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Stellar systems are broadly divided into collisional and non-collisional. Thelatter are large-N systems with long relaxation timescales and can be simulateddisregarding two-body interactions, while either computationally expensivedirect N-body simulations or approximate schemes are required to properly modelthe former. Large globular clusters and nuclear star clusters, with relaxationtimescales of the order of a Hubble time, are small enough to display somecollisional behaviour and big enough to be impossible to simulate with direct$N$-body codes and current hardware. We introduce a new method to simulatecollisional stellar systems, and validate it by comparison with direct $N$-bodycodes on small-$N$ simulations. The Multi-Particle collision for Dense stellarsystems Code (MPCDSS) is a new code for evolving stellar systems with theMulti-Particle Collision method. Such method amounts to a stochastic collisionrule that allows to conserve exactly the energy and momentum over a cluster ofparticles experiencing the collision. The code complexity scales with $N \logN$ in the number of particles. Unlike Monte-Carlo codes, MPCDSS can easilymodel asymmetric, non-homogeneous, unrelaxed and rotating systems, whileallowing us to follow the orbits of individual stars. We evolve small ($N = 3.2\times 10^4$) star clusters with MPCDSS and with the direct-summation codeNBODY6, finding a similar evolution of key indicators. We then simulatedifferent initial conditions in the $10^4 - 10^6$ star range. MPCDSS bridgesthe gap between small, collisional systems that can be simulated with direct$N$-body codes and large noncollisional systems. MPCDSS in principle allows usto simulate globular clusters such as Omega Cen and M54 and even the nuclearstar cluster, beyond the limits of current direct N-body codes in terms of thenumber of particles.

Introducing a new multi-particle collision method for the evolution of dense stellar systems. Crash-test N-body simulations