# The SolKz Stokes benchmark

# The SolKz Stokes benchmark#

The SolKz benchmark is another variation on the same theme as The SolCx Stokes benchmark,
it solves a Stokes problem with a spatially variable
viscosity, but this time the viscosity is not a discontinuous function.
Instead, it grows exponentially with the vertical coordinate so that its
overall variation is again \(10^6\). The forcing is again chosen by imposing a
spatially variable density variation. For details, refer again to [Duretz *et al.*, 2011].

The following input file, only a small variation of the one in the previous
section, solves the benchmark (see `benchmarks/solkz/`

):

```
# A description of the SolKZ benchmark for which a known solution
# is available. See the manual for more information.
set Additional shared libraries = ./libsolkz.so
############### Global parameters
set Dimension = 2
set Start time = 0
set End time = 0
set Output directory = output
set Pressure normalization = volume
############### Parameters describing the model
subsection Geometry model
set Model name = box
subsection Box
set X extent = 1
set Y extent = 1
end
end
subsection Boundary velocity model
set Tangential velocity boundary indicators = left, right, bottom, top
end
subsection Material model
set Model name = SolKzMaterial
end
subsection Gravity model
set Model name = vertical
end
############### Parameters describing the temperature field
subsection Initial temperature model
set Model name = perturbed box
end
############### Parameters describing the discretization
subsection Discretization
set Stokes velocity polynomial degree = 2
set Use locally conservative discretization = false
end
subsection Mesh refinement
set Initial adaptive refinement = 0
set Initial global refinement = 4
end
############### Parameters describing what to do with the solution
subsection Postprocess
set List of postprocessors = SolKzPostprocessor, visualization
end
```

The output when running ASPECT on this parameter file looks similar to the one shown for the SolCx case. The solution when computed with one more level of global refinement is visualized in Fig. 147 and Fig. 148. The velocity solution computed with three more levels of global refinement and plotted over the viscosity field is shown in Fig. 149.