CRKSPH - A Conservative Reproducing Kernel Smoothed Particle Hydrodynamics Scheme

Abstract

We present a formulation of smoothed particle hydrodynamics (SPH) that utilizes a first-order consistent reproducing kernel, a smoothing function that exactly interpolates linear fields with particle tracers. Previous formulations using reproducing kernel (RK) interpolation have had difficulties maintaining conservation of momentum due to the fact the RK kernels are not, in general, spatially symmetric. Here, we utilize a reformulation of the fluid equations such that mass, linear momentum, and energy are all rigorously conserved without any assumption about kernel symmetries, while additionally maintaining approximate angular momentum conservation. Our approach starts from a rigorously consistent interpolation theory, where we derive the evolution equations to enforce the appropriate conservation properties, at the sacrifice of full consistency in the momentum equation. Additionally, by exploiting the increased accuracy of the RK method's gradient, we formulate a simple limiter for the artificial viscosity that reduces the excess diffusion normally incurred by the ordinary SPH artificial viscosity. Collectively, we call our suite of modifications to the traditional SPH scheme Conservative Reproducing Kernel SPH, or CRKSPH. CRKSPH retains many benefits of traditional SPH methods (such as preserving Galilean invariance and manifest conservation of mass, momentum, and energy) while improving on many of the shortcomings of SPH, particularly the overly aggressive artificial viscosity and zeroth-order inaccuracy. We compare CRKSPH to two different modern SPH formulations (pressure based SPH and compatibly differenced SPH), demonstrating the advantages of our new formulation when modeling fluid mixing, strong shock, and adiabatic phenomena.

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Cited by in corpus (34)

• Simulating cosmic structure formation with the GADGET-4 code
• SWIFT: A modern highly-parallel gravity and smoothed particle hydrodynamics solver for astrophysical and cosmological applications
• PySPH: a Python-based framework for smoothed particle hydrodynamics
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• The Lagrangian hydrodynamics code MAGMA2
• Enabling particle applications for exascale computing platforms
• Primordial Earth mantle heterogeneity caused by the Moon-forming giant impact
• SPHINCS_BSSN: A general relativistic Smooth Particle Hydrodynamics code for dynamical spacetimes
• The Kelvin-Helmholtz instability and smoothed particle hydrodynamics
• Algorithms for uniform particle initialization in domains with complex boundaries
• The Role of Giant Impacts in Planet Formation
• Modeling the Lyman-$\alpha$ forest with Eulerian and SPH hydrodynamical methods
• The Borg Cube Simulation: Cosmological Hydrodynamics with CRK-SPH
• Techniques for second order convergent weakly-compressible smoothed particle hydrodynamics schemes without boundaries
• Smoothed Particle Radiation Hydrodynamics: Two-Moment method with Local Eddington Tensor Closure
• A simple, entropy-based dissipation trigger for SPH
• Simulating neutron star mergers with the Lagrangian Numerical Relativity code SPHINCS_BSSN
• Simulating Hydrodynamics in Cosmology with CRK-HACC
• Conservative, density-based smoothed particle hydrodynamics with improved partition of the unity and better estimation of gradients
• REMIX SPH -- improving mixing in smoothed particle hydrodynamics simulations using a generalised, material-independent approach
• Sub-stellar engulfment by a main sequence star: where is the lithium?
• Efficient smoothed particle radiation hydrodynamics I: Thermal radiative transfer
• Adaptive Compressible Smoothed Particle Hydrodynamics
• Efficient smoothed particle radiation hydrodynamics II: Radiation hydrodynamics
• Implicit Molecular Stresses in Weakly-Compressible Particle-Based Discretization Methods for Fluid Flow
• Self-gravitating barotropic equilibrium configurations of rotating bodies with SPH
• Total Lagrangian Smoothed Particle Hydrodynamics with An Improved Bond-Based Deformation Gradient for Large Strain Solid Dynamics
• A Formulation of Consistent Particle Hydrodynamics in Strong Form
• No dilute core produced in simulations of giant impacts on to Jupiter
• Evidence on the incompatibility of smoothed particle hydrodynamics and eddy viscosity models for large eddy simulations
• Validating the CROCODILE model within the AGORA galaxy simulation framework
• Optimized smoothing kernels for SPH
• CRKSPH-compatible discretization of the SUPG and SAAF transport equations
• Shock-capturing particle hydrodynamics with reproducing kernels