CAFE: A New Relativistic MHD Code

TL;DR

The paper introduces CAFE, a new 3D relativistic MHD code, demonstrating its capabilities through extensive standard tests in relativistic hydrodynamics and magnetohydrodynamics, including shock, instability, and blast wave scenarios.

Contribution

CAFE is a novel independent code for 3D relativistic MHD, implementing advanced shock capturing and divergence control methods, with comprehensive testing in various regimes.

Findings

Successfully tested with standard RMHD and RHD problems

Demonstrated accurate shock capturing with high-order methods

Validated divergence control techniques

Abstract

We introduce CAFE, a new independent code designed to solve the equations of Relativistic ideal Magnetohydrodynamics (RMHD) in 3D. We present the standard tests for a RMHD code and for the Relativistic Hydrodynamics (RHD) regime since we have not reported them before. The tests include the 1D Riemann problems related to blast waves, head-on collision of streams and states with transverse velocities, with and without magnetic field, which is aligned or transverse, constant or discontinuous across the initial discontinuity. Among the 2D and 3D tests, without magnetic field we include the 2D Riemann problem, a one dimensional shock tube along a diagonal, the high speed Emery wind tunnel, the Kelvin-Helmholtz instability, a set of jets and a 3D spherical blast wave, whereas in the presence of a magnetic field we show the magnetic rotor, the cylindrical explosion, a case of Kelvin-Helmholtz instability and a 3D magnetic field advection loop. The code uses High Resolution Shock Capturing methods and we present the error analysis for a combination that uses the HLLE flux formula combined with linear, PPM and fifth order WENO reconstructors. We use the flux-CT and the divergence cleaning methods to control the divergence free magnetic field constraint.