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A Stable Finite-Volume Method for Scalar-Field Dark Matter

Hopkins, Philip F. (2018) A Stable Finite-Volume Method for Scalar-Field Dark Matter. . (Unpublished)

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We describe and test a new numerical method to solve the Schrodinger equation in self-gravitating systems, e.g. Bose-Einstein condensates or 'fuzzy'/ultra-light dark matter. The method is a finite-volume Godunov scheme with stable, higher-order accurate gradient estimation, based on a generalization of recent mesh-free finite-mass Godunov methods. It couples easily to particle-based N-body gravity solvers (with or without other fluids, e.g. baryons), manifestly conserves momentum and energy, is numerically stable, and computationally efficient. We consider a variety of test problems and demonstrate that it can accurately recover exact solutions and remains stable even in noisy, poorly-resolved systems, with dramatically reduced noise compared to other proposed implementations. This is non-trivial because the 'quantum pressure' is neither isotropic nor positive-definite and depends on higher-order gradients of the density field. We implement and test the method in the code GIZMO.

Item Type:Report or Paper (Discussion Paper)
Related URLs:
URLURL TypeDescription Paper ItemGIZMO
Hopkins, Philip F.0000-0003-3729-1684
Additional Information:We thank Victor Robles for a number of helpful discussions. Support for PFH was provided by an Alfred P. Sloan Research Fellowship, NSF Collaborative Research Grant #1715847 and CAREER grant #1455342. Numerical calculations were run on the Caltech compute cluster “Wheeler,” allocations from XSEDE TG-AST130039 and PRAC NSF.1713353 supported by the NSF, and NASA HEC SMD-16-7592.
Funding AgencyGrant Number
Alfred P. Sloan FoundationUNSPECIFIED
Subject Keywords:methods: numerical— hydrodynamics— cosmology: theory— elementary particles— dark matter
Record Number:CaltechAUTHORS:20190206-105628264
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:92727
Deposited By: George Porter
Deposited On:08 Feb 2019 15:22
Last Modified:08 Feb 2019 15:22

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