[Paper Review] Reliability of astrophysical jet simulations in 2D: On inter-code reliability and numerical convergence

Martin Krause, M. Camenzind|ArXiv.org|Oct 22, 2001

Computational Fluid Dynamics and Aerodynamics12 references19 citations

TL;DR

This study evaluates the numerical convergence and inter-code reliability of 2D astrophysical jet simulations using the NIRVANA MHD code, comparing results with two established codes (Lind et al. 1989 and Kössl & Müller 1988). It finds that while global jet properties converge at ~100 ppb in hydrodynamic cases, the magnetized jet simulation fails to converge due to a moving Mach disk, and high-resolution runs reveal new instabilities like small-scale Kelvin-Helmholtz and Rayleigh-Taylor modes that enhance mass entrainment.

ABSTRACT

In the present paper, we examine the convergence behavior and inter-code reliability of astrophysical jet simulations in axial symmetry. We consider both, pure hydrodynamic jets and jets with a dynamically significant magnetic field. The setups were chosen to match the setups of two other publications, and recomputed with the MHD code NIRVANA. We show that NIRVANA and the two other codes give comparable, but not identical results. We find that some global properties of a hydrodynamical jet simulation, like e.g. the bow shock velocity, converge at 100 points per beam radius (ppb) with NIRVANA. The situation is quite different after switching on the toroidal magnetic field: In this case, global properties converge even at 10 ppb. In both cases, details of the inner jet structure and especially the terminal shock region are still insufficiently resolved, even at our highest resolution of 70 ppb in the magnetized case and 400 ppb for the pure hydrodynamic jet. In the case of our highest resolution simulation, we can report two new features: First, small scale Kelvin-Helmholtz instabilities are excited at the contact discontinuity next to the jet head. This slows down the development of the long wavelength Kelvin-Helmholtz instability and its turbulent cascade to smaller wavelengths. Second, the jet head develops Rayleigh-Taylor instabilities which manage to entrain an increasing amount of mass from the ambient medium with resolution. This region extends in our highest resolution simulation over 2 jet radii in the axial direction.

Motivation & Objective

• To assess the numerical convergence of 2D astrophysical jet simulations using the NIRVANA MHD code.
• To compare results across multiple codes (NIRVANA, Lind et al. 1989, Kössl & Müller 1988) to evaluate inter-code reliability.
• To investigate how artificial viscosity and numerical resolution affect the simulation of jet structures and shock dynamics.
• To determine the resolution requirements for convergence of global jet parameters and internal structures like the terminal shock and contact discontinuity.
• To examine the emergence of instabilities—Kelvin-Helmholtz and Rayleigh-Taylor—under varying resolution in both hydrodynamic and magnetized jet scenarios.

Proposed method

• Recomputed benchmark jet simulations (hydrodynamic and magnetized) using the NIRVANA MHD code with varying spatial resolutions (10 to 400 points per beam radius).
• Applied axial symmetry (2D) to model astrophysical jets under conditions matching prior studies by Lind et al. (1989) and Kössl & Müller (1988).
• Used finite-volume MHD solvers with Rusanov flux and artificial viscosity to handle shocks and discontinuities.
• Tracked convergence of global properties such as bow shock velocity and Mach disk position across resolution levels.
• Analyzed time-series data and contour plots to identify development of instabilities and structural evolution in the jet head and cocoon.
• Performed high-resolution simulations (up to 400 ppb for hydrodynamic, 70 ppb for magnetized) to detect resolution-dependent features like small-scale turbulence and mass entrainment.

Experimental results

Research questions

• RQ1 To what extent do different MHD codes produce convergent results for the same astrophysical jet setup?
• RQ2 How does numerical resolution affect the convergence of global jet parameters such as bow shock velocity and Mach disk position?
• RQ3 What role does artificial viscosity play in differences between code outputs, especially in shock and contact discontinuity resolution?
• RQ4 Do high-resolution simulations reveal new physical features—such as small-scale instabilities or enhanced mass entrainment—that are missed at lower resolution?
• RQ5 Why does the magnetized jet simulation with NIRVANA show a moving Mach disk, indicating non-convergence, despite apparent convergence in global parameters?

Key findings

• Global properties of hydrodynamic jet simulations converge at approximately 100 points per beam radius (ppb) in the NIRVANA code.
• The magnetized jet simulation shows convergence of global features (e.g., bow shock shape, velocity) at as low as 10 ppb, but the Mach disk moves toward the inflow boundary, indicating non-convergence.
• At the highest resolution (400 ppb for hydrodynamic, 70 ppb for magnetized), small-scale Kelvin-Helmholtz instabilities emerge ahead of long-wavelength modes, damping their growth and delaying turbulent cascade.
• In the highest-resolution magnetized simulation, Rayleigh-Taylor instabilities develop and entrain increasing mass from the ambient medium, extending over 2 jet radii in the axial direction.
• Despite high resolution, the inner jet structure and terminal shock region remain poorly resolved, with turbulent evolution persisting even at 400 ppb in the hydrodynamic case.
• The discrepancy between FLOW and NIRVANA in the magnetized case—especially the non-convergent Mach disk in NIRVANA—challenges previous simulation results and suggests code-dependent convergence behavior, particularly under magnetic field influence.