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(sec:benchmarks:advection)=

Advection stabilization benchmarks

The underlying PDEs of the temperature and compositional field are typically advection-dominated and as such, require a stabilization scheme, see {ref}sec:advection-stabilization for an introduction for the methods implemented in ASPECT.

We have several benchmarks to test the robustness, quality of solutions (size of overshoots, smearing of sharp interfaces). Here, we give a short summary of the benchmarks implemented:

  • Dropping box (benchmarks/drop_*.prm): This is a simple 2d box with a prescribed, constant, vertical velocity. An initial condition creates a square box with a high temperature, which is advected vertically. See {numref}fig:benchmark-drop.

  • Rotating Shapes: benchmarks/rotate_shape_*.prm: A collection of shapes in a 2d box rotated by 360 degrees by a prescribed velocity. See {numref}fig:benchmark-rotate-shape.

Both benchmarks have the identical setup in the temperature and a compositional field. The only difference is that the temperature equation contains a (small) physical diffusion term.

Description of benchmark files

<img src="drop.png" />

 Dropping box benchmark at final time. Left: entropy viscosity. Right: SUPG.

<img src="rotate_shape.png" />

 Rotating shapes benchmark at final time: Left: reference. Middle: Entropy viscosity. Right: SUPG.

:::{toctree} ../README.md :::