In general, this MR should allow `\varrho`

and `\nu`

to be varied in the tests in test/freeflow/navierstokes. Background is that they are in the input files already but sometimes cannot be varied so far.

`\partial_t \left(\varrho u\right) + \partial_x\left(\varrho u u\right) + \partial_y \left(\varrho u v\right) -2\partial_x\left(\varrho\nu\partial_x u\right) - \partial_y\left(\varrho\nu\left(\partial_y u + \partial_x v\right)\right) + \partial_x p - \varrho g_x - q_{v,x} =0 `

`\partial_t \left(\varrho v\right) + \partial_x\left(\varrho u v\right) + \partial_y \left(\varrho v v\right) -2\partial_y\left(\varrho\nu\partial_y v\right) - \partial_x\left(\varrho\nu\left(\partial_y u + \partial_x v\right)\right) + \partial_y p - \varrho g_y - q_{v,y} =0 `

- Donea

Now the source term is calculated in a more automatic fashion.

- Sincos

Now the source term is calculated in a more automatic fashion.

- Angeli

Let `f(t) = e^{-5\nu\pi^2 t}.`

Then terms in f(t) are storage and diffusion. Terms in f(t)^2 are advection and pressure gradient. As terms in f(t) and f(t)^2 have to cancel separately, the pressure gradient need a density like the advection term. When running the old code version it looks as if it was OK for `\varrho \neq 1`

. But if I output the pressure and advective terms directly, I see that with my version they fit each other and with the current they don't. I suppose it is just other terms much larger that the pressure and advective terms don't have such a big effect.

- Channel

1d and 3d already use the dynamic viscosity, as it should be. With this MR also 2d uses the dynamic viscosity. Without the change of this MR, calculations of `\varrho\neq 1`

are also meaningful (as the pressure does only enter the calculation in one single cell) but the analytical solution and with it the L2 errors where not.

- Kovasnay

It converges with other densities, if UMFPack is used instead of BIGCStab. To figure out where the density has to go, I was inspired by https://downloads.hindawi.com/archive/2014/959038.pdf. Without the change of this MR, calculations of `\varrho\neq 1`

are also meaningful (as the pressure `p(x)`

does only enter the calculation for one x-value) but the analytical solution and with it the L2 errors where not.

Closes #984 (closed)