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

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, meaning that its improved hydrodynamic treatment can be used for high-resolution simulations without prohibitive cost to run-speed.