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Dealing with density discontinuities in planetary SPH simulations

Ruiz-Bonilla, S and Borrow, J and Eke, V R and Kegerreis, J A and Massey, R J and Sandnes, T D and Teodoro, L F A (2022) 'Dealing with density discontinuities in planetary SPH simulations.', Monthly Notices of the Royal Astronomical Society, 512 (3). pp. 4660-4668.


Density discontinuities cannot be precisely modelled in standard formulations of smoothed particles hydrodynamics (SPH) because the density field is defined smoothly as a kernel-weighted sum of neighbouring particle masses. This is a problem when performing simulations of giant impacts between proto-planets, for example, because planets typically do have density discontinuities both at their surfaces and at any internal boundaries between different materials. The inappropriate densities in these regions create artificial forces that effectively suppress mixing between particles of different material and, as a consequence, this problem introduces a key unknown systematic error into studies that rely on SPH simulations. In this work, we present a novel, computationally cheap method that deals simultaneously with both of these types of density discontinuity in SPH simulations. We perform standard hydrodynamical tests and several example giant impact simulations, and compare the results with standard SPH. In a simulated Moon-forming impact using 107 particles, the improved treatment at boundaries affects at least 30 per cent of the particles at some point during the simulation.

Item Type:Article
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Publisher statement:© 2022 The Author(s). Published by Oxford University Press on behalf of Royal Astronomical Society. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (, which permits unrestricted reuse, distribution, and reproduction in any medium, provided the original work is properly cited.
Date accepted:24 March 2022
Date deposited:20 June 2022
Date of first online publication:31 March 2022
Date first made open access:20 June 2022

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