PHANTOM's fast multipole gravity solver violates total linear momentum conservation by computing leaf-cell-to-supercell forces without reverse pairs; in neutron star simulations this shifts the center of mass by up to about one stellar radius.
A Fast Algorithm for Particle Simulations // Journal of Computational Physics
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Non-conservation of linear momentum in widely used hierarchical methods in gravitational gas dynamics
PHANTOM's fast multipole gravity solver violates total linear momentum conservation by computing leaf-cell-to-supercell forces without reverse pairs; in neutron star simulations this shifts the center of mass by up to about one stellar radius.