XTROEM-FV: A new code for computational astrophysics based on very high-order finite volume methods. Part I: Magnetohydrodynamics

Jonatan Núñez-de La Rosa (1) , Claus-Dieter Munz (1)

1 Universität Stuttgart [Stuttgart]

The present work describes the building blocks of a new code for computational magnetohy-drodynamics based on very high-order finite volume methods on Cartesian meshes. Spatial high-order accuracy is obtained with a weighted essentially non-oscillatory (WENO) reconstruction operator up to seventh order, while the time discretization is performed with a fourth order Strong-Stability Preserving Runge-Kutta method. Based on a shock detection approach, the reconstruction operator employs a very high-order WENO scheme in smooth flow regions and a third order WENO scheme in those parts of the flow with discontinuities or shocks. The Generalized Lagrange multiplier method is employed to enforce the solenoidal constraint on the magnetic field. Extensive numerical computations in one and two space dimensions are reported. Convergence rates for smooth flows verify the high-order accuracy of the scheme, and tests with strong shocks, including the Orszag-Tang vortex, the cylindrical blast wave problem, the rotor problem, and the Kelvin-Helmholtz instability, confirm the robustness and stability of the approach.

Mots clés: methods: numerical; MHD; shock waves

Domaines: Physique Numérique [physics.comp-ph]; Analyse numérique [math.NA]

Jonatan Núñez-de La Rosa, Claus-Dieter Munz. XTROEM-FV: A new code for computational astrophysics based on very high-order finite volume methods. Part I: Magnetohydrodynamics. 2015. ⟨hal-01199723v2⟩