## ECHO

 swMATH ID: 22269 Software Authors: L. Del Zanna, O. Zanotti, N. Bucciantini, P. Londrillo Description: ECHO: a Eulerian conservative high-order scheme for general relativistic magnetohydrodynamics and magnetodynamics. We present a new numerical code, ECHO, based on an Eulerian Conservative High Order scheme for time dependent three-dimensional general relativistic magnetohydrodynamics (GRMHD) and magnetodynamics (GRMD). ECHO is aimed at providing a shock-capturing conservative method able to work at an arbitrary level of formal accuracy (for smooth flows), where the other existing GRMHD and GRMD schemes yield an overall second order at most. Moreover, our goal is to present a general framework, based on the 3+1 Eulerian formalism, allowing for different sets of equations, different algorithms, and working in a generic space-time metric, so that ECHO may be easily coupled to any solver for Einstein’s equations. Various high order reconstruction methods are implemented and a two-wave approximate Riemann solver is used. The induction equation is treated by adopting the Upwind Constrained Transport (UCT) procedures, appropriate to preserve the divergence-free condition of the magnetic field in shock-capturing methods. The limiting case of magnetodynamics (also known as force-free degenerate electrodynamics) is implemented by simply replacing the fluid velocity with the electromagnetic drift velocity and by neglecting the matter contribution to the stress tensor. ECHO is particularly accurate, efficient, versatile, and robust. It has been tested against several astrophysical applications, including a novel test on the propagation of large amplitude circularly polarized Alfven waves. In particular, we show that reconstruction based on a Monotonicity Preserving filter applied to a fixed 5-point stencil gives highly accurate results for smooth solutions, both in flat and curved metric (up to the nominal fifth order), while at the same time providing sharp profiles in tests involving discontinuities. Homepage: https://arxiv.org/abs/0704.3206 Related Software: RIEMANN; HLLE; HE-E1GODF; WhiskyMHD; HARM; Pluto; MOOD; Athena; Cosmos++; Einstein Toolkit; ADER-DG; Spritz; IllinoisGRMHD; GRHydro; Peano; FLASH; RAM; HARMRAD; WHAM; HLLC Cited in: 29 Publications
all top 5

### Cited by 71 Authors

 7 Dumbser, Michael 5 Balsara, Dinshaw S. 3 Kim, Jinho 2 Amano, Takanobu 2 Ciolfi, Riccardo 2 Cipolletta, Federico 2 Gaburro, Elena 2 Giacomazzo, Bruno 2 Kalinani, J. V. 2 Lee, Dongwook 2 Meliani, Zakaria 2 Mignone, Andrea 2 Tzeferacos, Petros 2 Wu, Kailiang 1 Bader, Michael 1 Bodo, Gianluigi 1 Bohn, Andy 1 Casse, Fabien 1 Castro, Manuel J. 1 Chen, Yuxi 1 Dauvergne, Frédéric 1 Deconinck, Herman 1 Del Zanna, L. 1 Delmont, P. 1 Deppe, Nils 1 Diener, Peter 1 Fambri, Francesco 1 Felker, Kyle Gerard 1 Field, Scott E. 1 Font, José A. 1 Foucart, François 1 Garain, Sudip K. 1 Giangrandi, E. 1 Giudici, B. 1 Goetz, Claus R. 1 Gombosi, Tamas I. 1 Grandclément, Philippe 1 Graziani, Carlo 1 Ha, Cong-Tu 1 Hébert, François 1 Keppens, Rony 1 Kidder, Lawrence E. 1 Lani, Andrea 1 Lee, Jaehwa 1 Lee, Youngjun 1 Lippuner, Jonas 1 Miller, Jonah M. 1 Munz, Claus-Dieter 1 Nunez, Manuel A. 1 Ott, Christian D. 1 Quintino, Tiago 1 Reyes, Adam 1 Scheel, Mark A. 1 Schnetter, Erik 1 Shahbazi, Khosro 1 Shu, Chi-Wang 1 Stone, James M. 1 Straub, Odele 1 Tang, Huazhong 1 Tavelli, Maurizio 1 Teukolsky, Saul A. 1 Toro, Eleuterio Francisco 1 van der Holst, Bart 1 van Marle, Allard Jan 1 Vanden Abeele, David 1 Vincent, F. H. 1 Vincent, Trevor 1 Vlasis, A. 1 Weinzierl, Tobias 1 Yalim, Mehmet Sarp 1 Zanotti, Olindo
all top 5

### Cited in 10 Serials

 16 Journal of Computational Physics 3 Classical and Quantum Gravity 2 Computers and Fluids 2 Journal of Scientific Computing 1 Mathematical Methods in the Applied Sciences 1 Numerische Mathematik 1 M$$^3$$AS. Mathematical Models & Methods in Applied Sciences 1 SIAM Journal on Scientific Computing 1 Living Reviews in Relativity 1 Axioms
all top 5

### Cited in 10 Fields

 25 Fluid mechanics (76-XX) 18 Numerical analysis (65-XX) 8 Partial differential equations (35-XX) 8 Relativity and gravitational theory (83-XX) 7 Astronomy and astrophysics (85-XX) 2 Optics, electromagnetic theory (78-XX) 1 Approximations and expansions (41-XX) 1 Mechanics of particles and systems (70-XX) 1 Mechanics of deformable solids (74-XX) 1 Statistical mechanics, structure of matter (82-XX)