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Smoothed particle hydrodynamics (SPH) is positioned as having ideal conservation properties. When properly implemented, conservation of total mass, energy, and both linear and angular momentum is guaranteed exactly, up to machine precision. This is particularly important for some applications in computational astrophysics, such as binary dynamics, mergers, and accretion of compact objects (neutron stars, black holes, and white dwarfs). However, in astrophysical applications that require the inclusion of gravity, calculating pairwise particle interactions becomes prohibitively expensive. In the Fast Multipole Method (FMM), they are, therefore, replaced with symmetric interactions between distant clusters of particles (contained in the tree nodes) Although such an algorithm is linear momentum-conserving, it introduces spurious torques that violate conservation of angular momentum. We present a modification of FMM that is free of spurious torques and conserves angular momentum explicitly. The new method has practically no computational overhead compared to the standard FMM.
Exact conservation of the angular momentum is worked out for an elastic medium with spins. The intrinsic anharmonicity of the elastic theory is shown to be crucial for conserving the total momentum. As a result, any spin-lattice dynamics inevitably i
We present here a minor modification of our numerical implementation of the Hall effect for the 2D Riemann solver used in Constrained Transport schemes, as described in Marchand et al. (2018). In the previous work, the tests showed that the angular m
Superfluid vortices are quantum excitations carrying quantized amount of orbital angular momentum in a phase where global symmetry is spontaneously broken. We address a question of whether magnetic vortices in superconductors with dynamical gauge fie
We analyze the laws of conservation of momentum and angular momentum in classical electrodynamics of material media with bound charges, and explore the possibility to describe the properties of such media via a discrete set of point-like charges of z
Tucker decomposition is proposed to reduce the memory requirement of the far-fields in the fast multipole method (FMM)-accelerated surface integral equation simulators. It is particularly used to compress the far-fields of FMM groups, which are store