Symmetries without symmetries in Smoothed Particle Hydrodynamics
AbstractWe introduce a technique to solve numerically the relativistic Euler’s equa-tions in scenarios with spherical symmetry using the standard SmoothedParticles Hydrodynamics method in cartesian coordinates. This implemen-tation allow us to increase the resolution of the simulations in order to obtainaccurate results. We test our implementation studying the evolution of a per-fect ﬂuid in a blast wave conﬁguration in a ﬁxed space-time . The techniquecan be easily generalized to axial symmetric problems. Keywords: Hydrodynamics, SPH, Numerical Implementation1. IntroductionPhysical scenarios involving ﬂuids are studied using diﬀerent numericalmethods. One of these standard methods is the Smoothed Particle Hydro-dynamics (SPH).Diﬀerent implementations for Newtonian and relativistic Euler’s equa-tions in three spatial dimension using SPH have been studied for many years[2, 3, 4, 5, 6]. The idea is to write the evolution equations in cartesian coordi-nates and using a Lagrangian scheme we follow the evolution of the elementsof the ﬂuid during the simulation. When the physical problem has sphericalsymmetry, the standard approach is to rewrite the evolution equations inspherical coordinates, try to ﬁnd the best way to adjust the parameters ofthe discretization and then evolve the system under that symmetry [10].