem is solved exactly (you need to implement second order BC's using the first and second cells near the boundary). Using the theory given in Hrvoje thesis you won't have the exact solution due to the first order treatment of BC's.

Regards!