Van Duker, N. (AM) – A Random Choice Hybrid Method for Resolving Shock Placement Errors in 1D Relativistic Hydrodynamics with Transverse Velocities

This report presents a one-dimensional Random Choice-based hybrid method for simulating special relativistic hydrodynamics (SRHD) flow problems. The proposed scheme combines a high-order accurate method and a random choice method, selectively applying the first to smooth flows and the second to shocks and discontinuities. This hybrid approach addresses the issue of incorrect wave placements in the presence of significant transverse velocity, commonly encountered in one-dimensional SRHD shock tube tests. In support of this development, we present a modified shock/contact detection switch, specifically tuned for relativistic flows. We find that our method improves both the accuracy and computational performance when compared against existing methods on a well-known family of pathological shock tube problems. Our analysis of these pathological problems provides a path forward for further improving existing higher-dimensional methods.

Event Host: Nathan Van Duker, Ph.D Student, Applied Mathematics

Advisor: Dongwook Lee