Toward COSMOSDG: An Open-Sourced hpr-Adaptive Discontinuous Galerkin Code for Hyper-Resolved Studies in Astrophysics
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Nemergut, Daniel
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This project is one step on the path to developing COSMOSDG, a discontinuous Galerkin (DG) radiation hydrodynamic and magnetohydrodynamic (MHD) code, capable of high-order convergence on unstructured grids, with adaptive-mesh-refinement and moving-mesh capabilities, which allow for ultra-high resolution astrophysical simulations. An ongoing component of my thesis has been to add test problems to compare our code with other MHD codes. These include the Orszag-Tang, Alfven wave, linear wave, shock tube, radiative Bondi, and torus problems. Another goal of this project was to implement a divergence free magnetic field evolution within COSMOSDG. The current method of accomplishing this cannot be extended to higher order on unstructured or refined grids. I developed a new method to evolve the magnetic vector potential and then recover the divergence-free magnetic field from this. I then verified that the vector potential evolution actually achieved a divergence-free evolution and converged at the expected order. COSMOSDG currently has third- and fourth-order spatial convergence which requires the same order of time convergence. This was not possible with the previous time integration scheme in COSMOSDG. Therefore, I researched a new scheme that is valid up to fourth order with the advantage that it can be used to evolve using a higher timestep than previously possible. COSMOSDG uses a message passing interface (MPI) library to run simulations in parallel across a large number of processors. I explored the possibility of running multiple OpenMP processes that utilize shared memory within each MPI process. Finally, COSMOSDG is intended for open-sourced, public development and use. To prepare for this, I configured COSMOSDG to be documented with Doxygen, documented several files as a proof of concept, and created guidelines for code documentation going forward. This project also created a user guide and website for developers and researches to become familiar with COSMOSDG.