We investigate the Kelvin-Helmholtz instability setup of Fjordholm et al. [1], where the sharp interface in the initial condition is randomly perturbed. The simulation is done with an entropy stable DGSEM with polynomial degree N=3 and 32 x 32 grid cells. The final time is t = 2.0. Trixi.jl [2] is used with the setup found in examples/tree_2d_dgsem/elixir_euler_kelvin_helmholtz_instability_fjordholm_etal.jl.

The following gif is showing 100 simulation results of the density distribution for different random interface perturbations:

Here is the average density distribution of all 100 results:

[1] Ulrik S. Fjordholm, Roger Käppeli, Siddhartha Mishra, Eitan Tadmor. Construction of approximate entropy measure valued solutions for hyperbolic systems of conservation laws, 2014. (https://arxiv.org/abs/1402.0909)
[2] Trixi.jl, a numerical simulation framework for hyperbolic conservation laws written in Julia. (https://github.com/trixi-framework/Trixi.jl)