An Arbitrary-Lagrangian-Eulerian solver for relativistic detonation waves
Abstract
In this paper we study the dynamics of relativistic detonation waves theoretically and numerically. The reaction is physically accounted for by an extra term in the definition of the total energy density and by an additional equation for the evolution of the mass fraction of the reactant, while leaving formally unmodified the equations of mass and energy-momentum conservation. In this way, the Rankine-Hugoniot relations maintain the same formal structure of the inert version. For the numerical solution we use a finite volume ALE scheme with a second order TVD space-time reconstruction for the homogeneous part of the system, where the mesh velocity is chosen equal to the shock speed, and we combine it through operator splitting with a locally implicit algorithm for the potentially stiff reaction source terms that arise in the equation of the reactant. We furthermore propose a particularly efficient algorithm for the conversion from the conserved to the primitive variables, which for the relativistic Euler equations is known to be nontrivial. Following this approach, we can successfully solve the Zel'dovich-von Neumann-Doering profile of a relativistic detonation wave, up to Lorentz factors of the shock front γs∼ 7. Our analysis allowed us to highlight a new special relativistic effect, which has remained unnoticed so far. While in Newtonian detonations the Zel'dovich pressure jump decreases monotonically with the mass flux through the shock front, in the relativistic case it shows a minimum and then rises monotonically as a function of the mass flux. This may have interesting physical implications on the amount of energy that can be extracted from a relativistic detonation wave.
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BibTeX
@misc{rinaldi2026arbitrarylagrangianeulerian,
title = {{An Arbitrary-Lagrangian-Eulerian solver for relativistic detonation waves}},
author = {Sara Rinaldi and Olindo Zanotti and Michael Dumbser},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2606.27113},
eprint = {2606.27113},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2606.27113},
}
RIS
TY - UNPB
TI - An Arbitrary-Lagrangian-Eulerian solver for relativistic detonation waves
AU - Sara Rinaldi
AU - Olindo Zanotti
AU - Michael Dumbser
PY - 2026
DA - 2026/10/27
PB - arXiv
DO - 10.48550/arxiv.2606.27113
UR - https://arxiv.org/abs/2606.27113
AB - In this paper we study the dynamics of relativistic detonation waves theoretically and numerically. The reaction is physically accounted for by an extra term in the definition of the total energy density and by an additional equation for the evolution of the mass fraction of the reactant, while leaving formally unmodified the equations of mass and energy-momentum conservation. In this way, the Rankine-Hugoniot relations maintain the same formal structure of the inert version. For the numerical solution we use a finite volume ALE scheme with a second order TVD space-time reconstruction for the homogeneous part of the system, where the mesh velocity is chosen equal to the shock speed, and we combine it through operator splitting with a locally implicit algorithm for the potentially stiff reaction source terms that arise in the equation of the reactant. We furthermore propose a particularly efficient algorithm for the conversion from the conserved to the primitive variables, which for the relativistic Euler equations is known to be nontrivial. Following this approach, we can successfully solve the Zel'dovich-von Neumann-Doering profile of a relativistic detonation wave, up to Lorentz factors of the shock front γ_s∼ 7. Our analysis allowed us to highlight a new special relativistic effect, which has remained unnoticed so far. While in Newtonian detonations the Zel'dovich pressure jump decreases monotonically with the mass flux through the shock front, in the relativistic case it shows a minimum and then rises monotonically as a function of the mass flux. This may have interesting physical implications on the amount of energy that can be extracted from a relativistic detonation wave.
ER -