Re: [Libmesh-users] Is JxGradW Available??

[John P. <jwp...@gm...>]

On Mon, Nov 19, 2018 at 11:10 PM Brandon Denton <bld...@bu...>
wrote:

> Good evening.
>
> No. I'm trying to solve compressible navier-stokes in conservative form.
>
> dU/dt + (Ai + Bi)dU/dxi + d/dxi(cij*dU/dxj) = 0
>
> After taking the inner product of the weighting functions (W) and the
> residual, integrated over the domain and apply the divergence theorem, I
> get the integrand for the domain as
>
> W*(Ai + Bi)dU/dxi + dW/dxi*(cij*dU/dxj)
>
> With the surface integrand as
>
> -W*(cij*dU/dxj)
>
> To do the domain integral via quadrature, I would need dW/dxi at the
> quadrature point. I know I can get JxW and calculate all components of Ai,
> Bi, cij and dU/dxi using context.interior_value and
> context.interior_gradient (after proper reorganization).
>
> I just can't seem to figure out dW/dxi. Since I still need the geometric
> jacobian J, I was wondering if JxdW/dxi was available or some way I could
> calculate it.
>

The "W" in your context is a test function while the W in "JxW" is the
quadrature weight.

The FE::get_phi() and FE::get_dphi() functions provide access to the test
function values and shape derivatives, respectively. Have a look at the
various examples and you should be able to figure out what's going on.

-- 
John