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Numerical solution of the compressible ideal magnetohydrodynamics system: Orszag-Tang Vortex Test. The scheme preserves positivity of density, positivity of internal energy, total energy, as well as involution constraints of the magnetic field. This work was carried out in collaboration with Prof. Murtazo Nazarov and Tuan Dao from Uppsala University (Division of Scientific Computing, Department of Information Technology). Check our article pre-print for more details Please set resolution of 2160p for full enjoyment.

Cold-plasma Diocotron instability using the Euler-Poisson model with a 'given' magnetic field. What you see in this movie is the evolution of the electron-density driven by the self-consistent electric field. Reproducing the Diocotron instability appears to be a mandatory milestone towards full Euler-Maxwell solvers that do not need to time-resolve cyclotron motions. This particular simulation uses time-step sizes 10,000 times larger than the electrostatic plasma and/or cyclotron oscillation periods.

Same as above, but the camera is placed on top. Youtube tends to default to low resolution: you might want to change resolution to 720p and watch it full screen.

Daru-Tenaud shock viscous-layer interaction. What is a challenging test? Is it a high Reynolds number problem? Well, not always. This is a seemingly innocuous low-Reynolds number problem, which exhibits a rather strong interaction of a shock wave with a viscous-layer. This is indeed a very challenging problem that can put to shame more than one compressible Navier-Stokes solver.

Fake triple point. This particular example contains discontinuous initial data with pressure contrast-ratio of one billion. It is not really possible to compute a genuine triple-point problem with a single-species model. The setup of the initial conditions is meant to "mimic", to some extent, the so-called triple-point problem while maximizing aesthetic impact.

Schardin's test (shock wave diffraction). Schlieren-like visualization of Schardin's test (right-moving shock towards a triangular obstacle). This simple test can be challenging for many schemes as it tends to produce negative density and/or negative internal energy near the vertices of the triangle, breaking down the whole computation. The numerical methods used to solve this problem make no special treatment of the vertices of the triangle: the scheme can be mathematically proven to be unconditionally robust (no mysterious hacks, no fixes, nor 'fudging factors' here).

Mach 3 step. This movie uses 640x1920 elements, so it's reasonable to enjoy it using full screen and 720p (HD). Here I am using a Q1-continuous finite element method with lumped mass matrix for the time derivative. Note the nice vortices originating in the upper left point where the three shocks meet. This is one of my very first computations of Euler's equations (early 2017). For more recent results, of much better quality, you might want to check Matthias Maier webpage.

Normal Field Instability with uniform magnetic field: also called Rosensweig instability. We are using using a two-phase diffuse-interface ferrofluid model.

Normal Field Instability with non-uniform magnetic field (a.k.a. the hedgehog). We are using using a two-phase diffuse-interface ferrofluid model.