REMIX SPH – improving mixing in smoothed particle hydrodynamics simulations using a generalised, material-independent approach

Journal of Computational Physics, vol. 532, pp. 113907

Abstract

We present REMIX, a smoothed particle hydrodynamics (SPH) scheme designed to alleviate effects that typically suppress mixing and instability growth at density discontinuities in SPH simulations. We approach this problem by directly targeting sources of kernel smoothing error and discretisation error, resulting in a generalised, material-independent formulation that improves the treatment both of discontinuities within a single material, for example in an ideal gas, and of interfaces between dissimilar materials. This approach also leads to improvements in capturing wider hydrodynamic behaviour unrelated to mixing. We demonstrate marked improvements in three-dimensional test scenarios, focusing on cases with particles of equal mass across the simulation. This choice is particularly relevant for use cases in astrophysics and engineering – specifically those in which particles are free to evolve over a large range of density scales – where bespoke choices of unequal particle masses in the initial conditions cannot easily be used to address emergent and evolving density discontinuities. We achieve these improvements while maintaining sharp discontinuities; without introducing additional equation of state dependence in, for example, particle volume elements; and without contrived or targeted corrections. Our methods build upon a fully compressible and thermodynamically consistent core-SPH construction, retaining Galilean invariance as well as conservation of mass, momentum, and energy. REMIX is integrated in the open-source, state-of-the-art Swift code and is designed with computational efficiency also in mind, which means that its improved hydrodynamic treatment can be used for high-resolution simulations without prohibitive cost to run-speed. • We present REMIX, a material-independent SPH formulation. • REMIX alleviates effects that typically suppress mixing at density discontinuities. • REMIX enables mixing and instability growth at material interfaces. • REMIX improves hydrodynamic behaviour unrelated to mixing. • REMIX is integrated in the open-source, state-of-the-art SWIFT code.

Authors 7

1. Thomas D. Sandnes corresponding

   Durham University

   Affiliation as printed

   Institute for Computational Cosmology, Department of Physics, Durham University, South Road, Durham, DH1 3LE, UK

2. V. R. Eke

   Durham University

   Affiliation as printed

   Institute for Computational Cosmology, Department of Physics, Durham University, South Road, Durham, DH1 3LE, UK

3. Jacob Kegerreis

   Ames Research Center · Search for Extraterrestrial Intelligence

   Affiliation as printed

   NASA Ames Research Center, MS 245-3, Moffett Field, 94035, CA, USA

   SETI Institute, 339 Bernardo Avenue, Suite 200, Mountain View, 94043, CA, USA

4. R. Massey

   Durham University

   Affiliation as printed

   Institute for Computational Cosmology, Department of Physics, Durham University, South Road, Durham, DH1 3LE, UK

5. Sergio Ruiz-Bonilla

   Durham University

   Affiliation as printed

   Institute for Computational Cosmology, Department of Physics, Durham University, South Road, Durham, DH1 3LE, UK

6. Matthieu Schaller Aachen Leiden Observatory Lorentz Institute for Theoretical Physics

   Leiden University · Leiden Observatory

   Affiliation as printed

   Leiden Observatory, Leiden University, PO Box 9513, NL-2300 RA Leiden, the Netherlands

   Lorentz Institute for Theoretical Physics, Leiden University, PO Box 9506, NL-2300 RA Leiden, the Netherlands

7. L. F. A. Teodoro

   University of Oslo · University of Glasgow

   Affiliation as printed

   Faculty of Mathematics and Natural Sciences, University of Oslo, Sem Sælands vei 24, 0371 Oslo, Norway

   School of Physics and Astronomy, University of Glasgow, G12 8QQ, Scotland, UK