Error Analysis of the Thornado Supernova Simulation Code

Abstract

The iron core collapse of a supernova throws 1.5 solar masses at speeds up to 35% the speed of light into a space with radius 50km, which creates a high density environment capable of generating neutrinos, producing gravitational waves, and driving chemical evolution of matter past iron. By designing a simulation of the process, we can better understand the origins and properties of these rare phenomena which are not seen anywhere else in the universe. Typically, supernovas are simulated with a finite volume method, but we want to incorporate a Nodal Discontinuous Galerkin Method to better utilize high performance computing because the DG method allows us to increase precision without increasing the number of computational elements. This project focuses on the fluid dynamics during collapse and the resulting shockwaves. To understand this, we improved on an existing simulation by comparing benchmark tests against published and theoretical results to identify and correct sources of error. The DG Method creates discontinuous functions across computational elements by solving the Euler fluid equations computed over Runge-Kutta time steps. The DG method allows for discontinuous functions to be built from polynomials defined in individual elements; however, it can lead to unphysical oscillation near discontinuities. We apply the characteristic slope limiter to reduce these affects, but when applied globally it leads to a 1% increase in absolute error. By introducing a Trouble Cell Indicator, which marks certain fluid elements based on the rate of change of observables, we can constrain the limiter to elements near shocks and manage the resulting absolute error. By constraining the limiter to discontinuous regions, we can remove what we know will be unrealistic without impacting naturally occurring oscillations.