A Global Simulation of an Accretion Disk with a Discontinuous Galerkin Method

As the demand for more accurate and efficient solving of highly non-linear time dependent equations are becoming more pressing, a novel Discontinuous Galerkin Spectral Element code has been developed by the department of Gasdynamics at Stuttgart University. This code has been used to simulate a global two dimensional magnetized fluid rotating around a compact central object, e.g. Accretion Disk. In this paper the various numerical details of the method, and the governing equations of the accretion disk are derived and expounded upon. The focus is on the gathering and elucidation of the theoretical information involved in simulating an accretion disk. An accretion disk can be described by the coupling of fluid dynamics and electromagnetism, known as magnetohydrodynamics. Smooth regions of the flow is solved with the DGSEM in order to achieve spectral accuracy, and in furtherance of resolving the regions of discontinuities, a finite volume WENO3 (weighted essential non-oscillatory) method is opted for a maximum of third order. At the cell boundaries the monotone flux is calculated with the Riemann solver known as the Lax-Friedrich solver. Since the MHD equations consist of conservation laws, the over-determined equations have been complemented with a Lagrange multiplier for divergence cleaning.The simulation was run on an equidistant square mesh with a resolution of 160x160 elements. The ideal magnetohydrodynamics equations were complimented with an adiabatic equation of state and a pseudo-Newtonian gravitational potential which approximates the effect of a non-rotating Kerr black hole. The magnetic field configuration chosen in this work was a toroidal field. The magneto-rotational instability is seen to quickly seed turbulence throughout the disk. Torsional waves also travel outwards eventually creating an excessive amount of spiralling.Validerat; 20150928 (global_studentproject_submitter