[Sral97]

Hello everyone,


I am fairly new to OpenFOAM and I have the following question:

The weak formulation of the laplace equation reads:

\integral_{\Omega} \phi * \laplace T d\Omega = - \integral_{\Omega} \grad{\phi} \grad{T} d\Omega,

assuming, that the testfunctions \phi are 0 on the boundary \partial \Omega.

But if i implement this in OpenFOAM like the following:

fvc::domainIntegrate(\phi * fvc::laplacian(T)).value()

and

fvc::domainIntegrate(fvc::grad(\phi) & fvc::grad(T)).value().

I obtain different values, but they should be the same in theory.

I already searched the internet.

Thanks already in advance

[Tobermory]

Presumably the answers are close, in which case what you have just demonstrated is that finite volume discretisation is not exact (2nd order at best), and so involves round-off errors.