Advection stabilization benchmarks#

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

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 Figure 1.

  • Rotating Shapes: benchmarks/rotate_shape_*.prm: A collection of shapes in a 2d box rotated by 360 degrees by a prescribed velocity. See Figure 2.

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.

../../../../../_images/drop.png

Fig. 188 Dropping box benchmark at final time. Left: entropy viscosity. Right: SUPG.#

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Fig. 189 Rotating shapes benchmark at final time: Left: reference. Middle: Entropy viscosity. Right: SUPG.#