Artificial viscosity smoothing
Artificial viscosity smoothing#
This section was contributed by Ryan Grove
Standard finite element discretizations of advection-diffusion equations introduce unphysical oscillations around steep gradients. Therefore, stabilization must be added to the discrete formulation to obtain correct solutions. In ASPECT, we use the Entropy Viscosity scheme developed by Guermond et al. in the paper . In this scheme, an artificial viscosity is calculated on every cell and used to try to combat these oscillations that cause unwanted overshoot and undershoot. More information about how does this is located at https://dealii.org/developer/doxygen/deal.II/step_31.html.
Instead of just looking at an individual cell’s artificial viscosity, improvements in the minimizing of the oscillations can be made by smoothing. Smoothing is the act of finding the maximum artificial viscosity taken over a cell \(T\) and the neighboring cells across the faces of \(T\), i.e.,
where \(N(T)\) is the set containing \(T\) and the neighbors across the faces of \(T\).
This feature can be turned on by setting the
Use artificial viscosity smoothing
flag inside the
Stabilization subsection inside the
subsection in your parameter file.
To show how this can be used in practice, let us consider the simple convection in a quarter of a 2d annulus cookbook in Section sec:shell-simple-2d, a radial compositional field was added to help show the advantages of using the artificial viscosity smoothing feature.
By applying the following changes shown below to the parameters of the already existing file
it is possible to produce pictures of the simple convection in a quarter of a 2d annulus such as the ones visualized in Figure Fig. 50.