Slimplectic Integrators: Variational Integrators for General Nonconservative Systems
This work provides a novel numerical method for astrophysicists needing long-term integration of systems with nonconservative interactions, such as gas dynamics or tidal dissipation.
The authors develop 'slimplectic' integrators, a new type of numerical integrator that preserves the benefits of symplectic integrators while being applicable to nonconservative systems, enabling accurate long-term tracking of energy and momenta in dissipative astrophysical problems.
Symplectic integrators are widely used for long-term integration of conservative astrophysical problems due to their ability to preserve the constants of motion; however, they cannot in general be applied in the presence of nonconservative interactions. In this Letter, we develop the "slimplectic" integrator, a new type of numerical integrator that shares many of the benefits of traditional symplectic integrators yet is applicable to general nonconservative systems. We utilize a fixed time-step variational integrator formalism applied to the principle of stationary nonconservative action developed in Galley, 2013; Galley, Tsang & Stein, 2014. As a result, the generalized momenta and energy (Noether current) evolutions are well-tracked. We discuss several example systems, including damped harmonic oscillators, Poynting-Robertson drag, and gravitational radiation reaction, by utilizing our new publicly available code to demonstrate the slimplectic integrator algorithm. Slimplectic integrators are well-suited for integrations of systems where nonconservative effects play an important role in the long-term dynamical evolution. As such they are particularly appropriate for cosmological or celestial N-body dynamics problems where nonconservative interactions, e.g. gas interactions or dissipative tides, can play an important role.